## 31.5$$P$$-values: Consistency with assumption?

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.