8.1 Quick revision
We recommend trying these Quick revision questions before your tutorial.
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 |
---|---|---|---|---|
Coeliac | 23 | 8.39 | 4.4 | 0.92 |
Non-coeliac | 23 | 8.17 | 4.1 | 0.86 |
Difference | 0.22 | 1.3 |
An exact 95% CI is given as for the difference is \(-2.32\) to \(2.76\).
- Using the 68--95--99.7 rule gives a slightly different CI.
Why?
- The difference is computed as 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:
- The researchers used an exact 95%CI, which gives very similar answers to using an approximate 95% CI. (The 68--95--99.7 rule gives approximate multipliers only.)
- 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.
References
Khalaf ME, Akbar A, Alkhubaizi Q, Qudeimat M. Caries among adult patients with controlled celiac disease: A cross-sectional study. Special Care in Dentistry. Wiley Online Library; 2020;40(5):457–63.