11: Power Analysis
- Page ID
- 45203
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The power of a statistical test is the probability that the test will reject the null hypothesis when the alternative hypothesis is true. Most of us are used to thinking that a hypothesis is either right or it is wrong: a doctor’s diagnosis is correct, the patient has the disease, or the patient does not; an experimental result is objectively true — i.e., true independent of the observer’s subjectivity — or it is false. As we work through a typical science curriculum, we may even take to heart that, unlike mathematicians, scientists don’t prove scientific ideas no matter how well supported by evidence. Our acceptance of scientific theories is provisional; if new evidence comes along, we revise and if warranted, we abandon the theory in favor of new explanation. However, even this point does not completely reflect the point we are making from statistical thinking. One of the more challenging concepts for new statistics students to understand is that outcomes of a doctor’s diagnosis or of an experiment are associated with probability.
The concept of statistical power helps to relate our ability to confidently conclude one outcome over another. Statistical power depends on
- What Type I error rate we set
- The effect size or difference between affected and unaffected groups
- The sample size
- The variability of the subjects
These concepts have all been introduced before, but the idea that even a well designed experiment may lack the capability of detecting “truth” is a new and important topic to add to your growing statistical thinking tool kit.
- 11.1: What is statistical power?
- Definition of statistical power: how likely is the test to reject the null hypothesis when the alternative hypothesis is true? Discussion of the different possible outcomes of an experiment with regard to truth.
- 11.2: Prospective and retrospective power
- Prospective power analysis as a component of experimental design. Retrospective power analysis as a means of considering whether a lack of statistical significance encountered in a completed test could be merely the result of low sample size.
- 11.3: Factors influencing statistical power
- Discussion of factors that affect statistical power, including the size of alpha, variance, effect size, and sample size.
- 11.4: Two-sample effect size
- Calculating effect size, a measure of the strength of the difference between two samples. Classifying small, medium, and large effect sizes and how they should be interpreted.
- 11.5: Power analysis in R
- Steps for using R to conduct power analysis