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Purpose
This procedure compares
multiple independent samples. It runs Friedman ANOVA and calculates Kendall
Concordance.
These two tests are somewhat different in nature, however, they
require similar user input. Friedman ANOVA is a nonparametric alternative to
one-way repeated measures analysis of variance. The Kendall concordance
statistic is similar to Spearman R (nonparametric correlation between two
variables) except that it expresses the relationship between multiple cases.
Preparations
Run Statistics→Nonparametric
Statistics →Comparing multiple dependent samples.... command.
Results
Friedman ANOVA.
The Friedman ANOVA by ranks test assumes that the variables (levels) under
consideration were measured on at least an ordinal (rank order) scale. The null
hypothesis for the procedure is that the different columns of data (i.e.
variables) contain samples drawn from the same population, or specifically,
populations with identical medians. Thus, the interpretation of results from
this procedure is similar to that of a repeated measures ANOVA.
Kendall concordance.
The Kendall
concordance coefficient expresses the simultaneous association (relatedness)
between k sets of rankings (i.e., cases; correlated samples). For example, this
statistic is commonly used to assess inter-judge reliability. Basically, the
concordance coefficient is the average of all Spearman Rs between cases;
specifically:
average Spearman R = (k * concordance -1) / (k-1)
Thus the general assumptions of this test are identical to
that of the Spearman rank order correlation.
The range of Kendall concordance is from 0 to +1. Values
close to zero represent lack of agreement in the rankings of the variables
(e.g., objects) among cases (e.g., judges), while values close to 1 represent
perfect agreement in the rankings of the variables (objects) among cases
(judges).
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