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

Sample Size and Statistical Power

In general, larger sample sizes have higher statistical power than smaller sample sizes. However, sample size and statistical power are affected by a number of parameters, including the magnitude of the expected effect size (size of expected difference between the groups) and the level of statistical significance adopted in the study.

ExampleQ:

A group of researchers is designing a study to investigate the role of a new diet in treating patients with mild hypertension. The researchers are using the following parameters to calculate the sample size required for the study: