What are the four factors that influence statistical power? Which three of those factors are under experimenter control?

Before determining the factors that influence statistical power, let's look at its general concept.

Statistical power is the probability that the null hypothesis will be rejected when the alternative hypothesis is true. That is, the probability of not committing a type II error. In general, power is a function of the possible distributions, often determined by a parameter, under the alternative hypothesis. As the power increases, the chances of a type II error will decrease. The likelihood of a type II error is known as the false-negative rate (?). Therefore, the power is equal to 1 - beta, which is also known as sensitivity. A power analysis can be used to calculate the minimum sample size required. In addition, it can be used to calculate the minimum effect of a given sample size. This concept is also used to make comparisons between different statistical analysis procedures.

Now, the four factors that influence statistical power are the following, the last three being those under the control of the experimenter:

1- The variability of the response or standard deviation of the study. Thus, the greater the variability of the response, the more difficult it will be to detect differences between the groups that are compared.

2- The level of statistical significance used in the test. A level of statistical significance is a statement of how unlikely a result can be, if the null hypothesis is true, to be considered significant.

3- The sample size used to detect the effect. This size determines the amount of sampling related to the test result. The larger the sample size, the power will be higher.

4- The magnitude of the effect of interest in the population. It can be quantified in terms of the effect size. A greater power, greater effect.