Column Comparisons

Column Comparisons use column letters to indicate which columns are significantly different from which other columns within a row of a table.

Worked example

As shown in the first row of the table below, 65% of people aged 18 to 24 preferred Coca-Cola, compared to 41% of people aged 25 to 29, 55% of people aged 30 to 39, etc. One approach to conducting significance tests on this table is, for each row, to compare the percentages of all possible pairs of columns. That is, test to see if the 18 to 24 year olds preference for Coca-Cola is different from the preference of people aged 25 to 29, is different to the people aged 30 to 39, and so on.

The table below shows P-Values computed between each of the columns' percentages in the first row. The p-values are bold where they are less than or equal to the significance level cut-off of 0.05. Each column's age category has been assigned a letter and the significant pairs of columns are A-B, A-D, A-F, A-G, C-D, and C-F. If we use greater than and less than signs to indicate which values are higher, we have: A>B, A>D, A>F, A>G, C>D, and C>F.

Although the six pairs are all significant at the 0.05 level, some have much lower p-values than others. If we use upper-case letters to indicate results significant at the 0.05 level and lower-case to indicate results significant at the 0.001 level we get: a>b, A>D, a>f, a>g, c>d, and c>f. (Often commercial studies use upper case for significant at the 0.05 level and lower case for significant at the 0.10 level.)

The table below places the letters indicating significance onto the table. Letters are only shown beneath the higher of the comparisons. Thus, only the 18 to 24 and 30 to 39 categories have letters for Coca-Cola. Tests have been shown for all the rows on the table.

This approach is sometimes referred to as pairwise comparisons, post hoc testing and multiple comparisons.