What is the purpose of using nonparametric tests in operations management decisions? Provide examples of what you look for when conducting these tests.
If a statistical variable understudy can be represented on a ratio or at least an interval scale of measurement, then it is said to have proper units. With some assumption made about the distribution of the variable (say normality, for example), the variable is fit to be tested parametrically. The t-test, the z-test etc are a few well-known parametric testing methods. But these tests lay different restrictions on the data.If a statistical variable is of the nominal or ordinal type only, then it does not qualify to be parametrically tested. Sometimes we may have obtained a sample which may not be a part of a well-defined population. In this case, there are no population parameters to fall back upon since the population is itself nonexistent or not well defined. Here we conduct a non-parametric test, which is essentially distribution-free. In this case, there are no requirements of normality or homogeneity in the data. This also means there can be a few outliers and their effect will be ignored.
An advantage of non-parametric tests is that sometimes, they give quick answers with little computation work. However, since these tests are non-parametric, it is difficult to quantitatively justify the observed differences.
Situations in real life where we need to apply non-parametric tests are plenty. For example, we use chi-square test to analyze the preferences people have for movies or for drinks. We use the same test to see if there is gender bias in the selection of candidates for a job. We use Wilcoxon Mann Whitney Test to analyze if square footage in three-bedroom homes is equal to that of four-bedroom homes by assigning ranks to the houses in the sample.
Presented below (for additional input only) is some information about the different parametric and non-parametric tests and their objectives:
Normal theory based test / Corresponding nonparametric test / Purpose of test
t test for independent samples / Mann-Whitney U test; Wilcoxon rank-sum test / Compares two independent samples
Paired t test / Wilcoxon matched pairs signed-rank test / Examines a set of differences
Pearson correlation coefficient / Spearman rank correlation coefficient / Assesses the linear association between two variables.
One way analysis of variance (F test) / Kruskal-Wallis analysis of variance by ranks / Compares three or more groups
Two way analysis of variance / Friedman Two way analysis of variance / Compares groups classified by two different factors