C. = 1 – probability of making a type II error – Explanation

Significance tests
A null hypothesis (H0) states that two treatments are equally effective (and is hence negatively
phrased). A significance test uses the sample data to assess how likely the null hypothesis is to be
correct.
For example:
there is no difference in the prevalence of colorectal cancer in patients taking low-dose aspirin
compared to those who are not’
The alternative hypothesis (H1) is the opposite of the null hypothesis, i.e. There is a difference
between the two treatments
The p value is the probability of obtaining a result by chance at least as extreme
as the one that was actually observed, assuming that the null hypothesis is true. It is therefore equal
to the chance of making a type I error
(see below).

Two types of errors may occur when testing the null hypothesis

• type I: the null hypothesis is rejected when it is true – i.e. Showing a difference between two groups when it doesn’t exist, a false positive. This is determined against a preset significance level (termed alpha). As the significance level is determined in advance the chance of making a type I error is not affected by sample size. It is however increased if the number of end-points are increased. For example if a study has 20 end-points it is likely one of these will be reached, just by chance.
• type II: the null hypothesis is accepted when it is false – i.e. Failing to spot a difference when one really exists, a false negative. The probability of making a type II error is termed beta. It is determined by both sample size and alpha

The power of a study is the probability of (correctly) rejecting the null hypothesis when it is false,
i.e. the probability of detecting a statistically significant difference

• power = 1 – the probability of a type II error
• power can be increased by increasing the sample size