They are qualitative data that can be coded into numerical values. In other words, categorical data are quantifiable qualitative data. We may perform statistical analysis on categorical data but not on non-quantifiable qualitative data.
In a study that examined the perception of nursing as a career in Hong Kong high school students, students were asked to rate their agreement on a number of statements, e.g., "Willing to work in a hospital as a nurse". The response scale used is
Totally disagree, Disagree, Agree, and Totally agree.
Note the scale can be coded numerically, e.g., 0=Totally disagree, 1=Disagree, 2=Agree, and 3=Totally agree. Thus, the data measured on this scale are categorical data. Additionally, the scale is also ordinal as we can rank subjects according to their responses on this scale.
In the same study as in Example 1, students were also asked for their gender and whether they studied biology. These are also categorical data but they are not ordinal this time.