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Statistical formula for the paired preference test
The paired preference element is usually specified as a row element to compare two rows for each column independently. However, you can specify it as a column element to compare two columns for each row independently. The following information assumes specification as a row.
The following table shows the formulae used for conducting the paired preference test in UNICOM Intelligence Professional.
Notation
Description
w o
Sum of the weights for the column.
w o 2
Sum of the squared weights for the column.
e o = (w o)2 / w o 2
Effective base for the column.
c i
Sum of the weights for the cell in the i throw.
c j
Sum of the weights for the cell in the j th row.
p i = c i/w o
Column proportion in the i throw.
p j = c j/w o
Column proportion in the j throw.
Test statistic
Under the null hypothesis:
H o : p i = p j
the paired preference test statistic is calculated by using the following expression: The test is undefined if p i = p j = 0 or if e o < 2.
p values
p values are computed using the t distribution with e o -1 degrees of freedom.
References
Kish, L (1965), Survey Sampling, New York: John Wiley and Sons. ISBN 0-471-48900-X.