## 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.