CHAPTER 3 Getting Statistical: A Short Review of Basic Statistics 49

a sample size to be able to perceive a clear parametric distribution when you make

a histogram. Fortunately, statisticians have developed other tests that you can use

that are not based on the assumption your data are normally distributed, or have

any parametric distribution. Unsurprisingly, these are called nonparametric tests.

Most of the common classic parametric tests have nonparametric counterparts

you can use as an alternative. As you may expect, the most widely known and

commonly used nonparametric tests are those that correspond to the most widely

known and commonly used classical tests. Some of these are shown in Table 3-2.

Most nonparametric tests involve first sorting your data values, from lowest to

highest, and recording the rank of each measurement. Ranks are like class ranks

in school, where the person with the highest grade point average (GPA) is ranked

number 1, and the person with the next highest GPA is ranked number 2 and so on.

Ranking forces each individual to be separated from the next by one unit of rank.

In data, the lowest value has a rank of 1, the next highest value has a rank of 2, and

so on. All subsequent calculations are done with these ranks rather than with the

actual data values. However, using ranks instead of the actual data loses informa-

tion, so you should avoid using nonparametric tests if your data qualify for

parametric methods.

Although nonparametric tests don’t assume normality, they do make certain

assumptions about your data. For example, many nonparametric tests assume

that you don’t have any tied values in your data set (in other words, no two

­participants have exactly the same values). Most parametric tests incorporate

adjustments for the presence of ties, but this weakens the test and makes the

results less exact.

Even in descriptive statistics, the common parameters have nonparametric coun-

terparts. Although means and standard deviations can be calculated for any set of

numbers, they’re most useful for summarizing data when the numbers are nor-

mally distributed. When you don’t know how the numbers are distributed, medi-

ans and quartiles are much more useful as measures of central tendency and

dispersion (see Chapter 9 for details).

TABLE 3-2

Nonparametric Counterparts of Classic Tests

Classic Parametric Test

Nonparametric Equivalent

One-group or paired Student t test (see Chapter 11)

Wilcoxon Signed-Ranks test

Two-group Student t test (see Chapter 11)

Mann-Whitney U test

One-way ANOVA (see Chapter 11)

Kruskal-Wallis test

Pearson Correlation test (see Chapter 15)

Spearman Rank Correlation test