RANKIND(1)

NAME
rankind - rank order statistics for independent samples

SYNOPSIS
rankind [-pry] [-w plotwidth] [-s splitter] [names]

DESCRIPTION
rankind analyses data from ordinally ranked data obtained from independent samples. The input consists of scores from several samples, conditions, or groups. The scores need not be ranks; they will be ranked by the program. Each group's data are separated by a special value called the splitter, which is by default -1.0, but can be changed with the -s option. For each group, the number of scores, extrema and quartiles are reported. These scores are then ranked and their medians and average ranks are tested using the median test, the Fisher Exact Test, the Mann-Whitney U test, and the Kruskal-Wallis one-way analysis of variance for ranks. These test the equality of location (e.g., median or average rank) of the conditions.

The Mann-Whitney U test and the Fisher Exact test are used only when there are two conditions. The Kruskal-Wallis H significance test tests the same hypothesis as the Mann-Whitney U. The Fisher Exact test is an exact test of the chi-square approximation of the Median test, however, it is a generally less powerful test than the Mann-Whitney or Kruskal-Wallis, both of which make more use of ordinal information in scores.

  Probability of Obtained Statistics
Functions computing probabilities of U and H could not be found when the program was written, so for small samples, statistical tables at the back of a text should be consulted. For large samples, normal and Chi-square approximations are adequate. According to Siegel's suggestions: With two conditions, a sample is large if the larger group has more than 20 values. When there are three conditions, a sample is small if all conditions have at most 5 values, and large otherwise.

  Ties
A correction for ties is applied to the Kruskal-Wallis and Mann-Whitney statistics according to Siegel's suggestions.

OPTIONS
[p] Show a plot of each condition's scores. The plots look like:
	<    ----------#----------------        >
in which the angle brackets show the extrema, the # shows the median, and the line shows the interquartile range: Q1-Q3 (the 25th percentile to the 75th percentile). [r] Request a report of average ranks for conditions. [s splitter] Scores from different conditions are separated by a special splitter value. By default, this value is -1. [w plotwidth] By default, the plotwidth is 60 characters. [y] When computing chi-square values, Yates' correction for continuity is applied. This option stops its use. There are no cases where Yates' correction should not be used, but the option is useful to check textbook examples for accuracy.

EXAMPLE

The following data are from Siegel, page 122. An analysis that includes a plot and names the conditions "absent" and "present" follows.
	> rankind -p absent present
	17 16 15 15 15 14 14 14 13 13 13 12 12 12 12 11 11 10 10 10 8 8 6
	-1
	13 12 12 10 10 10 10 9 8 8 7 7 7 7 7 6
The Fisher Exact two-tailed probability is .002550, while the chi-square approximation is 8.089 (p = .004453). The Mann-Whitney U of 304 has a probability of .000292 using a normal approximation (corrected for ties). The Kruskal-Wallis H of 11.9091 has a two-tailed probability of .000559, which is very close to twice the probability of the U test.

LIMITS
Use the -L option to determine the program limits.

MISSING VALUES
Missing data values (NA) are counted but not included in the analysis.

SEE ALSO
oneway(1) performs the normal-theory parametric counterparts to this non-parametric, distribution-free analysis. rankrel(1) analyses ordinal data for related conditions.

Siegel, S. (1956) Nonparametric Statistics for the Behavioral Sciences. New York: McGraw-Hill.

WARNING
When the program advises to check a table for exact probabilities of significance tests, it may still compute approximate values. These approximations should not be used for serious work.