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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 IBM® SPSS® Data Collection Survey Reporter.
| Notation | Description |
|---|---|
| wo | Sum of the weights for the column. |
| wo2 | Sum of the squared weights for the column. |
| eo = (wo)2 / wo2 | Effective base for the column. |
| ci | Sum of the weights for the cell in the ithrow. |
| cj | Sum of the weights for the cell in the jth row. |
| pi = ci/wo | Column proportion in the ithrow. |
| pj = cj/wo | Column proportion in the jthrow. |
Under the null hypothesis Ho : pi = pj
the paired preference test statistic is calculated using the following expression:
The test is undefined if pi = pj = 0 or if eo < 2.
p values are computed using the t distribution with eo -1 degrees of freedom.
Kish, L (1965), Survey Sampling, New York: John Wiley and Sons. ISBN 0-471-48900-X.