# ANOVA with single degrees of freedom

I was running ANOVA.

Does it make sense to use a variable with 1 degree of freedom as independent variable?

• I must be missing something; any factor with two levels has 1df, and a factor with two levels is certainly suitable for an IV in ANOVA. If you're looking at one-way ANOVA, it's no different from a t-test, so you'd probably do a t-test in that specfic situation, but the ANOVA would still be valid. If this doesn't cover what you're asking about you'll need to clarify the circumstances. Commented Apr 25, 2015 at 3:23

Certainly, why not? For instance, you could have

• a grouping factor with two levels
• a numerical covariate (ANCOVA)

Here is an example with both, using R:

> foo <- data.frame(DV=rnorm(10),IV=rnorm(10),group=rep(c("A","B"),5))
> anova(lm(DV~IV+group,foo))
Analysis of Variance Table

Response: DV
Df Sum Sq Mean Sq F value Pr(>F)
IV         1 0.0080 0.00802  0.0084 0.9296
group      1 0.1729 0.17285  0.1809 0.6834
Residuals  7 6.6880 0.95543

• Thank you very much. I indeed was working with a grouping factor which has 2 levels and suddenly got this doubt. Might have sounded stupid, but wanted to clarify anyway.
– Bach
Commented Apr 17, 2015 at 14:55
• No problem. 1 df = 1 parameter. If you have two groups, one of them will be the reference. And the (single) parameter will estimate the difference in DV between the reference group and the other ("non-reference") group. Generally, if you have $k$ factor levels, this takes $k-1$ df. Commented Apr 17, 2015 at 16:00