Many of the researchers decide to use k independent sample tests in management and economic researches when there are over three samples that are concerned. They’re also quite interested in seeking out the place the samples might come from – if they come from the same or identical populations. The analysis of variance and the F test are utilized in situations where the data are measured on an interval-ratio scale and the researchers can meet the wanted assumptions. A nonparametric test must be chosen when introductory analysis shows that the assumptions cannot be met or if the data have been measured on a nominal or ordinal scale.

The samples are approved to be independent. We take this as a condition of a totally randomized experiment when the subjects are set to specific treatment groups. The requirement of the evaluation of more than two independent sample means is also common.
The chi-square tests are very proper when there are k independent samples for which the nominal data have been collected. It can be utilized to classify the data at higher measurement levels, but after we make it smaller, the metric information is lost. The k-sample chi-square test is calculated within the same method as the two independent sample cases.

When we have an ordinal scale collected data or interval data that does not meet the F-test assumptions or for any reason is not suitable for a parametric test the researchers use the Kruskal-Wallis test. It is a one-way analysis of variance with the aid of ranks. It accepts an underlying continuous distribution as well as random selection and independence of samples.

With this test we rank all observations from the smallest to the largest.

K Related Samples Case

This test is used in situations where there are more than two levels of the grouping component, observations are matched or they are measured more than once, the data are at least interval. In experimental designs, it\’s a just right notion to measure the subjects several times. These multiple measurements are named trails.

The Cochran Q test (also a nonparametric test) is preferably used when the k related samples are measured on a nominal scale. It checks the hypothesis that the proportion of cases in one category is equal for various associated categories.

The Friedman two-way analysis of variance can also be preferable to use when the data are ordinal. It examines the matched samples, ranking every one of the cases and calculating the mean rank f