.TH RANKREL 1 "January 20, 1987" "\(co 1987 Gary Perlman" "|STAT" "UNIX User's Manual"
.SH NAME
rankrel \- rank order statistics for related samples
.SH SYNOPSIS
.B rankrel
[-ry] [-c maxcases] [names]
.SH DESCRIPTION
.I rankrel
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.
.PP
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.
.SS "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.
.SH OPTIONS
.de OP
.TP
.B -\\$1 \\$2
..
.OP c maxcases
Set the maximum number of input cases.
Use the -L option to see the default.
.OP r
Request a report of average ranks for conditions.
.OP s
Stop significance tests from printing.
This option is useful when the Spearman rho values are of primary interest.
.OP 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.
.br
.if t .ne 2i
.SH EXAMPLE
.PP
The following data are from Siegel, page 79.
The command names the conditions "school" and "home."
.nf
	> rankrel school home
	82	63
	69	42
	73	74
	43	37
	58	51
	56	43
	76	80
	65	62
.if n .sp
.if t .sp 6p
.ta .5i +.5i
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
.fi
.SH LIMITS
Use the -L option to determine the program limits.
.SH "MISSING VALUES
Cases with missing data values (NA) are counted but not included in the analysis.
.SH "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.
.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
school       8    43.00    57.00    67.00    74.50    82.00
home         8    37.00    42.50    56.50    68.50    80.00
Total       16    37.00    47.00    62.50    73.50    82.00

Binomial Sign Test:
	Number of cases school is above home:   6
	Number of cases school is below home:   2
	One-tailed probability (exact)          0.144531

Wilcoxon Matched-Pairs Signed-Ranks Test:
    Comparison of school and home
	T                                       4.000000
	N (number of differences)               8.000000
	z                                       1.928571
	One-tailed probability                  0.026892
	NOTE: Yates' correction for continuity applied
	Check a table for T with N = 8

Friedman Chi-Square Test for Ranks:
	Chi-square of ranks                     2.000000
	chisq       2.000000     df   1      p  0.157299
	Check a table for Friedman with N = 8

Spearman Rank Correlation (rho) [corrected for ties]:
	Check a table for Spearman rho with N = 8
  school     home 
            0.786 school
   0.786          home
..