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# Statistical Power

Statistical power refers to the probability that a statistical analysis will allow for the null hypothesis to be rejected. Statistical power is intimately linked to the concepts of a Type I and Type II error. For the purposes of this discussion, we will quickly review these terms.

A Type I Error is when a researcher mistakenly rejects the null hypothesis when in fact it is true. Conversely, a Type II Error takes place when a researcher fails to reject the null hypothesis and thinks that no difference exists, when it does. When the statistical power associated with a test is lower, meaning that the alpha value is smaller, the chances of a Type II Error occurring is greater1.

Essentially, statistical power can be defined as the chance of finding that a statistical difference does exist between two variables, without this difference being the result of a Type I Error2. Statistical power is a measure which can be computed and is denoted by a value which must be between 0 and 12. It is a general rule that a value of 0.8 or greater indicates that there is a high probability of finding a significant difference2.

To ensure that the statistical power associated with a test is high enough, increasing the sample size will raise the probability of finding a statistical difference2. This is logical because increasing the sample size means that the researcher is collecting more data to test. Furthermore, there are statistical programs which can be used to verify whether or not your sample size is large enough. If your calculated statistical power is less than 0.8, then you know that your sample size is not large enough.

Clearly, understanding this concept of statistical power is important for interpreting the validity of the results associated with hypothesis testing. The higher the statistical power associated with an analysis, the more relevant the findings will be.

References:

1. Villanova University. (2014). The Concepts of Statistical Power and Effect Size. Retrieved from: http://www83.homepage.villanova.edu/richard.jacobs/EDU%208603/lessons/stastical%20power.html

2. My Environmental Education Evaluation Resource Assistant. (2014). Power Analysis, Statistical Significance, & Effect Size. Retrieved from: http://meera.snre.umich.edu/plan-an-evaluation/related-topics/power-analysis-statistical-significance-effect-size

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