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.
