Before you could perform many of the hypothesis tests you learned about in previous chapters, you had to ensure that certain conditions about the population were satisfied. For instance, before you could perform a \(t\)-test, you had to verify that the population was normally distributed or the sample size was at least 30 . One advantage of the nonparametric tests shown in this chapter is that they are distribution free. That is, they do not require any particular information about the population or populations being tested. Another advantage of nonparametric tests is that they are easier to perform than their parametric counterparts. This means that they are easier to understand and quicker to use. Nonparametric tests can often be used when data are at the nominal or ordinal level.

Stronger evidence is needed to reject a null hypothesis in a nonparametric test than in a corresponding parametric test. That is, when you are trying to support a claim represented by the alternative hypothesis, you might need a larger sample when performing a nonparametric test. When the outcome of a nonparametric test results in failure to reject the null hypothesis, you should investigate the sample size used. It may be that a larger sample will produce different results.
Test In general, when information about the population (such as the condition of normality) is known, it is more efficient to use a parametric test. When information about the population is not known, however, nonparametric tests can be helpful.

EXERCISES

1. Insufficient Evidence Give an example of a nonparametric test in which there is not enough evidence to reject the null hypothesis.

2. Using an Inappropriate Test Discuss the nonparametric tests described in this chapter and match each test with its parametric counterpart, which you studied in earlier chapters.