Probabilities

Question 1

Examples of designs with intrinsic non-independence

Answer 1

• Serial measures within individuals, for example, growth studies where we have regular measurements of height and weight in a group of children over time. In such cases we must take the non-independence into account when we analyse these data
• Clustered studies where individuals fall naturally into groups or clusters, such as all patients in a particular general practice where the general practice is the cluster. An example is a cluster trial where clusters of individuals are randomly allocated to treatments so that everyone in a cluster receives the same treatment. It is essential to take the ‘clustering’ into account in such studies

Question 2

Definition of probability

Answer 2

The proportion of times an event happens in the long run which can be estimated from a proportion calculated in a sample

For example, the proportion of stillbirths out of total births in England and Wales in 2006 was 3602/673 203 = 0.0054. Since this was a census and therefore a large sample, we can use this as an estimate of the probability that a baby born in England and Wales will be stillborn

Question 3

Three basic rules of probability

Answer 3

1. A probability must lie between 0 and 1 inclusive
2. If two events are mutually exclusive so that they cannot both happen, the probability of either happening is the sum of the individual probabilities
3. If two events are independent then the probability of both occurring is the product of the individual probabilities