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.TH RANKIND 1 "January 20, 1987" "\(co 1987 Gary Perlman" "|STAT" "UNIX User's Manual"
.SH NAME
rankind \- rank order statistics for independent samples
.SH SYNOPSIS
.B rankind
[-pry] [-w plotwidth] [-s splitter] [names]
.SH DESCRIPTION
.I 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.
.PP
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.
.SS "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.
.SS Ties
A correction for ties is applied to the Kruskal-Wallis
and Mann-Whitney statistics according to Siegel's suggestions.
.SH OPTIONS
.de OP
.TP
.B -\\$1 \\$2
..
.OP p
Show a plot of each condition's scores.
The plots look like:
.nf
	<    ----------#----------------        >
.fi
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).
.OP r
Request a report of average ranks for conditions.
.OP s splitter
Scores from different conditions are separated by a special splitter value.
By default, this value is -1.
.OP w plotwidth
By default, the plotwidth is 60 characters.
.OP 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.
.br
.if t .ne 2i
.SH EXAMPLE
.PP
The following data are from Siegel, page 122.
An analysis that includes a plot and names the conditions "absent"
and "present" follows.
.nf
	> 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
.fi
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.
.SH LIMITS
Use the -L option to determine the program limits.
.SH "MISSING VALUES
Missing data values (NA) are counted but not included in the analysis.
.SH "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.
.sp
Siegel, S. (1956)
.ul
Nonparametric Statistics for the Behavioral Sciences.
New York: McGraw-Hill.
.SH 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.
.ig
             N      Min      25%   Median      75%      Max
Cond-1      23     6.00    10.25    12.00    14.00    17.00
Cond-2      16     6.00     7.00     8.50    10.00    13.00
Total       39     6.00     8.00    11.00    13.00    17.00

Median-Test:
	Fisher Exact One-Tailed Probability     0.001863
	Fisher Exact Other-Tail Probability     0.000687
	Fisher Exact Two-Tailed Probability     0.002550
	       Cond-1 Cond-2 
	above      15      3     18 
	below       6     13     19 
	           21     16     37 
	NOTE: Yates' correction for continuity applied
	chisq       8.089001     df   1      p  0.004453

Mann-Whitney U:
	U                                     304.000000
	U'                                     64.000000
	z(U) (corrected for ties)               3.438576
	One tailed p(z(U))                      0.000292

Kruskal-Wallis:
	H (not corrected for ties)             11.739130
	Tie correction factor                   0.985729
	H (corrected for ties)                 11.909088
	chisq      11.909088     df   1      p  0.000559
..
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