Analysing a binary vs. scale variable
You might be interested if one group had a higher mean, than another group. The variable that defines the groups is then a binary variable, while the variable with the scores should be a scale variable. The analysis can be done using the following steps:
Part 1: Descriptive statistics.
Use descriptive statistics to get an impression of the data, using:
- Statistical measures. The mean for central tendency, and standard deviation for dispersion
- Visualise the data with a split histogram.
Part 2: Inferential statistics
After the first impression determine what can be said about the population based on your sample data by:
- Performing a test to see if the means in the population will be equal (Welch t-test)
- Determine how big the difference will be (effect size Cohen’s d)
The example used in this chapter will be using as a binary variable gender (which had the options male or female), and the scale variable ‘grade’, which ranged from 0 to 100.
Let's begin with the statistical measures in the next section.