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Solution to question 3

(a)

We assume:

  1. That pocket depths are normally distributed in both groups
  2. The standard deviations in both groups are similar

This gives a 'magic number' of 7·8

m = 2 x 0·75 x 0·75 x 7·8 ÷ 0·25 ÷ 0·25

m = 140·1

m = 141 to nearest whole number

Total sample for whole study = 2 x 141 = 282

We would round up this figure to 290 or 300 to be on the safe side. We might also make explicit allowance for dropouts, if we suspect this might happen, by making the sample size even larger. The size of the increase for dropouts would normally depend on our experience with previous similar studies.

(b)

The four main factors affecting sample size are:

  1. Variability of the samples
  2. What difference do we want to detect
  3. What level of α we chose
  4. What power we choose

(c)

Pockets on the same person are not independent. Pockets measured on the same person are more likely to be similar to each other than they are to pockets on another person. To some extent we are repeatedly measuring the same quantity when we measure several pockets on the same person. If we measured 10 pockets on each of 30 patients we would, typically, see less variation than if we measured 1 pocket on each of 300 patients.

One way of dealing with this problem would be to take a summary measure for each patient, perhaps the mean pocket depth for each patient, and analyse these summary measurements.

A better, but more difficult, method of analysis would be to take some sort of modelling approach, where we could look at within patient and between patient variability at the same time.

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