# Degrees of freedom for a t ratio?

summary.glm() does not print degrees of freedom along side the t (or z) ratios. In many published studies, t ratios are reported with their p-values, but no DF. It seems to me that one should still give DF for t-ratios (as you would for a t-statistic).

Should DF be given along with t ratios? If so, how can you find the appropriate DF for each t ratio in a glm with multiple predictors and an interaction?

• What is a t ratio? Do you mean the t-statistic? – AdamO Oct 25 '18 at 16:03
• Since they are the same for each coefficient it would just take up valuable screen real estate. Try doing 2 * pt(,insert value of t here>, <insert value of residual df here>, lower.tail = FALSE) and compare with the glm output. – mdewey Oct 25 '18 at 16:07
• stats.stackexchange.com/questions/373629/… – Glen_b Oct 26 '18 at 1:38

## 1 Answer

In a GLM, we don't usually use the T-distribution unless we use a quasilikelihood. See relevant question here.

Let's assume that's what you mean; a GLM with quasilikelihood (variance proportional to some function of mean). An ordinary linear regression is the most common case. The distribution that the test-statistics take under the null is the same for each parameter when ideal modeling assumptions are met: T with $$n-p$$ degrees of freedom ($$p$$ number of parameters in model).

Thus it's trivial to report this DF more than once (for each parameter as you say). Furthermore, if the reader knows how many parameters are in the model, it's trivial to report the DF at all; nevertheless, some choose to report it anyway.

Most published studies will at least let you know the $$n$$, and if it matters, they're explicit about the $$p$$, but even when not, the $$p$$-value and confidence interval are calculated from this T-distribution. At the very least, this assures the reader that appropriate control has been made for the nuissance parameter of unknown residual variance.