CHAPTER 3 Getting Statistical: A Short Review of Basic Statistics 47

This inverse relationship between sample size and effect size takes on a very

simple mathematical form (at least to a good approximation): The required

sample size is inversely proportional to the square of the effect size that can

be detected. Or, equivalently, the detectable effect size is inversely propor-

tional to the square root of the sample size. So, quadrupling your sample size

allows you to detect effect sizes only one-half as large.

How to do power calculations

Power calculations can be an important step in the design of a research study

because they estimate how many individuals you will need in your sample to

achieve the objectives of your study. You don’t want your study to be underpow-

ered, because then it will have a high risk of missing real effects. You also don’t

want your study to be overpowered, because then it’s larger, costlier, and more

time-consuming than necessary. You need to include a power/sample-size calcu-

lation for research proposals submitted for funding and for any protocol you sub-

mit to a human research ethical review board for approval. You can perform power

calculations using several different methods:»

» ^{Computer software: The larger statistics packages such as SPSS, SAS, and R}

enable you to perform a wide range of power calculations. Chapter 4

describes these different packages. There are also programs specially

designed for conducting power calculations, such as PS and G*Power, which

are described in Chapter 4.»

» ^{Web pages: Many of the more common power calculations can be performed}

online using web-based calculators. An example of one of these is here:

https://clincalc.com/stats/samplesize.aspx.»

» ^{Rules of thumb: Some approximate sample-size calculations are simple}

enough to do on a scrap of paper or even in your head! You find some of

these in Chapter 25.

Going Outside the Norm with

Nonparametric Statistics

All statistical tests are derived on the basis of some assumptions about your data.

Most of the classical significance tests, including Student t tests, analysis of var-

iance (ANOVA), and regression tests, assume that your data are distributed

according to some classical sampling distribution, which is also called a frequency

distribution. Most tests assume your data has a normal distribution (see