Exception tests on a table use colors, arrows, or some other symbol to identify which cells on a table are significantly different from the other cells.
In the table below, 65% of people aged 18 to 65 prefer Coca-Cola An exception test compares this result with all the other results shown in the same rows of the table.
The table below shows the same data as above but with counts instead of percentages. For example, the 65% preference for Coke among the 18 to 24s is computed as 28 / 43.
We can compute the preference for Coca-Cola amongst the people not aged 18 to 24 as (16+38+17+18+18+8)/(39+69+60+39+50+22) = 42%.
A significance test computes the p-value of 65% versus 42% as being 0.0001. In the same way, we can compare each of the age categories with the combined results from the other age categories. The table below shows the resulting p-values of the seven significance tests.
|18 to 24||25 to 29||30 to 39||40 to 49||50 to 54||55 to 64||55 to 64|
|Compared to combined other categories||.0033||.6500||.0443||.0055||.8151||.1928||.4313|
The table below shows the significance tests for all the cells in the table. Arrows are used to indicate results significant at the 0.05 level. The length of the arrows is determined by the p-value. Smaller p-values are represented by longer arrows. In contrast to the column comparisons shown above, this approach to representing significance is a little easier to read as the arrows provide visual cues which highlight the nature of the patterns in the data and thus draw the reader's attention to exceptions.
Exception tests on a table are also referred to as:
- Cell comparisons.
- Significant residuals.