Interpreting and analysing data Statistics Interpreting and analysing data

So I conclude that drinking coffee makes peoples’ coordination worse.” Imagine an experiment to test whether drinking coffee changes the time it takes to perform a test of coordination. “The mean time to do the coordination test before drinking coffee was 36.8 s. The mean time to do the coordination test after drinking coffee was 36.9 s. So I conclude that drinking coffee makes peoples’ coordination worse.” Any comments about this conclusion? The difference is very small and there is no information about the number of times the experiment was done, whether it was with the same people, etc; encourage students to question the information, this is poorly written, don’t leave them thinking it is good!

“The mean time without the catalyst was 28.1 s. The mean time with the catalyst was 27.3 s. So I conclude that the catalyst speeds up the reaction.” You may need to tell students that a catalyst is a chemical which improves a reaction (in this example it makes it go faster). This conclusion seems more reasonable as the difference is bigger… but there are still questions to answer about the number of times it was carried out…

Significance Scenario A Scenario B Times without catalyst 28.0 28.1 28.1 28.2 Mean = 28.1 s Times with catalyst 27.1 27.2 27.4 27.5 Mean = 27.3 s Scenario B Times without catalyst 26.9 27.4 28.5 29.6 Mean = 28.1 s Times with catalyst 26.9 26.9 27.0 28.4 Mean = 27.3 s This gives much more credibility to any statement as you have more data to look at. Which scenario shows the catalyst makes a difference more clearly? Scenario A: all times are lower with a catalyst and are consistent both with and without the catalyst which shows that the addition of the catalyst is likely to have made a difference. Scenario B: most times are very similar with and without a catalyst and one which seems to be difference (29.6 and 26.9) could be a typographical error; it is not as clear that the catalyst has made a difference here as there is more variability in the data.

Being certain In maths you can be sure that some things are always true; you can prove them. ‘If you add two odd numbers you always get an even number.’ In statistics you cannot be so certain. You collect evidence from a sample, and you come to a conclusion about the population. ‘There is good evidence to suggest that the catalyst speeds up the reaction.’ ‘There is not enough evidence to suggest that coffee affects coordination.’ This is something which upsets many people about statistics – there just isn’t always (or even usually) a clear cut answer…

This is a sample presentation. The full presentation goes on to look at analysing data in a large data set.