Anatomy of a statistical hypothesis test

Definition

Research Question: Usually exploring a comparison, association or relationship

Level of measurement of data: Usually Categorical or Scale (Continuous)

Two possible outcomes:

Null Hypothesis (\(H_0\)): Assumes no difference, association, or relationship between the variables.
Alternative Hypothesis (\(H_1\)): Assumes a difference, association, or relationship between the variables.

P value interpretation

A decision between the two hypotheses is made by viewing the ‘p-value’ or ‘Sig-value’ in SPSS, which is the probability (or chance) of getting the collected data (or more extreme) under the assumption of the null hypothesis.

If this probability is small, \(H_0\) is rejected in favour of \(H_1\), termed a ‘statistically significant result’; otherwise ‘fail to reject \(H_0\)’, termed a ‘non-statistically significant result’.

What is ‘small’?

Conventionally, use \(p=0.05\); hence, if

\(p \le 0.05\) (‘p’ is less than or equal to 0.05’), reject \(H_0\) in favour of \(H_1\)
\(p > 0.05\) (‘p’ is greater than 0.05’), fail to reject \(H_0\) [NB Not always quite the same as ’accept \(H_0\)’]

Alternatively, interpret the p-value so that:

\(p > 0.1\) implies no evidence to reject \(H_0\)
\(0.05 < p < 0.1\) implies some weak evidence to reject \(H_0\)
\(0.01 < p < 0.05\) implies evidence to reject \(H_0\)
\(p < 0.01\) implies strong evidence to reject \(H_0\)

Always relate the outcome of the hypothesis testing back to the particular variables in the study: don’t just conclude with ‘reject the null hypothesis’.

For more resources, see sigma.coventry.ac.uk Adapted from material developed by Coventry University Creative Commons License