31.6 Conclusions: Comparing odds

As usual, a very small \(P\)-value (\(0.008\) to three decimals) means there is very strong evidence supporting \(H_1\): the evidence suggests a difference in the population odds in the two groups. We write:

The sample provides strong evidence (\(\chi^2=6.934\); two-tailed \(P=0.008\)) that the odds in the population of having most meals off-campus is different for students living with their parents (odds: 26) and students not living with their parents (odds: 4.375; OR: \(5.94\); 95% CI from \(1.35\) to \(26.1\)).

Again, as seen in Sect. 28.7, the conclusion includes three components: The answer to the RQ; the evidence used to reach that conclusion (‘\(\chi^2=6.934\); two-tailed \(P=0.008\)’); and some sample summary statistics (inclding the 95% CI for the odds ratio).

The conclusion also makes clear what the odds and the odds ratio mean. The odds are describing as the ‘odds… of having most meals off-campus,’ and the OR as then comparing these odds between ‘students living with their parents… and students not living with their parents.’

For two-way tables, RQs are best framed in terms of ORs or odds (but can be framed in terms of proportions or percentages, or associations or relationships).

For consistency: if the RQ is about the odds ratio, the hypotheses and conclusion should be about the odds ratio; if the RQ is about odds, the hypotheses and conclusion should be about the odds; and so on.