Results
Descriptive Statistics
From table below it is clear that Sussex students scored higher on both their JASP exam and the numeracy test than their Duncetown counterparts. Looking at the means, on average Sussex students scored an amazing 36% more on the JASP exam than Duncetown students, and had higher numeracy scores too (what can I say, my students are the best).
| Valid | Missing | Mean | Std. Deviation | Minimum | Maximum | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| exam | Duncetown University | 50 | 0 | 40.180 | 12.589 | 15.000 | 66.000 | ||||||||
| exam | Sussex University | 50 | 0 | 76.020 | 10.205 | 56.000 | 99.000 | ||||||||
| numeracy | Duncetown University | 50 | 0 | 4.120 | 2.067 | 1.000 | 9.000 | ||||||||
| numeracy | Sussex University | 50 | 0 | 5.580 | 3.071 | 1.000 | 14.000 | ||||||||
Distribution Plots
The histograms of these variables split according to the university attended show numerous things. The first interesting thing to note is that for exam marks, the distributions are both fairly normal. This seems odd because the overall distribution was bimodal. However, it starts to make sense when you consider that for Duncetown the distribution is centred around a mark of about 40%, but for Sussex the distribution is centred around a mark of about 76%. This illustrates how important it is to look at distributions within groups. If we were interested in comparing Duncetown to Sussex it wouldn't matter that overall the distribution of scores was bimodal; all that's important is that residuals within each group are from a normal distribution, and in this case it appears to be true. When the two samples are combined, these two normal distributions create a bimodal one (one of the modes being around the centre of the Duncetown distribution, and the other being around the centre of the Sussex data).
For numeracy scores, the distribution is slightly positively skewed (there is a larger concentration at the lower end of scores) in both the Duncetown and Sussex groups. Therefore, the overall positive skew observed before is due to the mixture of universities.
exam
Duncetown University
Sussex University
numeracy
Duncetown University
Sussex University
