# Sample Size Calculations

## Simply the number of subjects included in a study determined by a calculation.

Click **here** to download a fact sheet on Sample Size Calculations at the bench.

### What does it mean to calculate sample size?

The term sample size refers to the number of study subjects included in an experiment. Investigators generate this number by **1)** coming up with a null and alternative hypothesis in line with the primary outcome of the study, **2)** identifying appropriate variables (alpha, beta, measure of effect and variability) using literary evidence, expert opinion, or pilot studies, and **3)** inputting these variables into an equation or the __ University of British Columbia Power and Sample Size Calculator__.

### Who should calculate sample size?

Just as clinical scientists calculate sample sizes to determine the number of trial participants needed for each experimental group, preclinical scientists are equally as responsible for calculating sample size. This is particularly important for ‘confirmatory’ experiments that will inform future directions and development of an intervention.

### When should you calculate sample size?

Sample size should be calculated before the experiment begins. Similarly, determining the primary outcome of the experiment beforehand is important as this influences the sample size equation to be used as well as the variables to be inputted into the sample size equation.

### Why calculate sample size?

By not calculating sample size ahead of time, you may be either** a)** including too many study subjects or** b)** including too few study subjects in the experiment, which would result in either a waste of time and resources or the generation of inaccurate results that are not reflective of the true population, respectively. It is also important to report the sample size and the variables used to calculate the sample size in the manuscript.

## Optimal Practices

- You start by coming up with the primary outcome of interest for the study (tumour size), the null hypothesis (H0: There is no observed difference in mean tumour size between groups), and the alternative hypothesis (HA: There is an observed difference in mean tumour size between groups).
- You look to literary evidence, expert opinion, and pilot studies to come up with the following variables:
- Type I error rate(α): set at 0.05 by convention.
- Type II error rate (β): set at 0.2 by convention
- Measures of effect: |𝜇
_{1},𝜇_{2}|- Expected mean tumour size of control group (𝜇
_{1}) - Expected mean tumour size of treatment group (𝜇
_{2})

- Expected mean tumour size of control group (𝜇
- Variance: expected population standard deviation (sigma)

- You input the above variables (𝛼,𝛽,𝜇
_{1},𝜇_{2},𝑠𝑖𝑔𝑚𝑎) into theto generate the appropriate number of animals for each experimental group.**University of British Columbia Power and Sample Size Calculator** - You report your sample size in your manuscript as well as the alpha, beta, expected effect and variance (𝛼,𝛽,𝜇
_{1},𝜇_{2},𝑠𝑖𝑔𝑚𝑎) variables used to generate the sample size.

## Suboptimal Practices

_{1},𝜇

_{2},𝑠𝑖𝑔𝑚𝑎) used to calculate this sample size.