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# Sample size calculator

When preparing to conduct a trial, you will want to make sure that the experiment has sufficient statistical power. In other words, you want some confidence that you are likely to find the effect you are looking for. As outlined on the power page, there are several factors that impact the power of an analysis. Often, the only factor under your direct control is the sample size (i.e. number of subjects in the trial). Since larger trials take more time and resources than smaller trials, you probably want to determine the minimum sample size necessary to achieve an acceptable level of statistical power.

## Selecting the effect size

In order to estimate the necessary sample size, we need to know the effect size in advance. This is a chicken and egg problem: how can we know the effect size before we've conducted the study? There are two strategies available.

One approach is to use another data set to predict the likely effect size. For example, you may conduct a small pilot study to obtain a rough estimate. Alternatively, you can use the results from a related study, such as one published by another team conducting research on a similar topic.

A second approach is to use clinical judgment to specify the smallest effect size that you consider to be relevant. For example, if you feel that it is important to detect even small effects, you may select a value of 0.2 (see this page for a rough categorization of effect size levels).

## Sample size calculator

This calculator tells you the minimum number of participants necessary to achieve a given power. The following parameters must be set:

Test family
The online calculator currently supports the t-test and sample size estimation for correlation co-efficients. Please contact us if there are other test families that you would like included.
Sample groups
Select the "Same subjects" option if you will take multiple measurements from the same person (this is sometimes known as "paired", "related" or "repeated measures"), and "Independent groups" if the scores will be from two different groups of people.
Tail(s)
The number of tails depends on whether or not your hypothesis has an implied direction. There is more information on directionality here.
Effect size
See the discussion above to select an appropriate effect size.
Significance level
Alpha (α) is the probability of falsely rejecting the null hypothesis, and the most common value is 0.05. A more thorough discussion on setting the significance level can be found here.
Power
Statistical power is the ability of study to detect a result that is exists in nature. Generally, we want power to be as high as possible. However, setting it too high may result in a sample size that is not practical. A value of 0.8 is often used in practice.