### Introduction

### Pilot and exploratory experiments

### Confirmatory study

### General considerations prior to sample size calculation

### Type of comparison

*H*

_{1}and

*H*

_{0}are the alternative and null hypotheses, respectively. Let

*μ*and

_{t}*μ*be the true mean of the test and control group and

_{c}*p*and

_{t}*p*be the true proportion of the test and control group, respectively. Additionally, let

_{c}*δ*be the clinically significant difference in the equality test, the non-inferiority margin in the non-inferiority test, the superiority margin in the superiority test, and the equivalence margin in the equivalence test.

*μ*–

_{t}*μ*) > 0 is considered an improvement of the test group as compared to the control group. A typical approach to compare the mean or proportion differences in a study with two independent samples (groups) is to test the following hypotheses shown in Table 1.

_{c}### Primary variable

### Errors

*α*) and statistical power (1 –

*β*) must be considered when calculating a sample size. The significance level is the maximum allowable value of the type I error. The type I error indicates the probability of rejecting the null hypothesis when it is true. Statistical power is the probability of rejecting H

_{0}when it is false. If the type II error is set to

*β*, then the statistical power is set to 1 –

*β*. The power analysis is a method of sample size calculation that can be used to estimate the sample size required for a study, given the significance level and statistical power.

### Sample size calculation

### Precision analysis

*α*)% confidence interval, depends on its width. Because a narrower interval has a more precise interval, this method considers the maximum half-width of the 100(1 –

*α*)% [2].

*σ*

^{2}is known, the formula of sample size required from a 100(1 –

*α*)% confidence interval for

*μ*can be chosen as

*μ*.

### Power analysis

*σ*

^{2}is the known population variance, (3) the population variances of test and control group are equal to

*σ*

^{2}, (4)

*μ*–

_{t}*μ*is the true mean difference between a test group (

_{c}*μ*) and a control group (

_{t}*μ*), (5)

_{c}*μ*–

_{t}*μ*> 0 is considered an indication of improvement of the test group as compared to the control group, (6)

_{t}*δ*is the clinically significant difference in the equality test, the non-inferiority margin in the non-inferiority test, the superiority margin in the superiority test, and the equivalence margin in the equivalence test, (7) k is a constant for the allocation rate, (8)

*n*is the sample size of the test group, and

_{t}*n*is the sample size of the control group, and (9)

_{c}*z*,

_{α}*z*, and

_{β}*α*

^{th}, β

^{th}, and

### Other formulae of sample size calculation

### Sample size for dichotomous data

*H*

_{0}:

*p*–

_{c}*p*= 0 versus

_{t}*H*

_{1}:

*p*–

_{c}*p*≠ 0

_{t}*r*: the number of outcomes in the control group

_{c}*r*: the number of outcomes in the test group

_{t}*N*: the total number of animals in the control group

_{c}*N*: the total number of animals in the test group

_{t}*β*can be obtained by following equation:

*p*–

_{c}*p*|

_{t}*α*and

*β*, and is for two-sided test

### Sample size for comparing two group means

*H*

_{0}:

*μ*–

_{c}*μ*= 0 versus

_{t}*H*

_{1}:

*μ*–

_{c}*μ*≠ 0

_{t}*μ*: population mean of the control group

_{c}*μ*: population mean of the test group

_{t}*β*can be obtained from the following formula:

*α*and

*β*, and is for a two-sided test

### Sample size for paired studies

*H*

_{0}:

*μ*–

_{before}*μ*= 0 versus

_{after}*H*

_{1}:

*μ*–

_{before}*μ*≠ 0

_{after}*β*can be obtained using the following equation:

*α*and

*β*, and is for a two-sided test

### Nonparametric

*U*test) are applied, respectively, which are non-parametric methods. Non- parametric methods of (c) and (d) are corresponding to the parametric methods of (a) and (b), respectively. All alternative hypotheses are two-sided tests for equality with a significance level of 0.05, and the power is calculated by PASS 2020 [10].