**Introduction**

**Meaning of power**

**Table 1. Type I and type II errors**

**Foundations of statistical power**

**Figure 1. The three components of power.**

**Sample size**

*via*the Internet to assist the researcher to quickly determine sample size. One of the most useful can be found on the University of Iowa web site (2): http://www.stat.uiowa.edu/črlenth/Power/index.html. The user identifies the statistic to be used, and inputs information about effect size and the program will calculate the sample size required for a particular power level. For example, suppose the researcher plans to run a study on two randomly assigned samples, one of which has received an experimental treatment and the other has not. The typical test used to test group differences is the t-test. The home screen offers a screen menu on the site with a variety of statistical tests. When the user double clicks on one of the statistics in that menu, the graphical user interface (GUI) calculator comes up on the screen (Figure 2).

**Figure 2. University of Iowa online power calculator – test calculator.**

**Figure 3. Sample size needed with power changed to 0.80.**

**Figure 4. Sample size change due to change in effect size.**

**Effect size**

*Staphylococcus aureus*. The standard drug used produces a survival rate of 60%. A new drug produces a survival rate of 62% and in a sample of 2,204 subjects the effect sizes are 0.77 and 0.79 respectively (rounded). Generally, the new drug will be much more expensive. Is a 2% change in the outcome worth millions of dollars a year more in treatment costs? If the treatment costs are the same, are the side effects different? What effect size would the researcher demand in this type of drug study if either the cost of the new drug were much higher or if it produced unpleasant or dangerous side effects? These are the kinds of questions that must be considered when the researcher selects a minimum effect size.

**Significance level**

*P*-level, of a study is typically set by scientific convention. For example, in most social science studies the significance level should be 0.05 or less. In some drug studies, the

*P*-level must be much lower than 0.05 because of governmental review requirements for effectiveness and safety. Significance represents the likelihood of a Type I error. That is, it is the likelihood that the researcher will falsely claim a significant effect has been found when there is no effect in the population (see Table 1).

*P*-level of 0.10 or even 0.20. The purpose of the higher significance level in a pilot study is to avoid abandoning what might otherwise be a promising line of research on the basis of a pilot study that finds no effect for the treatment. Given the current tendency of editors to publish reports of pilot studies, readers should always keep in mind that studies reporting an effect at the P < 0.10 or higher levels should not be applied to patient populations, or should be applied to human populations only with the utmost oversight and care. Such studies are likely to result in population effects very different from the effects seen in the study sample.

*P*-level was set to 0.20. With a p-level of 0.05, the same study requires a sample size of 129 in each group to achieve significance (see Figure 4).

**Figure 5. Sample size change due to change in alpha level.**