RANKREL(1)                         |STAT                   January 20, 1987

NAME
     rankrel - rank order statistics for related samples

SYNOPSIS
     rankrel [-ry] [-c maxcases] [names]

DESCRIPTION
     _r_a_n_k_r_e_l analyses data from ordinally ranked data obtained from
     related/matched samples.  The input consists of scores from several
     samples, conditions, or groups.  Each condition's data are in a
     separate column.  The scores need not be ranks; they will be ranked by
     the program.  For each condition, the number of scores, extrema and
     quartiles are reported.  Conditions are compared for equality of
     location using the sign test, the Wilcoxon signed-ranks test, and the
     Friedman two-way analysis of variance of ranks.  A matrix of Spearman
     rank-order correlation coefficients (rho) is printed.

     The sign test and the Wilcoxon test are only used when there are two
     conditions.  When there are fewer than 25 paired cases that are
     different, the exact binomial probability is computed; for larger N,
     the normal approximation is used.

     Probability of Obtained Statistics
     Functions computing exact probabilities of Wilcoxon and Friedman 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.

OPTIONS
     -c maxcases
          Set the maximum number of input cases.  Use the -L option to see
          the default.

     -r   Request a report of average ranks for conditions.

     -s   Stop significance tests from printing.  This option is useful
          when the Spearman rho values are of primary interest.

     -y   When computing the normal approximation for the probability of
          the Wilcoxon test, 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 79.  The command names the
     conditions "school" and "home."
          > rankrel school home
          82   63
          69   42
          73   74
          43   37
          58   51
          56   43
          76   80
          65   62

     sign test: 0.144531 (one-tailed)
     Wilcoxon T = 4, N = 8
          p approximated with z: .026892 (one-tailed)
          tabled critical value for T for one-tailed p = .025: 4
     Friedman R = 2
     Spearman Rank Correlation (rho) = .786

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

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

SEE ALSO
     pair(1), regress(1), and anova(1) perform the normal-theory parametric
     counterparts to this non-parametric, distribution-free analysis.  To
     see a scatterplot of ranks, the ranksort(1) filter can be used as a
     pre-processor for the pair(1) plotting option.  rankind(1) analyses
     ordinal data for independent 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.
