## 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.