6.5.3. Multisample Median Test

Data entry is in multisample format (see 6.0.4. Multisample Tests). Each sample can be entered in a separate column (not necessarily of equal length), or they can be stacked in one or more columns and subsamples defined by an unlimited number of factor columns. Missing values are omitted by case.

A further dialogue allows you to override the median computed from data and enter any values. The two output options can also be selected from the same dialogue.

6.5.3.1. Multisample Median Test Results

Like the Two Sample Median Test, this is also used to determine whether the samples have been drawn from populations with the same median. But here, the number of samples is not limited to two. The number of cases less than or equal to and greater than the overall median is found for each sample. Then the chi-square statistic is calculated from the obtained frequencies.

The one-tail probability is reported using the chi-square distribution with M - 1 degrees of freedom.

6.5.3.2. Median Multiple Comparisons

A Tukey-HSD type comparison is made between all possible pairs of groups. The value used in comparisons is the number of cases greater than the overall median for each sample (i.e. the first column of the table displayed in test results).

If the total number of cases N is an odd number the standard error is computed as:

If N is an even number, then the standard error is:

where n is the harmonic mean of group sizes.

6.5.3.3. Multisample Median Test Example

Examples 10.12 on p. 201 and 11.11 on p. 227 from Zar, J. H. (1999). The null hypothesis “median elm tree height is the same on all four sides of a building” is tested at a 95% significance level. If they are found to be different, then we would also like to know which ones.

Open NONPARM1, select Statistics 1 → Nonparametric and West (C19 to C22) in the analysis by clicking [Variable]. Check the Test Results and the Multiple Comparisons boxes to obtain the following results: