Modifying a frequency table

A frequency table shows the numbers and proportions of 'individuals' in various categories. There are a few ways in which such tables can be modified, either to make the information clearer or to highlight particular aspects.

Reordering categories
In some frequency tables, there is a natural ordering of the categories (e.g. strongly agree, agree, indifferent, disagree and strongly disagree). The categories should be arranged in this order in the table. If there is no natural ordering, then it often helps to arrange the categories by the frequencies, with the highest frequency first and the lowest frequency last.

Alphabetic ordering of the categories is rarely best.


Combining categories
The information in the table may be clearer if the number of categories is reduced by combining some together. For example, published tables often categorise hospital operations into 50-100 different categories. A coarser categorisation (e.g. orthopaedic, cancer, ...) gives a more easily understood overview.

The frequency for a combined category is the sum of the frequencies for the categories that are being merged. The percentages are also added.


Looking at subsets of categories
It may be useful to 'hide' some categories in the table, and look only at the distribution of the remaining categories. This corresponds to looking only at a sub-group of the individuals.

The frequencies for the categories are unchanged, but the percentages should divide them by the total for the displayed categories, so they still add to 100%.

These techniques will be clearer in an example.

Road crashes by road feature

The table below shows the number of road crashes causing injury or death in New Zealand in 2012, categorised by the type of 'road feature' at the crash site.

The 'road features' were grouped into Intersections and Non-intersections in the report and are shown in different colours in the table. However the ordering of categories within the groups in the report was not particularly meaningful. Click the two checkboxes Sort by frequency to reorder the features by their frequency of accidents within each group.

Click the checkboxes Combine categories to combine the different types of intersections and non-intersections into a frequency table with two rows. This table highlights the differences between intersections and non-intersections.

Finally, expand the categories for Intersections and click Hide categories for the Non-intersections. This shows the distribution of road features for the accidents that occurred at intersections. Note that hiding the non-intersection categories restricts attention to the accidents that occurred at intersections. The total therefore changes to the number of accidents at intersections and the percentages become percentages out of this new total.