Non- parametric Statistics

Non-parametric tests are used to test significance in nominal and ordinal variables. The advantages of these tests is that simpler assumptions may be made about the data. Also smaller sample sizes may be used.

SPSS includes the following non-parametric tests:

Chi Square

This goodness-of-fit test compares the observed and expected frequencies in each category to test either that all categories contain the same proportion of values or that each category contains a user-specified proportion of values.

Examples. The chi-square test could be used to determine if a bag of jelly beans contains equal proportions of blue, brown, green, orange, red, and yellow candies. You could also test to see if a bag of jelly beans contains 5% blue, 30% brown, 10% green, 20% orange, 15% red, and 15% yellow candies.

Statistics. Mean, standard deviation, minimum, maximum, and quartiles. The number and the percentage of nonmissing and missing cases, the number of cases observed and expected for each category, residuals, and the chi-square statistic.

One-Sample Kolmogorov-Smirnov Test

The One-Sample Kolmogorov-Smirnov Test procedure compares the observed cumulative distribution function for a variable with a specified theoretical distribution, which may be normal, uniform, Poisson, or exponential. The Kolmogorov-Smirnov Z is computed from the largest difference (in absolute value) between the observed and theoretical cumulative distribution functions. This goodness-of-fit test tests whether the observations could reasonably have come from the specified distribution.

Example. Many parametric tests require normally distributed variables. The one-sample Kolmogorov-Smirnov test can be used to test that a variable, say income, is normally distributed.

Statistics. Mean, standard deviation, minimum, maximum, number of nonmissing cases, and quartiles.

Runs Test

The Runs Test procedure tests whether the order of occurrence of two values of a variable is random. A run is a sequence of like observations. A sample with too many or too few runs suggests that the sample is not random.

Examples. Suppose that 20 people are polled to find out if they would purchase a product. The assumed randomness of the sample would be seriously questioned if all 20 people were of the same gender. The runs test can be used to determine if the sample was drawn at random.

Statistics. Mean, standard deviation, minimum, maximum, number of nonmissing cases, and quartiles.

Non-parametric tests of Correlation

Rank order correlation coefficients are used on ordinal data. Spearman's Rho is the available statistic for this type of test.