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RANKIND(1) |STAT January 20, 1987
NAME
rankind - rank order statistics for independent samples
SYNOPSIS
rankind [-pry] [-w plotwidth] [-s splitter] [names]
DESCRIPTION
_r_a_n_k_i_n_d 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) _N_o_n_p_a_r_a_m_e_t_r_i_c _S_t_a_t_i_s_t_i_c_s _f_o_r _t_h_e _B_e_h_a_v_i_o_r_a_l
_S_c_i_e_n_c_e_s. 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.
These are the contents of the former NiCE NeXT User Group NeXTSTEP/OpenStep software archive, currently hosted by Netfuture.ch.