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SampSizeCal

The Online Computational Tool For Sample Sizes

By W. J. Zhang



User manual guide and suggested citation of this page:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155
Click here to download the offline tool.

Sampling Techniques
Comparing Means
Comparing Variabilities
Large Sample Tests for Proportions
Exact Tests for Proportions
Tests for Goodness-of-Fit and Contingency Tables
Time-to-Event
Group Sequential Methods
Bioequivalence
Dose Response Studies
Microarray Studies
Nonparametrics
Sample Size Estimation in Other Areas

Sampling Techniques >>> Simple Random Sampling
Population size (N):

Sample size (n; n<<N):

Number of candidate samples (m; m>1):





Explanation:
Probability Sampling Principle is a fundamental principle in sampling theory. It can be outlined as follows: (1) Define a set of candidate samples Si, i=1,2,…, each candidate sample contains some sampling units (subjects, individuals, etc.); (2) Assign a selection probability to each candidate sample; (3) With the help of the random number table, select a sample from the candidate sample set Si, i=1,2,…, through selection probability. By selecting a sample according to the above probability sampling principles, a suitable sampling theory can always be found to explain and analyze the data collected. The Simple Random Sampling is a type of probability sampling and is defined as follows: (1) Suppose the statistical population contains N sampling units; (2) Select n sampling units (n is the sample size) from the statistical population, and each sampling unit has an equal chance of being selected. The Simple Random Sampling is the basis of all random sampling techniques. In present method, produce m candidate samples, each with sample size n (n sampling units or subjects), that subjects (or sampling units, IDs) are randomly drawn from the total population of N subjects. Suppose that the sample size and the selection probability of all candidate samples are the same respectively. Randomly select one candidate sample from m candidate samples and use it as the sample. For example, N=5000, n=45, m=5.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Comparing Means >>> One-Sample Design
Comparing Means >>> One-Sample Design >>> Baseline Method
Use one of the following methods:
Significance Test Non-inferiority or Superiority Test Equivalence Test

Standard deviation (σ):

Expected difference between the sample mean and the reference value (d; d>0):

Margin of clinic significance (δ):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:

The baseline test is often used to compare the treatment group with the standard accepted value, or to compare the baseline data with the data after treatment. For Non-inferiority or Superiority Test, δ<0 if non-inferiority test is made and δ>0 if superiority test is made. For example, to make non-inferiority test on a drug for hypertension, for a community, known σ=20, d=9, and the margin is 11, then let δ=-11.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Comparing Means >>> One-Sample Design >>> One-Stage Test

Use one of the following error measures:
Difference d Relative error r

Standard deviation (σ):

Expected difference between the sample mean and total mean (d; d>0):

Expected relative error (r; 0<r<100):

Coefficient of variation (CV; 0<CV<1):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
The One-Stage Test is often used in field sampling studies. Expected relative error (r) is the percent (0, 100) of half-width of confidence interval against the mean. Coefficient of variation (CV) is the ratio of standard deviation vs. Krebs (1989) argues that CV=0.7 for plankton, CV=0.4 for crabs, CV=0.4 for shellfish (0.4), and CV=0.8 for roadside sampling.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Comparing Means >>> One-Sample Design >>> Two-Stage Test

Standard deviation in the first stage (σ1):

Expected difference between the sample mean and total mean (d; d>0):

Sample size in the first stage (n1; n1>0):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
The Two-Stage Test is often used in field sampling studies. In the first stage of sampling, the sample size n1 was used and the standard deviation achieved in this stage is σ1.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Comparing Means >>> One-Sample Design >>> Random Variable Follows the Poisson Distribution

Use one of the following error measures:
Difference d Relative error r

Total mean (μ):

Expected difference between the sample mean and total mean (d; d>0):

Expected relative error (r; 0<r<100):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
This method is often used in field sampling studies. It is assumed that the variable follows Poisson distribution. The Expected relative error (r) is the permissible relative error, i.e., the percent (0, 100) of half-width of confidence interval against the total mean.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Comparing Means >>> One-Sample Design >>> Random Variable Follows the Negative Binomial Distribution

Use one of the following error measures:
Difference d Relative error r

Total mean (μ):

Negative binomial parameter (k):

Expected difference between the sample mean and total mean (d; d>0):

Expected relative error (r; 0<r<100):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
This method is often used in field sampling studies. It is assumed that the variable follows negative binomial distribution. The expected relative error (r) is the permissible relative error, i.e., the percent (0, 100) of half-width of confidence interval against the total mean. k is the parameter of negative binomial distribution.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Comparing Means >>> One-Sample Design >>> Random Variable Follows the Binomial Distribution

Total proportion (w; 0<w<1):

Expected difference between the sample proportion and total proportion (d; 0<d<1):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
This method is often used in field sampling studies. It is assumed that the variable follows binomial distribution. w is the estimated proportion (0<w<1).

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Comparing Means >>> One-Sample Design >>> Probabilistic Distribution Independent

Total mean (μ):

Expected difference between the sample mean and total mean (d; d>0):

Regression constant of Iwao regression (α’):

Regression coefficient of Iwao regression (β’; β’≥1):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
This method is often used in field sampling studies. α’ and β’ are the parameters in Iwao regression on spatial distribution: M* = α’+ β’μ.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Comparing Means >>> Two-Sample Parallel Design
Use one of the following methods:
Known the standard deviation of between-group difference σ Known the standard deviations of two groups σ1 and σ2

Standard deviation of of between-group difference (σ):

Standard deviation for group 1 (σ1):

Standard deviation for group 2 (σ2):

Between-group difference (d; d>0):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
(1) Known the standard deviation σ. Suppose there are two groups, a treatment group and a control group (1:1 parallel control design; n observations are required for each group), we want to test the between-group difference significance. (2) Known the standard deviations of two groups (1:1 parallel control design; n observations are required for each group). Suppose the standard deviations of two groups are are σ1 and σ2 respectively. n is the sample size for each group.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Comparing Means >>> Two-Sample Parallel Design >>> Non-inferiority or Superiority Test, Equivalence test, Comparison of Paired Data
Use one of the following methods:
Non-inferiority or Superiority Test Equivalence Test Comparison of Paired Data

Standard deviation of of between-group difference (σ):

Between-group difference (d; d>0):

Margin of clinic significance (δ):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
For Non-inferiority or Superiority Test, δ<0 if non-inferiority test is made and δ>0 if superiority test is made. For example, to make non-inferiority test on hypertension difference of two groups (1:1 parallel control design; n observations, for detecting between-group difference, are required for each group), for a community, known σ=20, the expected between-group difference d=8, and the margin is 10, then let δ=-10. For Non-inferiority or Superiority Test, δ≠d, and for Equivalence Test, |δ|≠d. For three methods above, 1:1 design; n observations are required for each group.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Comparing Means >>> Two-Sample Crossover Design
Use one of the following methods:
Significance Test Non-inferiority or Superiority Test Equivalence Test

Standard deviation of of between-group difference (σ):

Between-group difference (d; d>0):

Margin of clinic significance (δ):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
In Significance Test, for example, use the drugs A and B to treat hypertension. In the first trial, use A for a period and thereafter use B for the same period. In the second trial, use B first and thereafter A. If B reduces 5 mm Hg of blood pressure more than A (d=5), B is considered to be more effective. Set σ=10, α=0.0001, β=0.1, two-sided significance test, and calculate the sample size n (1:1 design; n observations are required for each group). For Non-inferiority or Superiority Test, δ<0 if non-inferiority test is made and δ>0 if superiority test is made. For the example above, to make two-sided non-inferiority test (1:1 design; n observations are required for each group). The margin is 1, i.e., δ=-1. For equivalence design, continue the example above, to make two-sided equivalence test (1:1 design; n observations are required for each group), δ=1.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Comparing Means >>> Multiple-Sample One-Way ANOVA
Number of groups (k):

Standard deviation of each group (σ):

α value (Confidence level=(1-α)×100%):
0.01 0.05

β value (Statistical power=(1-β)×100%):
0.1 0.2

Means of k groups:

Reset and enter or copy a line of your k means (space delimited) into this area.

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
Suppose one factor with k≥3 groups (levels). We hope to statistically compare the difference between means of k populations represented by k groups. For example, use five drugs to control a disease, the means of incidence reduction are 25, 30, 27, 20, 28; the standard deviation of incidence reduction of each drug is σ=5; two-sided test. α=0.01, β=0.1. Calculate the sample size of each group, n.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Number of groups (k):

Mean of control group (m):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Means and standard deviations of k groups:

Reset and enter or copy two lines of your space delimited data (1st line: k means; 2nd line: k standard deviations) into this area.

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
For example, the means of incidence reduction of two drugs (or dosages) are 18, 25, the value for the control group is 12, the σ for the incidence reduction of two drugs are 3.5 and 5. Conduct 1:1:1 parallel design, T=1; for n13, σ=3.5, d13=18-12=6; for n23, σ=5, d12=25-12=13. Calculate the sample size of each group, n, n= max{n13, n23}.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Comparing Means >>> Multiple-Sample One-Way ANOVA >>> Multiple-Sample Williams Design
Use one of the following methods:
Significance Test Non-inferiority or Superiority Test Equivalence Test

Number of groups (k):

Margin of clinic significance (δ):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Means of k groups:

Reset and enter or copy two lines of space delimited means and standard deviations into this area.

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
If the number of periods available for the crossover experiment is the same as the number of treatments, the crossover design that uses the generalized Latin square to balance the first-order lag effect with as few subjects as possible is the Williams design. Common Williams designs are three-group designs (a 6×3 crossover design) and four-group designs (a 4×4 crossover design). When the experimental groups are odd, the design result is a 2k×k crossover design, and when the experimental groups are even, the design result is a k×k crossover design. In Significance Test, for example, there are k groups, use three drugs A, B and C to treat a disease. Their incidence reduction are 16, 19, 13 and σ=3 respectively. Use Williams three-crossover design, the treatments are ABC, ACB, BAC, BCA, CAB, CBA. dij=4. Two-sided test. Calculate the sample size of each group, n, n=max{n1, n2, n3}. For Non-inferiority or Superiority Test, for example, if the margin is 5, then δ=-5. For Equivalence Test, in the example above, m=6, d12=16-19=3, d13=16-13=3, d23=19-13=6, σ=3. The sample size for detecting between-group difference (two-sided test) is n=max{n1, n2, n3}.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Comparing Variabilities >>> Estimation of Variance
Margin of variance ratio (v; 0<v<1):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
The method is often used in field sampling. v is the permissible limit of variance, represented by the ratio of confidence interval, as 0.35, 0.25, etc.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Comparing Variabilities >>> Repeated Parallel Controlled Design
Use one of the following methods:
Significance Test Non-inferiority or Superiority Test Equivalence Test

Standard deviation of the test group (σT):

Standard deviation of the reference group (σR):

Number of replications for each group (m; m>1):

Margin (δ):

α value (Confidence level=(1-α)×100%):
0.001 0.005 0.01 0.05

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
In Significance Test, assume that there are two groups and n and m are the number of cases and observations in a group respectively. For example, a parallel control experiment with 2 groups, each repeated 3 times (3 replications). According to the pilot study, the within-subject standard deviation of the group T is 0.4, and the within-subject standard deviation of the group R is 0.6. 1:1 significance design. α=0.001, β=0.10. Calculate the sample size for each group, n. In Non-inferiority or Superiority Test, δ<0 if non-inferiority test is made and δ>0 if superiority test is made.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Comparing Variabilities >>> Simple Random Effects Model
Use one of the following methods:
Significance Test Non-inferiority or Superiority Test Equivalence Test

Coefficient of variation of the test group (CVT; 0<CVT<1):

Coefficient of variation of the reference group (CVR; 0<CVR<1):

Number of replications for each group (m; m>1):

Margin of CVT-CVR (δ):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
In Significance Test, for example, a two-group parallel control experiment with 2 replications. According to the pilot study, the coefficient of variation of the treatment group was 45% (CVT), and that of the control group was 55% (CVR). α=0.0001, β=0.10. 1:1 significance design. Calculate the sample size for each group, n. In Non-inferiority or Superiority Test, δ<0 if non-inferiority test is made and δ>0 if superiority test is made.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Comparing Variabilities >>> Comparison of Between-Subject Variation
Use one of the following methods:
Significance Test Non-inferiority or Superiority Test

Between-subject standard deviation of the test group (σBT):

Between-subject standard deviation of the reference group (σBR):

Within-subject standard deviation of the test group (σWT):

Within-subject standard deviation of the reference group (σWR):

Number of replications for each group (m; m>1):

Margin of σBT2/σBR2 (δ):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
In Significance Test, for example, a parallel control experiment with two groups of 3 replications (m=3). According to the pilot study, the between-subject standard deviations of groups T and R were 0.2 (σBT) and 0.3 (σBR), respectively, and the within-subject standard deviations of groups T and R were 0.4 (σWT) and 0.5 (σWR), respectively. α=0.0001, β=0.10. 1:1 significance design. Calculate the sample size for each group, n. In Non-inferiority or Superiority Test, δ<0 if non-inferiority test is made and δ>0 if superiority test is made.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

   Back to Top   



Use one of the following methods:
Significance Test Non-inferiority or Superiority Test

Between-subject standard deviation of the test group (σBT):

Between-subject standard deviation of the reference group (σBR):

Within-subject standard deviation of the test group (σWT):

Within-subject standard deviation of the reference group (σWR):

Parameter ρ:

Number of replications for each group (m; m>1):

Margin of σBT2/σBR2 (δ):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
In Significance Test, for example, a two-group cross-control experiment with 2 replications (ABAB, BABA) (m=2). According to the pilot study, the between-subject standard deviations of groups T and R were 0.2 (σBT) and 0.3 (σBR), respectively, and the within-subject standard deviations of groups T and R were 0.4 (σWT) and 0.5 (σWR), respectively. ρ=0.7. α=0.0001, β=0.10. 1:1 significance design. Calculate the sample size for each group, n. In Non-inferiority or Superiority Test, δ<0 if non-inferiority test is made and δ>0 if superiority test is made.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Comparing Variabilities >>> Comparison of Overall Variation
Comparing Variabilities >>> Comparison of Overall Variation >>> Non-Repeated Parallel Controlled Trials
Use one of the following methods:
Significance Test Non-inferiority or Superiority Test Equivalence Test

Standard deviation of the test group (σT):

Standard deviation of the reference group (σR):

Margin (δ):

α value (Confidence level=(1-α)×100%):
0.001 0.005 0.01 0.05

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
Estimates of overall variation were obtained from standard 2×2 crossover/parallel designs or repeated 2×2 crossover/parallel designs. In the Significance Test of Non-Repeated Parallel Controlled Trials, a non-repeated parallel controlled trial. According to the pilot study, the within-subject standard deviation of the group T is 0.4, and the within-subject standard deviation of the group R is 0.6. 1:1 significance design. α=0.001, β=0.10. Calculate the sample size for each group, n. In Non-inferiority or Superiority Test, δ<0 if non-inferiority test is made and δ>0 if superiority test is made.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

   Back to Top   


Comparing Variabilities >>> Comparison of Overall Variation >>> Repeated Parallel Controlled Trials
Use one of the following methods:
Significance Test Non-inferiority or Superiority Test

Between-subject standard deviation of the test group (σBT):

Between-subject standard deviation of the reference group (σBR):

Within-subject standard deviation of the test group (σWT):

Within-subject standard deviation of the reference group (σWR):

Number of replications for each group (m; m>1):

Margin of σTT2/σTR2 (δ):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
In Significance Test, for example, a two-group parallel control experiment with 3 replications (m=3). According to the pilot study, the between-subject standard deviations of groups T and R were 0.2 (σBT) and 0.3 (σBR), respectively, and the within-subject standard deviations of groups T and R were 0.4 (σWT) and 0.5 (σWR), respectively. α=0.0001, β=0.10. 1:1 significance design. Calculate the sample size for each group, n. In Non-inferiority or Superiority Test, δ<0 if non-inferiority test is made (e.g., δ=-1.0) and δ>0 if superiority test is made.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Comparing Variabilities >>> Comparison of Overall Variation >>> Standard 2×2 Crossover Design
Use one of the following methods:
Significance Test Non-inferiority or Superiority Test

Between-subject standard deviation of the test group (σBT):

Between-subject standard deviation of the reference group (σBR):

Within-subject standard deviation of the test group (σWT):

Within-subject standard deviation of the reference group (σWR):

Parameter ρ:

Margin of σTT2/σTR2 (δ):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
In Significance Test, for example, a 2×2 standard crossover control experiment. According to the pilot study, the between-subject standard deviations of groups T and R were 0.2 (σBT) and 0.3 (σBR), respectively, and the within-subject standard deviations of groups T and R were 0.4 (σWT) and 0.5 (σWR), respectively. ρ=0.8. α=0.0001, β=0.10. 1:1 significance design. Calculate the sample size for each group, n. In Non-inferiority or Superiority Test, δ<0 if non-inferiority test is made (e.g., δ=-1.0) and δ>0 if superiority test is made.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Comparing Variabilities >>> Comparison of Overall Variation >>> Repeated 2×2 Crossover Design
Use one of the following methods:
Significance Test Non-inferiority or Superiority Test

Between-subject standard deviation of the test group (σBT):

Between-subject standard deviation of the reference group (σBR):

Within-subject standard deviation of the test group (σWT):

Within-subject standard deviation of the reference group (σWR):

Parameter ρ:

Number of replications for each group (m; m>1):

Margin of σTT2/σTR2 (δ):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
In Significance Test, for example, For example, a two-group cross-control experiment with 2 replications per subject (ABAB, BABA) (m=2). According to the pilot study, the between-subject standard deviations of groups T and R were 0.2 (σBT) and 0.3 (σBR), respectively, and the within-subject standard deviations of groups T and R were 0.4 (σWT) and 0.5 (σWR), respectively. ρ=0.8. α=0.0001, β=0.10. 1:1 significance design. Calculate the sample size for each group, n. In Non-inferiority or Superiority Test, δ<0 if non-inferiority test is made (e.g., δ=-1.0) and δ>0 if superiority test is made.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Use one of the following methods:
Significance Test Non-inferiority or Superiority Test Equivalence Test

Proportion (p; 0<p<1):

Difference of proportion (d; 0<d<1):

Margin of clinic significance (δ):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
p is the proportion of total population and d is the difference of proportion. Two-sided significance test. In Significance Test, for example, an old method can reduce a disease incidence by 40% and the new method is expected to reduce it by 80%, thus d=0.8-0.4=0.3. Specify the margin, for example, 0.05, then δ=-0.05 in Non-inferiority or Superiority Test and δ=0.05 in Equivalence Test.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Large Sample Tests for Proportions >>> Two-Sample Parallel Design
Use one of the following methods:
Significance Test Non-inferiority or Superiority Test Equivalence Test

Proportion for group 1 (p1; 0<p1<1):

Proportion for group 2 (p2; 0<p2<1):

Margin of clinic significance (δ):

Assignment of sample size between two groups (k; k=n1/n2):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n1) for group 1:


Estimated sample size (n2) for group 2:


Required sample size (n1) for group 1:


Required sample size (n2) for group 2:


Explanation:
Two-sided significance test. In Significance Test, for example, an old method can reduce a disease incidence by 40% and the new method is expected to reduce it by 80%, thus d=0.8-0.4=0.4. Specify the margin, for example, 0.05, then δ=-0.05 in Non-inferiority or Superiority Test and δ=0.05 in Equivalence Test. Calculate the sample size of each group.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Large Sample Tests for Proportions >>> Two-Sample Crossover Design
Use one of the following methods:
Significance Test Non-inferiority or Superiority Test Equivalence Test

Standard deviation of between-group difference (σ):

Between-group difference (d; 0<d<1):

Margin of clinic significance (δ):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
σ: the standard deviation of between-proportion difference (it can be determined in a pre-experiment); δ: the margin of between-proportion difference. In Significance Test, for example, use a test drug A and control drug B to treat a disease. Take the control drug for 1 month, wash out for 3 weeks, and then take the test drug for 1 month, and vice versa for the other group. If the test drug is expected to have a 10% (d=0.10) higher effective rate than the control drug, the test drug is considered to have promotional value. The standard deviation of the pilot study σ=0.3. Choose α=0.0001, β=0.1, two-sided significance test, 1:1 design. Calculate the sample size of each group, n. δ<0 if non-inferiority test is made and δ>0 if superiority test is made. For example, if the reshold is 5%, then δ=-0.05 for non-inferiority test.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Large Sample Tests for Proportions >>> One-Way Analysis of Variance
Proportion for group 1 (p1; 0<p1<1):

Proportion for group 2 (p2; 0<p2<1):

Proportion for control group (p; 0<p<1):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
For example, the incidence reduction of two treatment drugs are 40% and 60% respectively and the value for the control is 15%, d13=0.4-0.15=0.25, d23=0.6-0.15=0.45; 1:1:1 parallel design, T=1. The sample size of each group is n= max{n13, n23}.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Large Sample Tests for Proportions >>> One-Way Analysis of Variance >>> Overall Between-Proportion Comparison
Number of groups (k):

Maximum proportion (pmax; 0<pmax<1):

Minimum proportion (pmin; 0<pmin<1):

α value (Confidence level=(1-α)×100%):
0.01 0.05

β value (Statistical power=(1-β)×100%):
0.1 0.2

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
For example, we want to study the therapeutic effect of different intensities of pharmaceutical interventions on hypertension levels. It is estimated that the strong intervention group has a treatment rate of 85%, the weak intervention group has a treatment rate of 65%, and the control group has a treatment rate of 20%. A two-sided test is required, α=0.0001, β=0.1, and the ratio of the sample size of the three groups is 1:1:1 (that is, the number of cases in the three groups is equal, n). Use this method to calculate the sample size required.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Use one of the following methods:
Significance Test Non-inferiority or Superiority Test Equivalence Test

Number of groups (k):

Standard deviation of between-group difference (σ):

Between-group difference (d; 0<d<1):

Margin of clinic significance (δ):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
In Significance Test, for example, the incidence reduction of two dosages (dosages 1 and 2) of a drug and the control are 75%, 65% and 20%. We are interesting in the difference between dosage 1 and the control (d=0.75-0.2=0.55), the standard deviation of proportion difference between dosage 1 and control is σ=0.5 (i.e., 50%); use Williams three-crossover design (k=6). δ<0 if non-inferiority test is made and δ>0 if superiority test is made. In Non-inferiority or Superiority Test, for example, if the reshold is 10%, then δ=-0.1 for for non-inferiority test.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Large Sample Tests for Proportions >>> Relative Risk - Parallel Design
Use one of the following methods:
Significance Test Non-inferiority or Superiority Test Equivalence Test

Proportion for treatment group (pt; 0<pt<1):

Proportion for control group (pc; 0<pc<1):

Margin of clinic significance for Log OR (δ):

Assignment of sample size between two groups (k; k=nt/nc):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (nt) for treatment group:


Estimated sample size (nc) for control group:


Required sample size (nt) for treatment group:


Required sample size (nc) for control group:


Explanation:
In Significance Test, odds ratio OR=(pt/(1-pt))/(pc/(1-pc)). OR>1 means that treatment has a significant effect and OR<1 no significant effect. For example, the incidence reduction of a treatment drug in pre-experiment is 35%, and the value for control drug is 20%; use OR as the assess index for treatment drug' effect; two-sided test (k=1, i.e., nt=nc). In Non-inferiority or Superiority Test, for the margin of 0.1 (i.e., 10%), δ=-0.1. Follow the example above.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Large Sample Tests for Proportions >>> Relative Risk - Crossover Design
Use one of the following methods:
Significance Test Non-inferiority or Superiority Test Equivalence Test

Odds ratio (OR) (OR=(pt/(1-pt))/(pc/(1-pc))):

Standard deviation of between-proportion difference (σ):

Margin of clinic significance for Log OR (δ):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
Known that the proportions of treatment group and control group are pt and pc respectively. Odds ratio OR=(pt/(1-pt))/(pc/(1-pc)). OR>1 means that treatment has a significant effect and OR<1 no significant effect. In Significance Test, For example, the incidence reduction of a treatment drug and the standard method are 40% (pt) and 25% (pc) respectively. Use OR as the assess index for treatment drug's effect; σ=0.3 (30%). 1:1 crossover control design and two-sided test. In Non-inferiority or Superiority Test, δ<0 if non-inferiority test is made and δ>0 if superiority test is made. For the margin of 0.1 (i.e., 10%), δ=-0.1 for non-inferiority test. Sample size for each group is n. Follow the example above.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Large Sample Tests for Proportions >>> Intervention-Control Comparison
Proportion for group 1 (p1; 0<p1<1):

Proportion for group 2 (p2; 0<p2<1; p1≠p2):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
For two independent populations with proportions p1 and p2 respectively, assume that p1-p2 follows normal distribution.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Proportion for control group (p0; 0<p0<1):

Proportion for treatment group (p1; 0<p1<1; p0≠p1):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
For example, known the incidence probability p0 (e.g., 0.1) and p1 (e.g., 0.2) in control group and treatment group respectively, the sample size for each group is n.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Large Sample Tests for Proportions >>> Two-Stage Sampling For Proportion
Sample size for 1st sampling (n1):

Proportion achieved in 1st sampling (p1; 0<p1<1):

Expected difference of proportion (d; 0<d<1):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
Two-stage sampling can be used in proportion (p) estimation. In the first sampling, n1 samples are taken and p1 is calculated; in the second sampling, n-n1 samples are taken. Here n is just the sample size for 2nd sampling(n-n1).

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Exact Tests for Proportions >>> Binomial Test
Proportion for group 1 (e.g. control group) (p0; 0<p0<1):

Proportion for group 2 (e.g. treatment group) (p1; 0<p1<1):

α value (Confidence level=(1-α)×100%):
0.05 0.1

β value (Statistical power=(1-β)×100%):
0.1 0.2

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
The sample size estimation of the binomial distribution test is suitable for accurate testing of smaller sample's count data. For example, in the preliminary trial, the cure rate of a new anti-tumor drug was 60% (p1) and the cure rate of standard treatment was 40% (p0). Single-group design, binomial distribution test, α=0.05, β=0.1. Find the number of cases needed for each group, n.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Exact Tests for Proportions >>> Fisher’s Exact Test
Proportion for group 1 (e.g. control group) (p0; 0<p0<1):

Proportion for group 2 (e.g. treatment group) (p1; 0<p1<1):

α value (Confidence level=(1-α)×100%):
0.05 0.1

β value (Statistical power=(1-β)×100%):
0.1 0.2

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
In a two-group parallel control design, if the theoretical number in the four-cell table is less than 5, or the total number of observations is less than 40, Fisher’s exact test is required. To accurately estimate the sample size, we need to query Table 4 to obtain the sample size for different proportions. For example, in the preliminary trial, the cure rate of a new anti-tumor drug for treating a certain cancer was 40% (p1), and the cure rate of standard treatment was 10% (p0). The two groups were parallel controlled in a 1:1 design, two-sided difference test, α=0.05, β=0.1. Query the number of cases needed for each group, n.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Exact Tests for Proportions >>> Optimal Multiple-Stage Designs for Single Arm Trials


Proportion for group 1 (e.g. control group) (p0; 0<p0<1):

Proportion for group 2 (e.g. treatment group) (p1; 0<p1<1):

β value (Statistical power=(1-β)×100%):
0.1 0.2



Optimal Two-Stage:


Explanation:
In this design, we allow the experiment to terminate after a certain number of failures. The sample size for this design can be obtained by consulting this method. For example, a new anti-tumor drug is undergoing phase II clinical trials. The effectiveness of standard treatment is 20% (p0), and if the effectiveness of the new drug reaches 40% (p1), it is considered to have clinical value. Optimal Two-Stage Designs, α=0.05, β=0.1. This method is only for α=0.05. The result of this example (β=0.1) is: 8/24,24/63,7/24,21/53. It menas that there are in total of 24 cases in the first phase, and 8 of them are effective, then the second phase of the trial can be carried out. In the second phase, 7 more cases need to be continued to reach 24 cases. If at least 7 cases are effective, further research can be conducted.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Proportion for group 1 (e.g. control group) (p0; 0<p0<1):

Proportion for group 2 (e.g. treatment group) (p1; 0<p1<1):

β value (Statistical power=(1-β)×100%):
0.1 0.2



Flexible Two-Stage:


Explanation:
This design gives multiple choices for the number of cases in the two stages. The sample size and boundary value of the optimized and flexible two-stage design can be found using this method. For example, a new anti-tumor drug is undergoing phase II clinical trials. The effectiveness of standard treatment is 20% (p0), and if the effectiveness of the new drug reaches 40% (p1), it is considered to have clinical value. Flexible Two-Stage Designs, α=0.05, β=0.1. This method is only for α=0.05. The result of this example (β=0.1) is: 4/18-20,5/21-24,6/25 ----- 13/48,14/49-51,15/52-55. It means that the first stage of the study requires 18-20 cases, and if at least 4 cases are effective, the second stage trial can be carried out. In the second stage, we will continue to do 28 to 30 cases, bringing the total number to 48. If 13 cases are effective, further research can be conducted.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Proportion for group 1 (e.g. control group) (p0; 0<p0<1):

Proportion for group 2 (e.g. treatment group) (p1; 0<p1<1):

β value (Statistical power=(1-β)×100%):
0.1 0.2



Optimal Three-Stage:


Explanation:
It is basically the same as the two-stage one. This design gives multiple choices for the number of cases in the two stages. The sample size and boundary value of the optimized and flexible three-stage design can be found using this method. For example, a new anti-tumor drug is undergoing phase II clinical trials. The effectiveness of standard treatment is 20% (p0), and if the effectiveness of the new drug reaches 40% (p1), it is considered to have clinical value. Optimal Three-Stage Designs, α=0.05, β=0.1. The result is: 3/17 --> 7/30 --> 14/50. It means that the first stage of the study requires 17 cases, and if at least 1 case is effective, the second stage trial can be carried out. In the second stage, we will continue to do 13 cases, bringing the total number to 30. If at least 7 cases are effective, the third stage trial can be carried out. In the third stage, we will continue to do 20 cases, bringing the total number to 50 cases. If at least 14 cases are effective, continue the further reaserch.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Proportion for group 1 (e.g. control group) (p0; 0<p0<1):

Proportion for group 2 (e.g. treatment group) (p1; 0<p1<1):

β value (Statistical power=(1-β)×100%):
0.1 0.2



Minimum Three-Stage:


Explanation:
It is basically the same as the two-stage one. This design gives multiple choices for the number of cases in the two stages. The sample size and boundary value of the optimized and flexible three-stage design can be found using this method. For example, a new anti-tumor drug is undergoing phase II clinical trials. The effectiveness of standard treatment is 20% (p0), and if the effectiveness of the new drug reaches 40% (p1), it is considered to have clinical value. Minimum Three-Stage Designs, α=0.05, β=0.1. The result is: 2/16 --> 6/28 --> 13/45. It means that the first stage of the study requires 16 cases, and if at least 2 cases are effective, the second stage trial can be carried out. In the second stage, we will continue to do 12 cases, bringing the total number to 28. If at least 6 cases are effective, the third stage trial can be carried out. In the third stage, we will continue to do 17 cases, bringing the total number to 45 cases. If at least 13 cases are effective, continue the further reaserch.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

   Back to Top   



Proportion for group 1 (e.g. control group) (p0; 0<p0<1):

Proportion for group 2 (e.g. treatment group) (p1; 0<p1<1):

λ value:
0.9 0.8

ρ value:
0 0.5

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
In Flexible Designs for Multiple-Arm Trials, we need to specify a clinically meaningful boundary value [-δ, δ] in advance. If the difference in proportions is greater than δ, then the group with the larger proportion will be selected. If the proportion difference is less than or equal to δ, other factors need to be considered in the selection. This design is not to compare the advantages and disadvantages between groups, but to maintain the existence of advantageous treatments as accurately as possible for further research. In Flexible Designs for Two-Arm Trials, known δ=0.05. Suppose that λ is a pre-specified threshold. The sample sizes of the two groups of flexible designs can be found when ρ=0 or ρ=0.5. For example, known ρ=0, λ=0.9. The result is 71. Each group needs 71 cases. In total of 86 cases are required if 20% of loss in samples is expected.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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λ value:
0.9 0.8

ρ value:
0 0.5

Proportion difference (d):
0.2 0.3 0.4 0.5

Number of arms (r):
3 4

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
In Flexible Designs for Multiple-Arm Trials, we need to specify a clinically meaningful boundary value [-δ, δ] in advance. If the difference in proportions is greater than δ, then the group with the larger proportion will be selected. If the proportion difference is less than or equal to δ, other factors need to be considered in the selection. This design is not to compare the advantages and disadvantages between groups, but to maintain the existence of advantageous treatments as accurately as possible for further research. In Flexible Designs for Multiple-Arm Trials, known δ=0.05. Suppose that λ is a pre-specified threshold. The sample sizes of the multiple groups of flexible designs can be found when λ=0.8 or λ=0.9, ρ=0 or ρ=0.5, r=3 or r=4 and d=0.2 or d=0.3 or d=0.4 or d=0.5. For example, known ρ=0, λ=0.9, r=3, and the new drug is expected to be 30% more effective than the control (d=0.3). The result is 77. Each group needs 77 cases. In total of 93 cases are required if 20% of loss in samples is expected.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Number of categories (r):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Proportions of r categories for observations (1st line) and literature sources (2nd line):

Reset and enter or copy two lines of space delimited observed and literature proportions into this area.

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
For example, to analyze the effect of a drug in the pilot study, preliminary trials have shown that the proportions of marked effect, effect and ineffect of the drug in treating the disease are about 20%, 55% and 25% respectively. According to literature reports, the proportions of marked effect, effect and ineffect of existing antihypertensive drugs are 15%, 50% and 20%, respectively. r=3, α=0.0001, β=0.1.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Tests for Goodness-of-Fit and Contingency Tables >>> Test for Independence - Single Stratum
Number of row categories (r):

Number of column categories (c):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Cases of r row categories and c column categories:

Reset and enter or copy space delimited cases matrix into the area above.

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
For r×c contingency table data (two-way) without stratum, this method is commonly used for sample size estimation (Two-group parallel design and two-sided test). For example, to analyze the effect of a drug, preliminary trials have shown that the marked effective proportion, effective proportion and ineffective proportion of the drug in treating the disease are about 15%, 58% and 25% respectively, and the marked effective proportion, effective proportion and ineffective proportion of the control are about 8%, 30% and 16% respectively.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Tests for Goodness-of-Fit and Contingency Tables >>> Test for Independence - Multiple Strata
Number of layers (centers) (h):

Number of groups (g):

Number of responses (r):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Cases of h layers, g groups (G lines in each layer) and r(=2) responses (r columns):

Reset and enter or copy space delimited cases matrix into the area above.
In the demo data, there are 3 layers, 2 groups per layer and 2 responses per group.

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
The test for independence of multiple strata is used in multi-center (multi-stratum) clinical trials. The later can not only guarantee the repeatability and representativeness of experimental results, but also facilitate the selection of subjects within the expected time. Multi-center clinical trials produce multi-level contingency table data. When the response rate is binary data, the Cochran-Mantel-Haenszel Test is a commonly used method. For example, make a three-center clinical trial for a drug and the control and observe the proportion of adverse events. Three strata are used (h=3). Two-group 1:1 parallel design, and two-sided test. πh=1/3. α=0.0001, β=0.1. This method is temporarily for r=2. Sample size for each layer=n/3.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Proportion from positive to negative (p10; 0<p10<1):

Proportion from negative to positive (p01; 0<p01<1):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
In clinical trials, to study the changes in the data of the two categories before and after the trial, McNemar test is usually used. The McNemar test is suitable for comparisons before and after binary variables. For example, use a drug to treat the disease. p10=0.6 (60%), p01=0.2 (20%). Two-sided significance test.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Number of responses (r):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

r responses before treatment (r rows) and after treatment (r columns):

Reset and enter or copy space delimited cases matrix into the area above.

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
In clinical trials, to study the changes in the data of the two categories before and after the trial, Stuart-Maxwell test is usually used. For example, to study the possibility of the effect-changing trend of using a drug to treat the disease.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Standard deviation for A→B (σ1):

Standard deviation for B→A (σ2):

Difference of residual effects between the A→B and B→A orders (γ):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
Residual effects refer to some reasons caused by the previous stage of treatment (such as the withdrawal effect caused by drug resistance, psychological effects, and legacy effects caused by changes in the patient's physical condition due to medication) that interfere with the treatment effect of the next stage. For example, to understand the residual effect, in a trial for the drugs A and B, γ=0.6, σ1=3.6, σ2=3.9.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Time-to-Event >>> Exponential Model
Time-to-Event >>> Exponential Model >>> Significance Test
Hazard ratio of group 1 (λ1):

Hazard ratio of group 2 (λ2; λ2≠λ1):

Exponential parameter (γ; γ≠λi):

Expected time for trials (the time from the start to the end of trials) (T):

Expected time for all subjects to be enrolled (T0; T0≤T):

Assignment of sample size between two groups (k; k=n1/n2):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n1) for group 1:


Estimated sample size (n2) for group 2:


Required sample size (n1) for group 1:


Required sample size (n2) for group 2:


Explanation:
Survival time usually does not follow the normal distribution, and sometimes it approximately follows the exponential distribution, Weibull distribution, Gompertz distribution, etc. In most cases, it does not follow any regular distribution type. In the Significance Test, suppose that survival time follows the exponential distribution. We want to test the significance of difference between two groups of endpoints (survival rates). For example, to study the effect of two treatment methods on the time to transformation of malignant tumor to cancer. The observation time lasted for 5 years (T=5, (T0=1). Assume that the hazard ratios of the two groups are (λ1=0.5 and (λ2=0.8, respectively. γ=0.00001. Estimate the sample size for each group.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Time-to-Event >>> Cox Proportional Hazards Model
Use one of the following methods:
Significance Test Non-inferiority or Superiority Test Equivalence Test

Hazard rate of group 1 (p1; p1>0):

Hazard rate of group 2 (p2; p2>0):

Hazard ratio of two groups (b):

Occurrence rate of specified event (d; d>0):

Margin of logrithm of hazard ratio (δ):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
In Significance Test, for example, compare the therapeutic effect of a new method and a traditional method. In the pilot test, the hazard ratio of the traditional method and the new method is b=3, 70% of the patients will be observed local infection (d=0.7), when p1=0.4, p2=0.4, two groups 1:1 parallel control. Make significance test. Each group requires n cases. In non-inferiority or superiority test, adopt 1:1 two groups of parallel control design. Based on the Cox Proportional Hazards Model for survival analysis, test whether the difference between the two groups of endpoints is non-inferior or superior to the known margin; δ<0 if non-inferiority test is made and δ>0 if superiority test is made. For example, take superiority test, δ=0.4 for superiority test. In equivalence design, adopt 1:1 two groups of parallel control design. Based on the Cox Proportional Hazards Model for survival analysis, test the equivalence of two groups of endpoints.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Time-to-Event >>> Logrank Test (Time Series Test): Significance Test
Total event rate of experimental group (pe; 0<pe<1):

Annual hazard rate of experimental group (herate):

Total event rate of control group (pc; 0<pc<1):

Annual hazard rate of control group (hcrate):

Experimental years(year):

Number of replications (k):

Rate of annual visiting loss (vloss; 0<vloss<1):

Annual non-compliance rate (noncomp; 0<noncomp<1):

Drop-in in control group (dropin; 0<dropin<1):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
The survival analysis based on the Logrank test (also known as the time series test), is based on the premise that the null hypothesis is established, and the difference between the actual number of deaths with two survival times and the theoretical number of deaths (expected number of deaths) calculated based on the number of initial observations and the theoretical death probability should not be large; if the difference is large, the null hypothesis is invalid, and the difference between the two survival curves can be considered to be statistically significant. For example, in a trial of two years (year=2), it is assumed that the annual harzard rate of the experimental group is 0.8 (herate; the annual event rate is 1−e−0.8), the annual hazard rate of the control group is 0.4 (hcrate; the annual event rate is 1−e−0.4), and the annual loss rate was 2% (vloss), the annual non-compliance rate was 5% (noncomp), and 8% (dropin) of the patients in the control group chose other treatments (drop-in) similar to those in the experimental group. The total event rate was 86% (pe) in the treatment group and 60% (pc) in the control group. Let k=10. Calculate the sample size, n.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Group Sequential Methods >>> Between-Mean Comparison
Between-mean difference of two groups (μ1−μ2):

Total variances of two groups (σ12+σ22):

Number of stages (k):

α value (Confidence level=(1-α)×100%):
0.01 0.05 0.1

β value (Statistical power=(1-β)×100%):
0.1 0.2

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
The most used group sequential experiments are staged experiments. It is required to divide the whole experiment into k consecutive stages, and in each phase, 2n subjects join the experiment, and are randomly assigned to the experimental group and the control group, and each group has n subjects. When the ith (i≤k) stage test is over, the experimental results from stage 1 to stage i are accumulated for statistical analysis. If H0 is rejected, the test can be ended, otherwise continue to the next stage of the test. If H0 cannot be rejected after the end of the last kth stage, H0 is acceptable. In group sequential experiments, repeated significance tests are required, and the significance level of each stage needs to be adjusted, and the adjusted significance level becomes the nominal significance level. In group sequential design, there are two conceptual ways of dividing time points, one is calendar time and the other is information time. Calendar time is based on the progress of the trial duration to determine when to conduct interim analysis; the meaning of information time refers to the percentage of the sample size observed at a certain observation point in the total sample size of the plan, measured by the amount of information that can be observed with which to decide when to conduct an interim analysis. In Pocock’s Test, the same margin and nominal significance level were used for each stage. For example, for k=8 and α=0.01, it is 3.078 (see user manual guide for details). For a 5-phase (k=5) group sequential trial comparing the efficacy of a drug and a control, according to the pilot test, the overall standard deviation is 3 (σ2=9: σ12=9, σ22=9), μ1−μ2=1; Pocock design; calculate the sample size for each stage, n.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Group Sequential Methods >>> Between-Mean Comparison >>> O’Brien and Fleming Test
Between-mean difference of two groups (μ1−μ2):

Total variances of two groups (σ12+σ22):

Number of stages (k):

α value (Confidence level=(1-α)×100%):
0.01 0.05 0.1

β value (Statistical power=(1-β)×100%):
0.1 0.2

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
The most used group sequential experiments are staged experiments. It is required to divide the whole experiment into k consecutive stages, and in each phase, 2n subjects join the experiment, and are randomly assigned to the experimental group and the control group, and each group has n subjects. When the ith (i≤k) stage test is over, the experimental results from stage 1 to stage i are accumulated for statistical analysis. If H0 is rejected, the test can be ended, otherwise continue to the next stage of the test. If H0 cannot be rejected after the end of the last kth stage, H0 is acceptable. In group sequential experiments, repeated significance tests are required, and the significance level of each stage needs to be adjusted, and the adjusted significance level becomes the nominal significance level. In group sequential design, there are two conceptual ways of dividing time points, one is calendar time and the other is information time. Calendar time is based on the progress of the trial duration to determine when to conduct interim analysis; the meaning of information time refers to the percentage of the sample size observed at a certain observation point in the total sample size of the plan, measured by the amount of information that can be observed with which to decide when to conduct an interim analysis. In O’Brien and Fleming Test, different margins for different stages, and the margin is set higher in the early stage and lower in the later stage (see user manual guide for details). For a 5-phase (k=5) group sequential trial comparing the efficacy of a drug and a control, according to the pilot test, the overall standard deviation is 3 (σ2=9: σ12=9, σ22=9), μ1−μ2=1; O’Brien and Fleming design; calculate the sample size for each stage, n.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Between-mean difference of two groups (μ1−μ2):

Total variances of two groups (σ12+σ22):

Number of stages (k):

α value (Confidence level=(1-α)×100%):
0.01 0.05 0.1

β value (Statistical power=(1-β)×100%):
0.1 0.2

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
The most used group sequential experiments are staged experiments. It is required to divide the whole experiment into k consecutive stages, and in each phase, 2n subjects join the experiment, and are randomly assigned to the experimental group and the control group, and each group has n subjects. When the ith (i≤k) stage test is over, the experimental results from stage 1 to stage i are accumulated for statistical analysis. If H0 is rejected, the test can be ended, otherwise continue to the next stage of the test. If H0 cannot be rejected after the end of the last kth stage, H0 is acceptable. In group sequential experiments, repeated significance tests are required, and the significance level of each stage needs to be adjusted, and the adjusted significance level becomes the nominal significance level. In group sequential design, there are two conceptual ways of dividing time points, one is calendar time and the other is information time. Calendar time is based on the progress of the trial duration to determine when to conduct interim analysis; the meaning of information time refers to the percentage of the sample size observed at a certain observation point in the total sample size of the plan, measured by the amount of information that can be observed with which to decide when to conduct an interim analysis. Wang and Tsiatis Test is an extension of Pocock Test and O’Brien and Fleming Test. It is the Pocock Test when ρ=0 and τ=0. It is the O’Brien and Fleming Test when ρ=0.5 and τ=0 (see user manual guide for details). For a 5-phase (k=5) group sequential trial comparing the efficacy of a drug and a control, according to the pilot test, the overall standard deviation is 3 (σ2=9: σ12=9, σ22=9), μ1−μ2=1; Wang and Tsiatis design; calculate the sample size for each stage, n.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

   Back to Top   



Between-mean difference of two groups (μ1−μ2):

Total variances of two groups (σ12+σ22):

Number of stages (k):

Margin (δ):
0 0.25 -0.25 -0.5

β value (Statistical power=(1-β)×100%):
0.1 0.2

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
The most used group sequential experiments are staged experiments. It is required to divide the whole experiment into k consecutive stages, and in each phase, 2n subjects join the experiment, and are randomly assigned to the experimental group and the control group, and each group has n subjects. When the ith (i≤k) stage test is over, the experimental results from stage 1 to stage i are accumulated for statistical analysis. If H0 is rejected, the test can be ended, otherwise continue to the next stage of the test. If H0 cannot be rejected after the end of the last kth stage, H0 is acceptable. In group sequential experiments, repeated significance tests are required, and the significance level of each stage needs to be adjusted, and the adjusted significance level becomes the nominal significance level. In group sequential design, there are two conceptual ways of dividing time points, one is calendar time and the other is information time. Calendar time is based on the progress of the trial duration to determine when to conduct interim analysis; the meaning of information time refers to the percentage of the sample size observed at a certain observation point in the total sample size of the plan, measured by the amount of information that can be observed with which to decide when to conduct an interim analysis. The above three group sequential tests can stop the test when H0 is rejected and H1 is accepted, i.e., the test can be stopped if the test drug is effective. However the Inner Wedge Test is a method that stops the test when H0 is accepted, that is, the test can be stopped when the test drug is ineffective (see user manual guide for details). For a 5-phase (k=5) group sequential trial comparing the efficacy of a drug and a control, according to the pilot test, the overall standard deviation is 3 (σ2=9: σ12=9, σ22=9), μ1−μ2=1; Inner Wedge design; calculate the sample size for each stage, n.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Group Sequential Methods >>> Between-Proportion Comparison
Use one of the following methods:
Pocock’s Test O’Brien and Fleming Test Wang and Tsiatis Test

Proportion of group 1 (p1):

Proportion of group 2 (p2):

Number of stages (k):

α value (Confidence level=(1-α)×100%):
0.01 0.05 0.1

β value (Statistical power=(1-β)×100%):
0.1 0.2

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
The most used group sequential experiments are staged experiments. It is required to divide the whole experiment into k consecutive stages, and in each phase, 2n subjects join the experiment, and are randomly assigned to the experimental group and the control group, and each group has n subjects. When the ith (i≤k) stage test is over, the experimental results from stage 1 to stage i are accumulated for statistical analysis. If H0 is rejected, the test can be ended, otherwise continue to the next stage of the test. If H0 cannot be rejected after the end of the last kth stage, H0 is acceptable. In group sequential experiments, repeated significance tests are required, and the significance level of each stage needs to be adjusted, and the adjusted significance level becomes the nominal significance level. In group sequential design, there are two conceptual ways of dividing time points, one is calendar time and the other is information time. Calendar time is based on the progress of the trial duration to determine when to conduct interim analysis; the meaning of information time refers to the percentage of the sample size observed at a certain observation point in the total sample size of the plan, measured by the amount of information that can be observed with which to decide when to conduct an interim analysis (see user manual guide for details). For example, for a 5-phase (k=5) group sequential trial comparing the efficacy of a drug and a control, according to the pilot test, p1=0.7, p2=0.3. Calculate the sample size for each stage, n.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Group Sequential Methods >>> Survival Analysis
Parameter θ:

Number of stages (k):

α value (Confidence level=(1-α)×100%):
0.01 0.05 0.1

β value (Statistical power=(1-β)×100%):
0.1 0.2

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
The most used group sequential experiments are staged experiments. It is required to divide the whole experiment into k consecutive stages, and in each phase, 2n subjects join the experiment, and are randomly assigned to the experimental group and the control group, and each group has n subjects. When the ith (i≤k) stage test is over, the experimental results from stage 1 to stage i are accumulated for statistical analysis. If H0 is rejected, the test can be ended, otherwise continue to the next stage of the test. If H0 cannot be rejected after the end of the last kth stage, H0 is acceptable. In group sequential experiments, repeated significance tests are required, and the significance level of each stage needs to be adjusted, and the adjusted significance level becomes the nominal significance level. In group sequential design, there are two conceptual ways of dividing time points, one is calendar time and the other is information time. Calendar time is based on the progress of the trial duration to determine when to conduct interim analysis; the meaning of information time refers to the percentage of the sample size observed at a certain observation point in the total sample size of the plan, measured by the amount of information that can be observed with which to decide when to conduct an interim analysis (see user manual guide for details). For example, for a 5-phase (k=5) group sequential trial comparing the efficacy of a drug and a control, according to the pilot test, θ=0.4. Calculate the sample size for each stage, n.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Group Sequential Methods >>> Re-Estimation of Sample Size
Proportion of effective cases in group 1 (p1; 0<p1<1):

Proportion of effective cases in group 2 (p2; 0<p2<1):

Proportion of cases in two groups (h; 0<h<1):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
In the interim analysis of some group sequential trials, it is necessary to re-estimate the sample size based on the accumulated data, and it should be noted that blind re-estimation may cause bias. Shih et al. proposed a random double-blind sample size re-estimation method based on the observed results after 50% of the samples were completed. For example, in the two-center clinical trial, center A (group 1) assigns patients to the trial group with a probability of 60%, center B (group 2) assigns patients to the trial group with a probability of 40%, and the entire trial assigns patients to the trial group with a probability of 45% (h). In the interim analysis, 50% sample size was completed, the effective rate of center A is 70% (p1), and the effective rate of center B is 60% (p2). Re-estimate the sample size required for the next stage, n.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Bioequivalence >>> Average Bioequivalence
Within-subject standard deviation (σ):

Difference between two groups (d):

Margin of average bioequivalence (δ; log(0.8)≤δ≤log(1.25)):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
In a standard 2 (sequential) × 2 (period) crossover experiment, namely two treatments T and R, subjects were randomly divided into two groups, the first group received T treatment in the first period and R in the second period, and the experimental order was TR. The second group received R treatment in the first period and T treatment in the second period, and the experimental order was RT. δ: the margin of average bioequivalence (log(0.8)≤δ≤log(1.25)); For example, pre-design an average bioequivalence study comparing inhalation and subcutaneous administration of a drug in a 2×2 crossover design. According to the pilot study, the within-subject standard deviation is 0.5, the margin of average equivalence is δ=log(1.25), and the difference d=0.08, σ=0.5. α=0.0001, β=0.10. Calculate the sample size for each group, n.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Bioequivalence >>> Individual Bioequivalence
Between-subject standard deviation of the test group (σBT):

Between-subject standard deviation of the reference group (σBR):

Within-subject standard deviation of the test group (σWT):

Within-subject standard deviation of the reference group (σWR):

Difference between test group and reference group (δ):

Parameter ρ:

Parameter θIBE:

Parameter a:

Parameter b:

α value (Confidence level=(1-α)×100%):
0.001 0.005 0.01 0.05

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
The sample size based on a 2×4 crossover design (TRTR, RTRT) for individual bioequivalence. For example, predesign an individual bioequivalence study comparing inhalation and subcutaneous administration of a drug in a 2×4 crossover design. According to the pilot study, σBT=0.1, σBR=0.2, σWT=0.2, σWR=0.2, ρ=0.8, δ=0, a=b=0.5, θIBE=6. α=0.0001, β=0.10. Calculate the sample size for each group, n.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Bioequivalence >>> In-vitro Trial
Between-subject standard deviation of the test group (σBT):

Between-subject standard deviation of the reference group (σBR):

Within-subject standard deviation of the test group (σWT):

Within-subject standard deviation of the reference group (σWR):

Difference between test group and reference group (δ):

Parameter θBE:

α value (Confidence level=(1-α)×100%):
0.005 0.01 0.05

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
The sample size based on a 2×4 crossover design (TRTR, RTRT) for in-vitro trial. For example, predesign an individual bioequivalence study comparing inhalation and subcutaneous administration of a drug in a 2×4 crossover design. According to the pilot study, σBT=0.3, σBR=0.2, σWT=0.5, σWR=0.3, δ=0.1, θBE=1.5. α=0.0001, β=0.10. Calculate the sample size for each group, n.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Dose Response Studies >>> Continuous Response
Standard deviation (σ):

Number of test groups (k):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Data of groups ci and percent improvement from baseline for groups ui (i=0,1,2,...,k):

Reset and enter or copy two lines of space delimited data into this area.

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
The research on dose-response relationship mainly includes: the dose-response relationship between different dose groups, the shape of the dose-response relationship curve, and the optimal dose. Usually, a randomized parallel control design is used to study the dose-response relationship, and the effectiveness of the drug is proved by measuring the variance. 1:1 design. For example, a four-group parallel controlled dose-response trial, including 1 control group and 3 test groups (k=3; doses are 10 mg, 20 mg, 30 mg respectively). According to the pilot study, σ=0.2, c0=−6 (control group)), c1=1, c2=2, c3=3, u0=0.05 (control group), u1=0.1, u2=0.2, u3=0.25. α=0.0001, β=0.1. Calculate the sample size for each group, n.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Dose Response Studies >>> Binary Response
Number of test groups (k):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Data of groups ci and response rate for groups pi (i=0,1,2,...,k):

Reset and enter or copy two lines of space delimited data into this area.

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
The research on dose-response relationship mainly includes: the dose-response relationship between different dose groups, the shape of the dose-response relationship curve, and the optimal dose. Usually, a randomized parallel control design is used to study the dose-response relationship, and the effectiveness of the drug is proved by measuring the variance. 1:1 design. For example, a four-group parallel controlled dose-response trial, including 1 control group and 3 test groups (k=3; doses are 10 mg, 20 mg, 30 mg respectively). According to the pilot study, c0=−6 (control group), c1=1, c2=2, c3=3, p0=0.05 (control group), p1=0.1, p2=0.2, p3=0.25. α=0.0001, β=0.1. Calculate the sample size for each group, n.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Dose Response Studies >>> Minimum Effective Dose (MED)
Standard deviation (σ):

Student's t-value with degree of freedom k and confidence degree α :

Margin (δ):

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
The minimum effective dose method based on the Williams test. For example, design a dose-response trial using the Williams test to detect the minimum effective dose. According to the pilot study, σ=0.4, t=3, δ=0.15. α=0.0001, β=0.1. Calculate the sample size for each group, n.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Dose Response Studies >>> Cochran-Armitage Test for Trend
Number of test groups (k):

Margin (δ):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Data of di (1st line) and pi (2nd line) (i=0,1,2,...,k):

Reset and enter or copy two lines of space delimited data into this area.

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
The research on dose-response relationship mainly includes: the dose-response relationship between different dose groups, the shape of the dose-response relationship curve, and the optimal dose. Usually, a randomized parallel control design is used to study the dose-response relationship, and the effectiveness of the drug is proved by measuring the variance. For example, design a four-group (1 control group and k=3 test groups) Cochran-Armitage trend detection dose-response trial. According to the pilot study, d0=1, d1=2, d2=3, d3=4, p0=0.1, p1=0.2, p2=0.4, p3=0.5. δ=1. α=0.0001, β=0.1. Calculate the sample size, n.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Microarray Studies >>> False Discovery Rate
Microarray Studies >>> False Discovery Rate >>> Fixed Effect Test
Use one of the following methods:
One-sided fixed effect test Two-sided fixed effect test

Total number of tested genes (m):

Number of prognostic genes (m1):

Number of actual rejections (r1; r1≤m1):

False discovery rate (f; 0≤f<1):

Distribution ratio of group 1 (a1; a1=1-a2):

Distribution ratio of group 2 (a2; a2=1-a1):

Size of the effect of prognostic genes (δ):

Expected loss in sample size (%):




α value (Confidence level=(1-α)×100%):


β value (Statistical power=(1-β)×100%):


Estimated sample size (n):


Required sample size (n):


Explanation:
The sample size of microarray data is small and the number of variables is large. The traditional t-test and Wilcoxon test need to be adjusted when they are applied. There are FDR (fasle discover rate) control, FWER (family-wise error rate) control, etc., based on control indices; single-step method, step-wise method, resampling-based method, based on the control operation procedures, and frequency school method and Bayes school method, based on different schools. Multiple testing is an extension of the traditional concept of multiple comparisons. The null hypothesis H0 is verified by repeated testing of multiple variables on the same question. This hypothesis is a series of hypotheses (a family of hypotheses), rather than a single hypothesis.
(1) One-sided fixed effect design. For example, design a microarray study of 2000 candidate genes (m=2000). It is estimated that there are 30 (m1=30) genes that are differently expressed between the two groups, and the actual number of rejected genes is about 18 (r1=18). FDR(f)=0.01. δ=1, a1=a2=0.5. Calculate the sample size for each group, n.
(2) Two-sided fixed effect design. For example, design a microarray study of 2000 candidate genes (m=2000). It is estimated that there are 30 (m1=30) genes with different expression between the two groups, and the actual number of rejected genes is about 18 (r1=18). FDR(f)=0.01. δ=1, a1=a2=0.5. Calculate the sample size for each group, n.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Microarray Studies >>> False Discovery Rate >>> Variable Effect Test
Use one of the following methods:
One-sided variable effect test Two-sided variable effect test

Total number of tested genes (m):

Number of prognostic genes (m1):

Number of actual rejections (r1; r1≤m1):

False discovery rate (f; 0≤f<1):

Distribution ratio of group 1 (a1; a1=1-a2):

Distribution ratio of group 2 (a2; a2=1-a1):

Size of the effect of prognostic genes (δ):

Expected loss in sample size (%):


Data of prognostic genes (i) and sizes of the effect of prognostic genes (δi) (i=1,2,...,m1):

Reset and enter or copy two lines of space delimited data into this area.



Estimated sample size (n):


Required sample size (n):


Explanation:
The sample size of microarray data is small and the number of variables is large. The traditional t-test and Wilcoxon test need to be adjusted when they are applied. There are FDR (fasle discover rate) control, FWER (family-wise error rate) control, etc., based on control indices; single-step method, step-wise method, resampling-based method, based on the control operation procedures, and frequency school method and Bayes school method, based on different schools. Multiple testing is an extension of the traditional concept of multiple comparisons. The null hypothesis H0 is verified by repeated testing of multiple variables on the same question. This hypothesis is a series of hypotheses (a family of hypotheses), rather than a single hypothesis.
(1) One-sided variable effect design. For example, design a microarray study of 2000 candidate genes (m=2000). It is estimated that there are 30 (m1=30) genes with different expression between the two groups, and the actual number of rejected genes is about 18 (r1=18). FDR(f)=0.01. δj=1, if 1≤i≤10, and δj=0.5, if 11≤i≤30. a1=a2=0.5. Calculate the total sample size for each group, n.
(2) Two-sided variable effect design. For example, design a microarray study of 2000 candidate genes (m=2000). It is estimated that there are 30 (m1=30) genes with different expression between the two groups, and the actual number of rejected genes is about 18 (r1=18). FDR(f)=0.01. δj=1, if 1≤i≤10, and δj=0.5, if 11≤i≤30. a1=a2=0.5. Calculate the sample size for each group, n.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Nonparametrics >>> Test for Independence
Probability p1 (0<p1<1):

Probability p2 (p1≤p2<1):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
Nonparametric tests are hypothesis tests that do not rely on statistical parameters. They are suitable for hypothesis testing of unknown distribution types, skewed data, hierarchical data, etc. In Test for Independence, For example, it has been observed that in a pilot study that as the x increases, y also tends to increase. A clinical trial is designed to verify the above conjecture. According to the pilot study, p1=0.4, p2=0.6. α=0.0001, β=0.10. Calculate the sample size, n.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Sample Sizes Estimation in Other Areas >>> ANOVA with Repeated Measures
Sum of variances of all groups (σ2):

Difference (δ):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
The ANOVA with repeated measures can be repeated measures under the same condition, or repeated measures under different conditions. The ANOVA with repeated measures can be used to examine whether there are significant differences between various treatments, to find differences among subjects, or to find interaction between various treatments and groups of subjects. In parallel controlled clinical trials, it is mainly used to evaluate effectiveness and safety. For example, a test drug and a traditional drug are tested in parallel on experimental animals, and each experimental animal records disease scores repeated three times. According to the pilot study, σ2=5.5, δ=1.2. α=0.0001, β=0.10. Calculate the total sample size for all groups, n.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Sample Sizes Calculation in Other Areas >>> QT/QTc >>> Parallel Control Design
Between-subject standard deviation (σb):

Within-subject standard deviation (σw):

Number of replications per subject (K):

Clinical difference (d):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
The QT interval refers to the time course of ventricular depolarization and repolarization, that is, the time course from the starting point of the QRS complex to the end point when the T wave returns to baseline. Delayed cardiac repolarization will create a special cardiac electrophysiological environment in which arrhythmias are prone to occur, the most common of which is torsade de pointes (TdP), but other types of ventricular tachyarrhythmias can also occur. Since the degree of QT prolongation can be regarded as a relative biomarker of arrhythmogenic risk, there is usually a qualitative relationship between QT prolongation and TdP, and it is more important for those drugs that may cause QT prolongation. Since the QT interval is inversely related to heart rate, it is routine to correct the measured QT interval to a less heart rate dependent QTc interval through various formulas. However, it is unclear whether there is a necessary link between the occurrence of arrhythmia and an increase in the QT interval or the absolute value of QTc. Most drugs that cause TdP can significantly prolong the QT/QTc interval (i.e., QT/QTc). Because QT/QTc interval prolongation is an electrocardiographic finding associated with increased sensitivity for detecting arrhythmias, adequate safety evaluation of new drugs before marketing should include a detailed characterization of their effects on the QT/QTc interval.
In Parallel Control Design, for example, a non-antiarrhythmic drug conducts a comprehensive ECG parallel control study to determine its effect on the QT/QTc interval. According to the prel-trial, σb=2.5, σw=0.5, d=2, K=5. α=0.0001, β=0.10. Calculate the sample size for each group, n.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Sample Sizes Calculation in Other Areas >>> QT/QTc >>> Parallel Control Design with Covariates
Between-subject standard deviation (σb):

Within-subject standard deviation (σw):

Mean of group 1(σ1):

Mean of group 2 (σ2):

Standard deviation of group 1(τ1):

Standard deviation of group 2 (τ2):

Number of replications per subject (K):

Clinical difference (d):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
The QT interval refers to the time course of ventricular depolarization and repolarization, that is, the time course from the starting point of the QRS complex to the end point when the T wave returns to baseline. Delayed cardiac repolarization will create a special cardiac electrophysiological environment in which arrhythmias are prone to occur, the most common of which is torsade de pointes (TdP), but other types of ventricular tachyarrhythmias can also occur. Since the degree of QT prolongation can be regarded as a relative biomarker of arrhythmogenic risk, there is usually a qualitative relationship between QT prolongation and TdP, and it is more important for those drugs that may cause QT prolongation. Since the QT interval is inversely related to heart rate, it is routine to correct the measured QT interval to a less heart rate dependent QTc interval through various formulas. However, it is unclear whether there is a necessary link between the occurrence of arrhythmia and an increase in the QT interval or the absolute value of QTc. Most drugs that cause TdP can significantly prolong the QT/QTc interval (i.e., QT/QTc). Because QT/QTc interval prolongation is an electrocardiographic finding associated with increased sensitivity for detecting arrhythmias, adequate safety evaluation of new drugs before marketing should include a detailed characterization of their effects on the QT/QTc interval.
In Parallel Control Design with Covariates, for example, a comprehensive electrocardiogram parallel control study was conducted on a non-antiarrhythmic drug. The Cmax of the drug is known to have an impact on the QT/QTc interval to clarify its impact on the QT/QTc interval. According to the prel-trial, σb=2.5, σw=0.5, v1=1.1, v2=1.3, τ1=2.1, τ2=2.2, d=2, K=5. α=0.0001, β=0.10. Calculate the sample size for each group, n.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Sample Sizes Calculation in Other Areas >>> QT/QTc >>> Crossover Control Design
Between-subject standard deviation (σb):

Within-subject standard deviation (σw):

Standard deviation for additional variation (σp):

Number of replications per subject (K):

Clinical difference (d):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
The QT interval refers to the time course of ventricular depolarization and repolarization, that is, the time course from the starting point of the QRS complex to the end point when the T wave returns to baseline. Delayed cardiac repolarization will create a special cardiac electrophysiological environment in which arrhythmias are prone to occur, the most common of which is torsade de pointes (TdP), but other types of ventricular tachyarrhythmias can also occur. Since the degree of QT prolongation can be regarded as a relative biomarker of arrhythmogenic risk, there is usually a qualitative relationship between QT prolongation and TdP, and it is more important for those drugs that may cause QT prolongation. Since the QT interval is inversely related to heart rate, it is routine to correct the measured QT interval to a less heart rate dependent QTc interval through various formulas. However, it is unclear whether there is a necessary link between the occurrence of arrhythmia and an increase in the QT interval or the absolute value of QTc. Most drugs that cause TdP can significantly prolong the QT/QTc interval (i.e., QT/QTc). Because QT/QTc interval prolongation is an electrocardiographic finding associated with increased sensitivity for detecting arrhythmias, adequate safety evaluation of new drugs before marketing should include a detailed characterization of their effects on the QT/QTc interval.
In Crossover Control Design, for example, a comprehensive ECG crossover control study was conducted on a non-antiarrhythmic drug to determine its effect on the QT/QTc interval. According to the prel-trial, σb=2.5, σw=0.5, σp=0.1, d=2, K=5. α=0.0001, β=0.10. Calculate the sample size for each group, n.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Sample Sizes Calculation in Other Areas >>> QT/QTc >>> Crossover Control Design with Covariates
Between-subject standard deviation (σb):

Within-subject standard deviation (σw):

Mean of group 1(v1):

Mean of group 2 (v2):

Standard deviation of group 1(τ1):

Standard deviation of group 2 (τ2):

Standard deviation for additional variation (σp):

Number of replications per subject (K):

Clinical difference (d):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
The QT interval refers to the time course of ventricular depolarization and repolarization, that is, the time course from the starting point of the QRS complex to the end point when the T wave returns to baseline. Delayed cardiac repolarization will create a special cardiac electrophysiological environment in which arrhythmias are prone to occur, the most common of which is torsade de pointes (TdP), but other types of ventricular tachyarrhythmias can also occur. Since the degree of QT prolongation can be regarded as a relative biomarker of arrhythmogenic risk, there is usually a qualitative relationship between QT prolongation and TdP, and it is more important for those drugs that may cause QT prolongation. Since the QT interval is inversely related to heart rate, it is routine to correct the measured QT interval to a less heart rate dependent QTc interval through various formulas. However, it is unclear whether there is a necessary link between the occurrence of arrhythmia and an increase in the QT interval or the absolute value of QTc. Most drugs that cause TdP can significantly prolong the QT/QTc interval (i.e., QT/QTc). Because QT/QTc interval prolongation is an electrocardiographic finding associated with increased sensitivity for detecting arrhythmias, adequate safety evaluation of new drugs before marketing should include a detailed characterization of their effects on the QT/QTc interval.
In Crossover Control Design with Covariates, for example, a comprehensive electrocardiogram crossover control study was conducted on a non-antiarrhythmic drug. The Cmax of the drug is known to have an impact on the QT/QTc interval to clarify its impact on the QT/QTc interval. According to the prel-trial, σb=2.5, σw=0.5, v1=1.1, v2=1.3, τ1=1.8, τ2=1.0, σp=0.1, d=2, K=8. α=0.0001, β=0.10. Calculate the sample size for each group, n.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155:100-155 .

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Sample Sizes Estimation in Other Areas >>> Quality of Life (QOL)
Parameter c:

Difference (d):

Margin (ϕ; ϕ<d):

η value:
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
Since chronic non-infectious diseases are difficult to cure, it is difficult to use cure rate to evaluate treatment effects, and the role of survival rate is also limited. Therefore, quality of life is used as an evaluation item for new drugs. For example, a drug is undergoing a clinical trial based on the QOL. According to the pilot study, c=0.3, d=0.2, ϕ=0.1. η=0.2, α=0.0001, β=0.10. Calculate the sample size, n.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Sample Sizes Estimation in Other Areas >>> Vaccine Clinical Trials
Disease incidence in test group (pT; 0<pT<1):

Disease incidence in test group (pC; 0<pC<1):

Expected difference (d):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
The most important goal of evaluating a vaccine is its ability to prevent disease, which usually requires a large-sample placebo-controlled design. For example, it is planned to implement a vaccine clinical trial, compared with placebo, and the index uses the reduction in disease incidence. According to the pilot study, the incidence rate of the vaccine group is 2% (pT), and the incidence rate of the control group is 5% (pC), d=0.1. α=0.0001. Two-group 1:1 parallel control. Two-sided test. Calculate the sample size for each group, n.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Sample Sizes Estimation in Other Areas >>> Vaccine Clinical Trials >>> Evaluation of Vaccine Efficacy with Extremely Low Disease Incidence
Disease incidence in test group (pT; 0<pT<1):

Disease incidence in test group (pC; 0<pC<1):

Parameter θ (0<θ<1):

Parameter θ0 (0<θ0<1):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
The most important goal of evaluating a vaccine is its ability to prevent disease, which usually requires a large-sample placebo-controlled design. For example, it is planned to implement a vaccine clinical trial, compared with placebo, and the index uses the reduction in disease incidence. According to the pilot study, the incidence rate of the vaccine group is 0.2% (pT), and the incidence rate of the control group is 0.5% (pC), θ=0.3, θ0=0.5. α=0.0001, β=0.10. Two-group 1:1 parallel control. Two-sided test. Calculate the sample size for each group, n.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Disease incidence in test group (pT; 0<pT<1):

Disease incidence in control group (pC; 0<pC<1):

Mean of test group (μT; 0<μT<1):

Mean of control group (μC; 0<μC<1):

Standard deviation of test group (σT; 0<σT<1):

Standard deviation of control group (σC; 0<σC<1):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

β value (Statistical power=(1-β)×100%):
0.1 0.2 0.15 0.05

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
The most important goal of evaluating a vaccine is its ability to prevent disease, which usually requires a large-sample placebo-controlled design. According to the pilot study, the incidence rate of the vaccine group is 2% (pT), and the incidence rate of the control group is 5% (pC), μT=0.2, μC=0.4, σT=0.3, σC=0.4. α=0.0001, β=0.10. Two-group 1:1 parallel control. Two-sided test. Calculate the sample size for each group, n.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Sample Sizes Estimation in Other Areas >>> Sensitivity and Specificity Estimation
Sensitivity or specificity (p; 0<p<1):

Permissible error (d; 0<d<1):

α value (Confidence level=(1-α)×100%):
0.0001 0.0005 0.001 0.005

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
This is a single sample trial aimed to assess the value of a technique in finding a phenomenon (e.g., a disease). d: permissible error (e.g., 0.1), p: sensitivity (pse, e.g., 0.8) or specificity (psp, e.g., 0.9). Use the maximum of n from pse and psp.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Sample Sizes Estimation in Other Areas >>> Distance Based Sampling
Number of distance measuring for each point (r; r≥1):

Coefficient of variation for estimating population density (CV; 0<CV<1):

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
This method is usually in field studies. n: the number of random points for measuring distance.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Sample Sizes Estimation in Other Areas >>> Linear Transect Sampling
Sample Sizes Estimation in Other Areas >>> Linear Transect Sampling >>> Sample Size for Linear Transect Sampling
Coefficient of variation for density estimation along a linear transect (CV; 0<CV<1):

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
This method is usually in field studies. n: the number of sampling points along a linear transect.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Sample Sizes Estimation in Other Areas >>> Linear Transect Sampling >>> Transect Length for Linear Transect Sampling
Length of linear transect in the first sampling (L1):

Number of subjects (e.g., animals) found in the first sampling (n1):

Coefficient of variation for density estimation along a linear transect (CV; 0<CV<1):

Coefficient b (1.5≤b≤4):

Expected loss in transect length (%):




Estimated transect length (L):


Required transect length (L):


Explanation:
This method is usually in field studies. For example, assume that the CV for density estimation is 0.1, i.e., the half-width of confidence interval at α=0.05 is ±20% of the true density. 10 subjects are found along a linear transect of 30 km. The length of linear transect to be investigated should be: α=3/0.12*(30/10)=900 km.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Sample Sizes Estimation in Other Areas >>> Mark-Recapture Sampling
Coefficient of variation for population size estimation (CV; 0<CV<1):

Expected loss in sample size (%):




Estimated sample size (n):


Required sample size (n):


Explanation:
This method is usually in field studies. n: the number of marked animals recaptured in the second sampling in Petersen mark-recapture sampling. or the total number of marked animals recaptured in the sequential samplings in Schnabel mark-recapture sampling.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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Sample Sizes Estimation in Other Areas >>> Stratified Random Sampling
Number of layers (L):

Permissible error (d; d>0):

α value (Confidence level=(1-α)×100%):
0.01 0.05

Expected loss in sample size (%):


Size of layer i (Ni) and standard deviation for layer i (si) (i=1,2,...,L):

Reset and enter or copy two lines of space delimited data into this area.



Estimated sample size (n):


Required sample size (n):


Explanation:
This method is usually in field studies. n: the sample size for total population. For example, there are 6 layers (i.e., 6 sub-populations), layer sizes are 400, 30, 61, 18, 70 and 120 respectively and their corresponding standard deviations are 557, 406, 347, 227, 123 and 979 respectively. Total population size is 699 in this example. Generally the number of layers should be not greater than 6 in field studies.

User manual guide:
Zhang W.J. 2024. SampSizeCal: The platform-independent computational tool for sample sizes in the paradigm of new statistics. Network Biology, 14(2): 100-155 .

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SampSizeCal©, 2023 - W. J. Zhang (E-mail: zhwj@mail.sysu.edu.cn, wjzhang@iaees.org)
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