31.5 \(P\)-values: Comparing odds

The differences between the observated sample statistic (the sample OR) and the hypothesised population parameter (the population OR of one) is summarised by \(\chi^2=6.934\) (approximately equivalent to \(z=2.63\)). Using the 68–95–99.7 rule, a small \(P\)-value is expected.

The corresponding two-tailed \(P\)-value reported by jamovi (Fig. 31.1, under the p column) and SPSS (Fig. 31.2, in the Asymptotic Significance (2-sided) column and Pearson Chi-Square row) is very small (\(0.008\) to three decimals).

Recall that, for two-way tables of counts, the alternative hypotheses are always two-tailed, so a two-tailed \(P\)-value is always reported.

Click on the hotspots in the following image, to see what the SPSS output tells us.