# Solution to MCQ Self Test 1

## Marking

1. FTTTF 2. TFFTF 3. TFTTF 4. FFTFT
5. FTFTF 6. FFTFF 7. FTFTF 8. FTFFT

Score +1 for a correct answer, −1 for an incorrect answer, and 0 if you did not answer. You can rate your performance as follows:- below 15: work much harder, 15-19: work harder, 20-24: adequate, 25-24: good, 30-34: excellent, 35 or more: take over the class.

## Notes on the questions

1. (a) this would be random sampling (b) prevents bias in recruitment, e.g. not recruiting a poor prognosis patient who will be allocated to placebo (c) we can use probability, significance tests etc., because the two groups are samples from the same populations (d) they should be similar, the only differences being those due to chance (e) their own characteristics should not influence the choice of treatment.

2. A qualitative variable is one where individuals are divided into separate groups, without any numerical relationship. Parity is a discrete quantitative variable, diastolic blood pressure and height are continuous.

3. A continuous variable is one where all values over some range are possible. Age last birthday is a whole number of years, family size is a whole number of people, they are both discrete.

4. (a) less (b) modality and skewness are not related (c) that is what `skew to the right' means (d) depends only on whether the variance is greater than one (e) because the median is less than the mean.

5. (a) "significant" does not mean "important", hundreds of drugs would do this (b) this is what the test means (c) all we know is that it is better than nothing (d) only with a probability of 0.002, which is very small (e) this is the significance level. We do not know what the magnitude of the difference is.

6. (a) it might be as good as the standard, or even better (b) failing to show that there is a difference does not show that there isn't one (c) this is what the test means (d) depends on the sample size. We would need a confidence interval to answer this (e) see b

7. (a) The patients know whether they are at home. (b) Written informed consent should be obtained whenever possible and it is certainly possible here (c) the confidence interval does not include zero so this is statistically significant (d) the standard deviation is zero, so they must all equal the mean (e) we can never conclude that there is no difference, only that we have not shown that there is one.

8. (a, b) the confidence interval is chosen so that the intervals from 95% of possible samples will include the population value. Another way of saying this is that before we take the sample, the probability that the confidence interval which the sample will provide will include the population value is 95%. A further sample will provide another estimate, which will be within two standard errors of the population value with probability 0.95, but which may be further than two standard errors from the estimate for the first sample. (In fact, two estimates from large samples of the same size will be up to 2 root 2 standard errors apart with probability 95%. The probability that they will be at most two standard errors apart is 84%.) (c) the difference would be zero if there were no effect (d) the difference in the sample definitely does lie between these limits, with probability one. It is the relative risk in the population which lies between them with probability 0.95 (e) the confidence interval contains the value which the relative risk would have if the null hypothesis were true.

Back to MCQ and EMI Self Test 1.