When Column Comparisons are displayed on a table the significance testing compares pairs of columns within each row. Column comparisons are also known as pairwise comparisons and post hocs.
Each column has been assigned a letter, A, B, C and D, shown at the bottom as the Column Names. Within each row, each column is compared with each other column. In this example, there are thus 6 pairs of comparisons within each row: A:B, A:C, A:D, B:C, B:D and C:D.
Letters are shown to indicate statistical significance. Thus, the 83% for Strongly Agree with Allows to keep in touch is shown as being significantly different to the other columns (i.e., B, C and D).
Similarly, the 12% for Disagree a little with Technology fascinating is significantly different to the 1% and 9% of columns A and c. That A is in capitals indicates that the difference is significant at the 0.001 level, whereas the lowercase c indicates a difference at the 0.05 level.
Column comparisons with banners and spans
If a table contains Spans, the pairwise testing is conducted within the lowest span level. In the table below, the gender categories are compared and the age categories are compared, but age is not compared with gender.
Situations where column comparisons are not computed
It is not always possible to conduct a pairwise comparison and dashes are used when this is the case. If we look at the bottom row, dashes are shown for all the comparisons, indicating that a test has not been performed.
There are a variety of situations where pairwise tests will not be computed:
- If the user has turned off specific comparisons (see How to Specify Columns to be Compared in a Table).
- If the sample size is 0.
- If the sample size for one of the columns is less than the specified Minimal sample size for testing (as set in Statistical Assumptions).
- If percentages are being compared and both are either 0% or both are 100%.
- If the column category is a net of other columns shown on the table and the NET has been created by dragging and dropping on the table (as opposed to being a constructed variable).
Situations where column comparisons are not available
It is not possible to turn on the Column Comparisons when:
- The table has a single column.
- The table has a Numeric - Multi variable set selected in the table columns. Displayr does not perform pairwise comparisons between numeric variables when they are used in a crosstab. See How to Conduct Column Comparisons Between Variables in a Numeric - Multi Variable Set for an alternative approach.
- The table has a two-dimensional question (Binary - Grid, Numeric - Grid, or Nominal - Multi) in the table columns.
- The table shows a Ranking or Experiment variable set in the table columns.
Contradictory results between column comparisons and other tests
There is no reason to expect that column comparisons and other statistical tests (e.g., those indicated with Arrows) will give the same results, as:
- The tests have different null hypotheses and samples (i.e., the default tests involve Testing the Complement of a Cell, which has a large sample size).
- Multiple Comparison Corrections can have a bigger impact upon Column Comparisons (because comparing columns involves a greater number of comparisons).
- Different statistical tests can be selected for column comparisons than for other tests (see Statistical Assumptions).