## Finding the Minimum Sample Size

When completing your thesis or dissertation, you will most likely be collecting data and running some statistical analysis on the data that you collect. When writing proposals for their theses and dissertations, students commonly overlook *a priori* power analysis which can be critical in their study.

### What is power?

Statistical power is the ability for statisticians to use statistical tests to determine if significance exists between variables in a study. Power (though in a different metric) is the inverse of the alpha level. Insufficient statistical power increases the likelihood of a type II (or beta) error, which occurs when researchers fail to reject null hypotheses [link to article Introduction to Null Hypothesis Significance Testing] when alternative hypotheses are discovered to be true.

### What are the factors relating to power?

Many factors relate to statistical power, such as sample size, significance level, effect size, beta level, number of groups being compared, etc. Increasing the sample size, significance level, or effect size will increase statistical power. Having more group comparisons will lower statistical power.

### What is *a priori* power?

The term *a priori* comes from Latin and means “from the earlier.” It is a type of power analysis that researchers calculate prior to data collection to determine the minimum sample size to find significance (if significance exists). Calculating a minimum sample size helps researchers maximize their resources. By knowing the minimum number of participants needed for significance, researchers do not waste time collecting more data than they need to determine significance between variables. Additionally, knowing the minimum sample size also helps researchers confirm that they have sufficient data to find significance, which decreases chances of a type II error.

### How do you calculate* a priori* power?

*A priori* power is calculated from the factors related to power, factors that were previously discussed in the “What are the factors relating to power?” section. Before collecting your data, you will need to determine your alpha level (typically .05), to estimate the expected effect size (it is best to be moderate in your estimation), and to count number of groups being compared (if applicable). The last step is to determine how much power you want for your study. Ideally, when running this type of power analysis, you should set your power to .90; however, some statisticians argue that power as low as .80 is acceptable.

There are many software programs researchers and students can use; G*Power is the most common free software program used.

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