### Definitions and Notation

In this chapter, a two-way table represents the
crosstabulation of variables X and Y.
Let the rows of the table be labeled by the
values *X*_{i}, *i* = 1, 2, ... , *R*, and the
columns by *Y*_{j}, *j* = 1, 2, ... , *C*.
Let *n*_{ij} denote the cell frequency in the
*i*th row and the *j*th column and define the following:

*Scores*

PROC FREQ uses scores for the variable values when
computing the Mantel-Haenszel chi-square, Pearson correlation,
Cochran-Armitage test for trend, weighted kappa coefficient, and
Cochran-Mantel-Haenszel statistics. The SCORES= option in the
TABLES statement specifies the score type that PROC FREQ uses.
The available score types are TABLE, RANK, RIDIT, and MODRIDIT
scores. The default score type is TABLE.
For numeric variables, table scores are the values of the
row and column levels. If the row or column variables are
formatted, then the table score is the internal numeric value
corresponding to that level. If two or more numeric values
are classified into the same formatted level, then the internal
numeric value for that level is the smallest of these values.
For character variables, table scores are defined as the row
numbers and column numbers (that is, 1 for the first row,
2 for the second row, and so on).

Rank scores, which you can use to obtain nonparametric analyses,
are defined by

Note that rank scores yield midranks for tied values.
Ridit scores (Bross 1958; Mack and Skillings 1980)
also yield nonparametric analyses, but they
are standardized by the sample size.
Ridit scores are derived from rank scores as

Modified ridit (MODRIDIT) scores (van Elteren 1960;
Lehmann 1975), which also yield nonparametric analyses,
represent the expected values of the
order statistics for the uniform distribution on (0,1).
Modified ridit scores are derived from rank scores as

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