2. Comparative box plots
In Week 5 you looked at presenting data using box plots. If these are drawn on the same axes, they can be used to easily compare the distribution of two or more datasets.
In the following activity, you will look at a past exam paper question from the Statistics GCSE. Exam papers are an excellent source of questions to adapt and use with learners. Using the associated mark scheme is a good way to understand the key statistical points for which examiners will be looking.
Activity 5
Below is a comparative box plot question typical of that given in a GCSE exam paper.
Some researchers investigated the recall of pleasant and unpleasant memories associated with particular words. They were interested in finding out whether pleasant or unpleasant memories could be recalled more quickly.
The box plots below show the memory recall time for the participants in the study.
Figure 10 Box plots comparing memory recall time for participants in a research study (Source: Dunn, G. and Master, D. (1982) ‘Latency models: the statistical analysis of response times’, Psychological Medicine, vol. 12, pp. 659–65)The learners are asked to do the following:
‘Compare the two distributions of recall times. Give three comparisons and interpret two of your comparisons.’ (5 marks)
Answer the comparison question above and then check with the mark scheme below how many of the 5 marks your comparison would gain.
Discussion
Here is the table of comparisons and associated interpretations as it would be provided in the mark scheme. IQR means interquartile range, this measure was covered in Week 3.
| Comparison | Interpretation |
Unpleasant greatest median or Unpleasant median > pleasant median |
e.g. It takes longer to recall unpleasant memories (than pleasant memories). Pleasant memories are recalled quicker (than unpleasant memories). |
Unpleasant has the greatest IQR or Unpleasant IQR > pleasant IQR or Unpleasant has the greatest range or Unpleasant range > pleasant range
|
e.g. Recall time of unpleasant memories is less consistent (than the recall time of pleasant memories). |
Unpleasant has a positive skew Note: the skew for pleasant is undefined due to the longer box below the median and the longer upper tail or There is an outlier shown in the pleasant recall times |
e.g. Recall times of unpleasant memories is more varied above the median. In one particular case, a participant took considerably longer than most to recall a pleasant memory. |
Table 1 Example of an exam mark scheme table for comparing data presented in box plots
As you can see from the table above, the expectation is that learners compare a measure of location, a measure of dispersion and describe the shape of the distribution or comment on the outlier. This is common for comparisons of datasets in statistics assessments. Here is how the marks may be awarded.
- Correct comparison of medians (1 mark)
- Correct comparison of spread (IQR or range) (1 mark)
- Correct comparison of skew/identification of outlier (1 mark)
- One correct interpretation (1 mark)
- One further correct comparison or interpretation (1 mark)
Equivalent/converse statements are allowed but the underlined words should be seen.