# How to interpret effect significance and effect size of Categories in Logistic Regression?

This is a follow up to this question on this site.

Let's say I'm doing a Logistic Regression with 2 Independent Variables (IVs). One IV is ordinal and named AGE, and the other is categorical and named SERVICE with 3 categories: A, B and C.

Let's say I get the following result:

Scenario 1:

Analysis of Deviance Table (Type II tests)
Df   Chisq Pr(>Chisq)
AGEP                1 1154.18  < 2.2e-16 ***
as.factor(SERVICE)  4  450.12  < 2.2e-16 ***

Coefficients:
Estimate  Std. Error z value Pr(>|z|)
(Intercept)                1.1     5.974e-02  -1.748 0458 ***
AGE                        1.2     1.038e-03 -33.973  < 2e-16 ***
as.factor(SERVICE)B        1.3     3.572e-02   5.175 2.27e-07 ***
as.factor(SERVICE)C        1.4     3.448e-02  -1.515 0.129877

(note: *** indicates significant p-value at some desired level)


Here's how I think one would interpret the results of the SERVICE variable:

• Being in the category A is a significant predictor of the outcome, with an effect size of 1.1 on the log of the odds ratio.
• Being in the category B is a significant predictor of the outcome, and is significantly different than being in category A, with an effect size of 1.3 on the log of the odds ratio.
• Being in the category C is not significantly different than being in category A (in its effect on the outcome).

Question 1: Is the above interpretation correct (for the SERVICE variable)?

Scenario 2:

Let's say I get the following result:

Analysis of Deviance Table (Type II tests)
Df   Chisq Pr(>Chisq)
AGEP                1 1154.18  < 2.2e-16 ***
as.factor(SERVICE)  4  450.12  < 2.2e-16 ***

Coefficients:
Estimate  Std. Error z value Pr(>|z|)
(Intercept)                1.1     5.974e-02  -1.748 0.20458
AGE                        1.2     1.038e-03 -33.973  < 2e-16 ***
as.factor(SERVICE)B        1.3     3.572e-02   5.175 2.27e-07 ***
as.factor(SERVICE)C        1.4     3.448e-02  -1.515 0.129877


Notice that Intercept is no longer significant.

Here's how I think one would interpret the results of the SERVICE variable:

• Being in the category A is not a significant predictor of the outcome.
• Being in the category B is a significant predictor of the outcome, with an effect size of 1.3 on the log of the odds ratio.
• Being in the category C is not a significant predictor of the outcome.

Question 2: Is the above interpretation correct (for the SERVICE variable)?

• I don't think you should say "Being in the category A is not a significant predictor of the outcome." It's A vs B (or C) changes the probability of the outcome. – Jeremy Miles Nov 19 '16 at 0:41
• This all looks terminally weird to me. how do the significance levels change when the p-values are the same? and why are the z not the result of the obvious divisions? – mdewey Nov 19 '16 at 21:18
• You don't know about the significance of the difference between B and C, without running the model again with a different reference category. Read up on dummy variables. – Jeremy Miles Nov 19 '16 at 21:30
• (Why does service have 8 df?) – Jeremy Miles Nov 19 '16 at 21:30
• @mdewey Good catch. It was a contrived example. I changed the p-value to be something appropriate to non-significance. – thanks_in_advance Nov 19 '16 at 21:33