Analysing a binary vs. scale variable
Impression of data: Mean and Standard Deviation
To begin analysing if there might be differences between two groups on their scores on a scale variable, we might begin by comparing some statistical measurements. Usually I'd recommend starting 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. Therefor I’d suggest to look at some statistical measurements.
The statistical measures of interest with a scale variable are usually the average (strictly 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 and students were asked to give the course a grade (ranging from 0 to 100, with 100 being perfect). Table 1 shows the descriptive measurements for male, female and the total students.
| Gender | M | SD | n |
|---|---|---|---|
Female |
54 |
26 |
12 |
Male |
60 |
19 |
34 |
Total |
58 |
21 |
46 |
Click here to see how to determine these values with SPSS, with R (Studio), with Excel, or with Python.
with SPSS
Three methods on how to obtain the means and standard deviation per category
using Means
using Explore
using Split file
with R (Studio)
with Excel
with Python
From Table 1 we can see that the male students gave the course on average a 60, which is higher than the female students who gave it on average a 54. The standard deviation of 19 of the male students grades, is lower than the one for the female students with 26. More information about the mean and standard deviation can be found here. Note that in APA style, the M for Mean, SD for Standard Deviation, and n for count are acceptable abbreviations.
Before we go and look if the difference is also significant, we might want to visualise the results. This will be discussed in the next section.
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