Numerical and categorical data
Most, but not all, assessment-related data are numerical. A numerical variable contains a number from each individual. A categorical variable classifies each individual into one of several groups. For example, 25 year 4 students in a class are asked to give an ending to a story whose beginning is read to them. Each student is assessed for the originality of their ending, with the following results
moderate, little-or-no, moderate, very, ...
Batches of categorical data like this can be summarised with a frequency table which displays the number of times that each distinct category apprears in the data set (the category's frequency). Frequency tables are often augmented with a column of proportions or percentages since they are easier to interpret than the raw frequencies.
Story completion
The frequency table below is based on a table published by the New Zealand National Education Monitoring Unit describing the originality of a story-completion exercise by 1440 year 4 students in 2000.
Choose the option Freq and proportion under the frequency table to see the proportion of the students of each type.
Finally, choose the option Freq and percentage to express the proportions as percentages. Although the percentages are simply 100 times the corresponding proportions, the leading zeros are suppressed so the information in the data stands out better.
Bar charts for categorical data
Although frequency tables provide easily digestible summaries of most batches of categorical data, the same information can also be displayed graphically. The simplest graphical display of categorical data is a bar chart. This is similar to a bar chart for discrete data, but the horizontal axis is a list of the possible categories rather than a numerical axis. The heights of the bars are still the frequencies or proportions for the different values.
The bar chart below again shows the originality ratings for the 1440 year 10 students in a 2000 story-completion exercise.
Clicking on any bar highlights it and the corresponding values on the frequency table.
Note that the bar chart is shown with both a frequency axis (on the left) and a proportion axis (on the right). It has the same shape whichever is used.
In the remainder of this section, we will not distinguish between discrete data where the possible values are small and categorical data — the same graphical displays can be used for both.