Comparisons

We often want to make comparisions. Examples of things that we might want to compare are:

These comparisons are often based on a collection of values from each 'thing', arranged in a two-way table in which one dimension (often rows) corresponds to the different groups. We will restrict attention to two-way tables in which the values all describe related values. Examples are:

Terminology

Although the terminology does not perfectly fit all examples, we will call the main things being compared groups. The related values from each group will be called measurements in different categories.

   Group    Measurement    Categories   
Region Number of households Household size
Age group Number of prisoners Average length of sentence
Country Life expectancy Gender
Year Expenditure Expenditure category

Note that the values in the first two examples for a frequency table for each group.

Graphical display

A simple bar chart can be drawn to display the values in each group. However if there are many groups, it is difficult to draw them close enough to each other to effectively compare them. We will describe some other graphical displays later in this section.

Monthly average rainfall in Thailand

The table below describes the average monthly rainfall in three cities in Thailand. The cities are treated as 'groups' and the months are the categories.

  Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec   Year  
Phuket 23.3 25.8 59.0 137.8 269.8 236.9 284.1 282.8 386.5 295.9 173.7 61.9 2,237.5
Bangkok 9.0 30.0 29.0 65.0 220.0 149.0 155.0 197.0 344.0 242.0 48.0 10.0 1,498.0
Chiang Mai 7.7 9.2 19.2 54.1 153.0 117.3 153.2 224.6 200.2 118.1 51.3 18.3 1,126.2

From the annual rainfall totals, it is clear that Phuket is wetter than the other cities. The bar charts below help to compare the seasonality of rainfall in the three locations.

Initially the three bar charts are drawn above each other. Click the checkbox Arrange in a single row to rearrange the bar charts horizontally.

What are the main differences between the rainfall patterns in the three cities?