Median test
Encyclopedia
In statistics
, Mood's median test is a special case of Pearson's chi-squared test
. It is a nonparametric test that tests the null hypothesis
that the median
s of the population
s from which two samples
are drawn are identical. The data in each sample are assigned to two groups, one consisting of data whose values are higher than the median value in the two groups combined, and the other consisting of data whose values are at the median or below. A Pearson's chi-squared test is then used to determine whether the observed frequencies in each group differ from expected frequencies derived from a distribution
combining the two groups.
The test has low power
(efficiency) for moderate to large sample sizes, and is largely regarded as obsolete. The Wilcoxon–Mann–Whitney U two-sample test should be considered instead. Siegel & Castellan (1988, p. 124) suggest that there is no alternative to the median test when one or more observations are "off the scale." The relevant difference between the two tests is that the median test only considers the position of each observation relative to the overall median, whereas the Wilcoxon–Mann–Whitney test takes the ranks of each observation into account. Thus the latter test is usually the more powerful of the two.
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, Mood's median test is a special case of Pearson's chi-squared test
Pearson's chi-squared test
Pearson's chi-squared test is the best-known of several chi-squared tests – statistical procedures whose results are evaluated by reference to the chi-squared distribution. Its properties were first investigated by Karl Pearson in 1900...
. It is a nonparametric test that tests the null hypothesis
Null hypothesis
The practice of science involves formulating and testing hypotheses, assertions that are capable of being proven false using a test of observed data. The null hypothesis typically corresponds to a general or default position...
that the median
Median
In probability theory and statistics, a median is described as the numerical value separating the higher half of a sample, a population, or a probability distribution, from the lower half. The median of a finite list of numbers can be found by arranging all the observations from lowest value to...
s of the population
Statistical population
A statistical population is a set of entities concerning which statistical inferences are to be drawn, often based on a random sample taken from the population. For example, if we were interested in generalizations about crows, then we would describe the set of crows that is of interest...
s from which two samples
Sampling (statistics)
In statistics and survey methodology, sampling is concerned with the selection of a subset of individuals from within a population to estimate characteristics of the whole population....
are drawn are identical. The data in each sample are assigned to two groups, one consisting of data whose values are higher than the median value in the two groups combined, and the other consisting of data whose values are at the median or below. A Pearson's chi-squared test is then used to determine whether the observed frequencies in each group differ from expected frequencies derived from a distribution
Frequency distribution
In statistics, a frequency distribution is an arrangement of the values that one or more variables take in a sample. Each entry in the table contains the frequency or count of the occurrences of values within a particular group or interval, and in this way, the table summarizes the distribution of...
combining the two groups.
The test has low power
Statistical power
The power of a statistical test is the probability that the test will reject the null hypothesis when the null hypothesis is actually false . The power is in general a function of the possible distributions, often determined by a parameter, under the alternative hypothesis...
(efficiency) for moderate to large sample sizes, and is largely regarded as obsolete. The Wilcoxon–Mann–Whitney U two-sample test should be considered instead. Siegel & Castellan (1988, p. 124) suggest that there is no alternative to the median test when one or more observations are "off the scale." The relevant difference between the two tests is that the median test only considers the position of each observation relative to the overall median, whereas the Wilcoxon–Mann–Whitney test takes the ranks of each observation into account. Thus the latter test is usually the more powerful of the two.