# Example exam questions

Formulae necessary for answering these questions can be found at the bottom of the page.

#### Question 1

**(a)** Give four factors in a study which might make a
sample size smaller.

(24 marks)

**(b)** A new toothpaste additive has been developed to
reduce plaque levels. You have been asked to design a study comparing a
toothpaste with the additive to one without it. The patients will come from
two randomly selected groups. Plaque scores will be measured on a continuous
scale of 0 to 5 and you can assume they are normally distributed

The difference in plaque score you want to detect is 0·4, the standard deviation of the plaque scores is 0·8. A t test will be carried out at a significance level, α, of 5% and you want to have 90% power.

How many patients will you need?

(30 marks)

**(c)** What is bias? Suggest some methods we might use to
avoid bias in a clinical study

(46 marks)

#### Question 2

**(a)** The following table shows how two dentists
categorised patients into those having bad halitosis and those who did
not.

How well do the two dentists agree in their diagnosis?

(30 marks)

Dentist 2 | ||||

Halitosis | Healthy | Total | ||

Dentist 1 | Halitosis | 15 | 12 | 27 |

Healthy | 8 | 65 | 73 | |

Total | 23 | 77 | 100 |

**(b)** A new treatment has been developed which claims to
prevent halitosis. 100 halitosis sufferers were divided randomly into two
groups. 50 patients received the new treatment and 50 patients received a
placebo. At the end of the trial (four weeks) they were examined by
dentist 1 to see if they had halitosis. The results were analysed using
a χ^{2} test and there was found to be a significant association
between the new treatment and lack of bad breath
(P = 0·002). (The treatment group had less halitosis
sufferers).

Does this result prove that new treatment prevents halitosis? (Explain your answer)

(40 marks)

**(c)** Would it have been better to examine the patients
once a week and analyse the 250 measurements for each group by a
χ^{2} test? Why?

(30 marks)

#### Question 3

A researcher is investigating the effectiveness of a dental health education program for patients will moderate to severe dental disease. One of the aims of the program is to effect a reduction in the pocket depths of the patients who are trained in the program. Pilot data seems to suggest that smokers and non-smokers show a different response in this respect. The researcher wants to set up a study that will be able to tell her if the difference in pocket depth reductions between smokers an non-smokers is 0·25mm or more

**(a)** If the standard deviation of the reductions in
pocket depth in the pilot study was 0·75mm how many patients should
be recruited to the study? Explain any assumptions you have made and the
values of any parameters you have used.

(40 marks)

**(b)** There are four main factors that affect sample size
calculations. State what they are and what effect they have on the sample
size.

Use examples to illustrate your answer.

(30 marks)

**(c)** Each patient has a number of pockets, they do not
all have the same number of pockets. When you tell the researcher the sample
size you have calculated she says that she intends to measure that number of
pockets.

Briefly explain why this is wrong and suggest an alternative.

(30 marks)

#### Question 4

Two of the clinicians involved in the above study screen patients for admission to the study. To be admitted to the study the patients must have a level of dental disease categorised as 'moderate' or 'severe'. After examining the same 64 patients they had described them according to the table below. They stated that as they showed 75% agreement they were satisfied with their performance.

**(a)** Explain why this wrong and work out an appropriate
measure of agreement between the dentists. Very briefly, how good is their
agreement?

(45 marks)

Dentist B | ||||

No disease or low level of disease | Moderate or severe level of disease | Total | ||

Dentist A | No disease or low level of disease | 16 | 8 | 24 |

Moderate or severe level of disease |
8 | 32 | 40 | |

Total | 24 | 40 | 64 |

**(b)** When the researcher had finally sorted out all the
problems with patient recruitment she proceeded with her study and reported
the following result: "The smokers were found to have 0·23mm
less pocket reduction than the non-smokers, this result was significant
(P = 0·03758)". Briefly explain how and why the
reporting of this result should have been improved

(30 marks)

**(c)** Briefly explain the difference between bias and
confounding, suggest a possible source of both of these in the study we have
been considering.

(25 marks)

### Formulae for example exam questions

#### Calculation of kappa

κ = | (Actual proportion of agreement) - (Expected proportion of agreement) |

1 - (Expected proportion of agreement) |

#### The sample size per group when comparing means of a normally distributed outcome

n = | 2 x (Standard deviation)^{2} |
x Magic number |

(Difference in means)^{2} |

#### 'Magic numbers':

Statistical power | ||||||||

50% | 60% | 70% | 80% | 90% | 95% | 99% | ||

Significance level | 5% | 3·8 | 4·9 | 6·2 | 7·8 | 10·5 | 13·0 | 18·4 |

1% | 6·6 | 8·0 | 9·6 | 11·7 | 14·9 | 17·8 | 24·0 |