31.6 Conclusions

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 ( $χ^{2} = 6.934$ ; 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 (‘ $χ^{2} = 6.934$ ; 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.