# Sample size calculation

Sample size calculation is a critical step in designing a medical research study, as it determines the number of participants required to ensure that the study is adequately powered to detect meaningful effects. A study with too few participants may not have enough statistical power to detect important differences, while a study with too many participants can be a waste of resources. Providing a sample size calculation will reflect the professionalism of researchers doing the study.

Calculate sample size

Sample size required:

To use the sample size calculator, follow these steps:

- Enter the effect size you want to detect. You can either estimate the effect size (small, medium, or large, as detailed below), or you can use Cohend' D formula, where we developed a specific effect size calculator to determine an appropriate effect size based on your research question and prior knowledge.
- Enter the desired significance level (alpha) and statistical power. These values are typically set to 0.05 and 0.80, respectively, but you can adjust them based on your specific needs.
- Click the "Calculate sample size" button to calculate the required sample size. The result will be displayed in the "Sample size required" field.
- Interpret the result based on the value displayed in the "Interpretation" field. If the calculated sample size is less than 30, consider increasing the sample size or using alternative statistical methods.

### Effect size estimation

Reporting the effect size can be as general as assuming it would be small, medium, or large. As a result, you can inout the following values for each

0.2 for small: prior literature found small difference between the groups you want to study. You should cite at least one study that support this.

0.5 for medium: prior literature found a medium difference between the groups you want to study. You should cite at least one study that support this.

0.8 for large: prior literature found a large difference between the groups you want to study. You should cite at least one study that support this.

These values were proposed by Cohen in 1988, and you can cite the following to support your assumption:

Reference: Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences. New York, NY: Routledge Academic.

### Effect size calculator

Calculate effect size (Cohen's d)

Effect size (Cohen's d):

Interpretation: A small effect size is typically around 0.2, a medium effect size around 0.5, and a large effect size around 0.8

To use the effect size calculator, follow these steps:

- Enter the mean of group 1, the mean of group 2, and the standard deviation of the sample.
- Click the "Calculate effect size" button to calculate the effect size. The result will be displayed in the "Effect size" field.
- Interpret the result based on the value displayed in the "Interpretation" field. A small effect size is typically around 0.2, a medium effect size around 0.5, and a large effect size around 0.8.

### Example

Here's an example using data from a study comparing the effectiveness of two weight loss programs. You search prior literature and found a previous study that had similar aim. According to the previous study, you found that the weight loss for the groups were:

Group 1: Mean = 8.2 kg, with standard deviation = 3.5 kg Sample size = 25

Group 2: Mean = 6.7 kg, with standard deviation = 2.8 kg Sample size = 30

Accordingly, the effect size will be = 0.495 (i.e., medium effect size).

The required sample size for your study at significance level (alpha) of 0.05 and statistical power of 0.80, with an estimated sample size of 0.495 will be 65. This represent the minimum number required and represent the total number in both groups, meaning that you can recruite 30 for one group and 35 for the other.