In some of my regression models (using the
rms package), I notice a distinct difference between the result of the Wald statistics (estimated using
anova.rms) and the estimated effect size (estimated using
summary.rms) and try to consolidate this:
In most instances, there is an obvious relationship (let's assume for simplicity p<0.05 as a significance threshold - it is a bit more complicated of course): significant Wald test, significant effect and vice versa. However, in some instances, I notice that while the Wald statistics suggests no significant association between independent variable and effect, the estimated effect actually is significant (both by estimated p-value and 95% CI).
How does one interpret this? One statistic tells me that it is unlikely that there is an association, the other tells me it does.
a <- ols(ep ~ sex + bmi + age + exposure, data=df) anova(a)
Wald Statistics Response: ep Factor Chi-Square d.f. P exposure 6.43 2 0.0402
Effects Response : ep Factor Low High Effect S.E. Lower 0.95 Upper 0.95 exposure -0.56 3.5 0.08 0.03 0.02 0.14