# Analysing a binary vs. scale variable

## Introduction

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.

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