Analysing a nominal and scale variable
Part 1: Impression of sample data
To begin analysing if there might be differences between different groups on their scores on a scale variable, we might begin by comparing some statistical measurements. Usually I'd recommend to start with a frequency table, which can still be useful, but if the range of the scale variable is very big it might not be very insightful.
The statistical measures of interest with a scale variable are usually the average (strickly speaking called the arithmetic mean) as a measure to indicate the center, and to indicate a bit about the variation the standard deviation is often reported. For example a course was given at three different locations (Diemen, Haarlem and Rotterdam), and students at each location were asked to give the course a grade (ranging from 0 to 100, with 100 being perfect). Table 1 shows the descriptive measurements across the three locations.
Click here to see how to determine these values with SPSS, R (Studio), Excel, or Python.
Three methods on how to obtain the means and standard deviation per category
using Split file
with R (Studio)
In the table we see the average (mean) per location and in total. We can see that in Diemen the students gave the course the highest average, while Haarlem and Rotterdam were close to each other. The ‘N’ column shows the number of cases (in the example students) in each group. In Haarlem there were 19, while only 13 in Rotterdam.
The last column shows something about the variation in each group, measured by something known as the standard deviation. It shows roughly how much each score was above or below the mean. A high standard deviation indicates a high variety in scores, which could indicate that people disagreed with each other, or that something is very unstable. In the example in Rotterdam students seem to disagree the most with each other, while in Diemen students tended to agree the most.
It can also be good to visualise the results, which will be the topic for the next page.
Nominal vs Scale