9.1 Quick revision
Researchers studied the impact of a gluten-free diet on dental cavities (Khalaf et al. 2020).
Some of the summary information regarding the number decayed, missing and filled teeth (DMFT) is shown below.
|Diet||Sample size||Mean||Standard deviation||Standard error|
A 95% CI is given as for the difference is -2.32 to 2.76.
- The difference is computed as the the number of DMFT for coeliacs minus non-coeliacs. True or false?
- One of the values for the CI is a negative value, which must be an error, since a negative number of DMFT is impossible. True or false?
- We are 95% confidence that the difference between the population means is:
- Both samples sizes are less than 25. What does this mean for the statistical validity of the CI?
- TRUE. If we take the coeliac mean minus the non-coeliac mean, we would have \(8.39 - 8.17 = 0.22\), which is what is given in the table.
- FALSE. The CI is for the difference in the DMFT. The value is not about the number of teeth; it is about the difference in the number of teeth between coeliacs and non-coeliacs. A negative value is fine if we understand what the CI is estimating.
- The positive value of 2.76 means (as we saw in the first Quick Revision question) that coeliacs have a mean of 2.76 more DMFT.
So the negative value of \(-2.32\) means that non-coeliacs have a mean of 2.32 more DMFT.
- The sample sizes are just less than 25, so the CI will probably be statistically valid (but we'd more certain about this if the sample sizes were 25 or more).