Graphs such as these can help you estimate the impact of various conditions on your experimental design. For example, there appears to be little bang for the buck in increasing the sample size above 200 observations per group. We’ll look at another plotting example in the next section.

10.3 Creating power analysis plots

Before leaving the pwr package, let’s look at a more involved graphing example. Suppose you’d like to see the sample size necessary to declare a correlation coefficient statistically significant for a range of effect sizes and power levels. You can use the pwr.r.test() function and for loops to accomplish this task, as shown in the following listing.

Listing 10.2 Sample-size curves for detecting correlations of various sizes

Listing 10.2 uses the seq function to generate a range of effect sizes r (correlation coefficients under H1) and power levels p b. It then uses two for loops to cycle

associations with observable traits. For example, these studies would focus on why some people get a specific type of heart disease.

Table 10.4 Specialized power-analysis packages

Finally, the MBESS package contains a wide range of functions that can be used for various forms of power analysis and sample size determination. The functions are particularly relevant for researchers in the behavioral, educational, and social sciences.

10.5 Summary

In chapters 7, 8, and 9, we explored a wide range of R functions for statistical hypothesis testing. In this chapter, we focused on the planning stages of such research. Power analysis helps you to determine the sample sizes needed to discern an effect of a given size with a given degree of confidence. It can also tell you the probability of detecting such an effect for a given sample size. You can directly see the tradeoff between limiting the likelihood of wrongly declaring an effect significant (a Type I error) with the likelihood of rightly identifying a real effect (power).

The bulk of this chapter has focused on the use of functions provided by the pwr package. These functions can be used to carry out power and sample-size determinations for common statistical methods (including t-tests, chi-square tests, and tests of proportions, ANOVA, and regression). Pointers to more specialized methods were provided in the final section.

Power analysis is typically an interactive process. The investigator varies the parameters of sample size, effect size, desired significance level, and desired power to observe their impact on each other. The results are used to plan studies that are more likely to yield meaningful results. Information from past research (particularly regarding effect sizes) can be used to design more effective and efficient future research.

An important side benefit of power analysis is the shift that it encourages, away from a singular focus on binary hypothesis testing (that is, does an effect exist or not), toward an appreciation of the size of the effect under consideration. Journal editors are increasingly requiring authors to include effect sizes as well as p values when reporting research results. This helps you to determine both the practical implications of the research and provides you with information that can be used to plan future studies.

In the next chapter, we’ll look at additional and novel ways to visualize multivariate relationships. These graphic methods can complement and enhance the analytic methods that we’ve discussed so far and prepare you for the advanced methods covered in part 3.