In hypothesis tests, analysts are usually concerned with the values of parameters, such as means or variances. To undertake such tests, analysts have had to make assumptions about the distribution of the population underlying the sample from which test statistics are derived. Given either of these qualities, the tests can be described as parametric tests.

All hypotheses tests that have been considered in this section are parametric tests.

For example, an F-test relies on two assumptions:

• Populations 1 and 2 are normally distributed.
• Two random samples drawn from these populations are independent.

The F-test is concerned with the difference between the variance of the two populations. Variance is a parameter of a normal distribution. Therefore, the F-test is a parametric test.

There are other types of hypothesis tests, which may not involve a population parameter or much in the way of assumptions about the population distribution underlying a parameter. Such tests are nonparametric tests.

Nonparametric tests have different characteristics:

• They are concerned with quantities other than parameters of distributions.
• They can be used when the assumptions of parametric tests do not hold for the particular data under consideration.
• They make minimal assumptions about the population from which the sample comes. A common example is the situation in which an underlying population is not normally distributed. Other tests, such as a median test or the sign test, can be used in place of t-tests for means and paired comparisons, respectively.

Nonparametric tests are normally used in three cases:

• When the distribution of the data to be analyzed indicates or suggests that a parametric test is not appropriate.
• When the data are ordinal or ranked, as parametric tests normally require the data to be interval or ratio. One might be ranking the performance of investment managers; such rankings do not lend themselves to parametric tests because of their scale.
• When a test does not involve a parameter. For instance, in evaluating whether or not an investment manager has had a statistically significant record of consecutive successes, a nonparametric runs test might be employed. Another example: if you want to test whether a sample is randomly selected, a nonparametric test should be used.

In general, parametric tests are preferred where they are applicable. They have stricter assumptions that, when met, allow for stronger conclusions. However, nonparametric tests have broader applicability and, while not as precise, do add to your understanding of phenomena, particularly when no parametric tests can be effectively used.