### Introduction

### Considerations during Sample Size Calculations

### Study objectives

### Hypotheses

*H*) and alternative hypotheses (

_{0}*H*). A null hypothesis is 'what the researcher wants to investigate,' while an alternative hypothesis is 'what the researcher wants to show.' If the previous example is used again, the null hypothesis is 'The (average) anesthesia induction time of the new intravenous anesthetic (μ

_{a}_{new}) is equal to the (average) anesthesia induction time of the conventional intravenous anesthetic (μ

_{old}),' and the alternative hypothesis is 'The (average) anesthesia induction time of the new intravenous anesthetic (μ

_{new}) is shorter than the (average) anesthesia induction time of the conventional intravenous anesthetic (μ

_{old}).' In fact, an accurate description of the alternative hypothesis in an inequality test is 'The (average) anesthesia induction time of the new intravenous anesthetic is not equal to the (average) anesthesia induction time of the conventional intravenous anesthetic.' However, in clinical studies, even when the hypothesis is established as if in a one-sided test, a two-sided test is performed in most cases in order to maintain a more conservative point of view, because the probability that a null hypothesis is rejected is higher in a one-sided test where the significance level is set to be high or low on one side. In other words, when a new treatment which does not cause an actual difference is regarded as if it did in fact cause a difference, the result may be used clinically.

### Study design

### Primary endpoint

### Type I error, type II error, and power

*α*), while not rejecting a false null hypothesis is a Type II error (

*β*). Therefore, power refers to the probability of avoiding a Type II error (1-

*β*), which is the probability that rejection of a null hypothesis is right when an alternative hypothesis is true.

#### Power analysis

### Effect size2)

#### Clinically significant difference

#### Population variance

**A. Study design:**Is the study design of the reference similar to that of the present study? The variance of an observation study may be greater than that of a randomized controlled study. If a multi-center clinical study is planned, questions such as 'Is the reference study designed similarly to the present study?' and 'Is the time interval from the treatment to outcome measurement similar?' should be taken into account.

**B. Study subjects:**Are the subjects of the reference similar to the subjects of the present study? Demographical similarity is necessary. In the case of a multi-center study, it should be verified as to whether the races or nationalities of the subjects are similar. In addition, questions such as 'Do the subjects have similar diseases or severity levels? and 'Was the study conducted during the same season or period (asthma, influenza, etc.)?' should be considered.

**C. Analysis:**Are the analytical methods and summary statistical methods applied to the references identical to those of the present study? In addition to the application of the same analytical methods, was a covariate (e.g., a reference value of a response variable) also analyzed if there was one? Including a covariate may reduce the variance estimate and the sample size [5].