# Confused about degrees of freedom

Everything I've read about degrees of freedom says more is better - it is an indication of a model's flexibility.

I'm now running a power analysis in R and I've noticed that lower degrees of freedom give higher power.

Example 1 (DF = N - 1):

library(pwr)

pwr.chisq.test(w = 0.7, N = 30, df = 29, sig.level = 0.05)

Chi squared power calculation

w = 0.7
N = 30
df = 29
sig.level = 0.05
power = 0.5115032

NOTE: N is the number of observations


Example 2 (DF = 1):

pwr.chisq.test(w = 0.7, N = 30, df = 1, sig.level = 0.05)

Chi squared power calculation

w = 0.7
N = 30
df = 1
sig.level = 0.05
power = 0.9695413

NOTE: N is the number of observations


I assume in this case DF is supposed to refer to the number of parameters? If that's correct, why is it also used as sample size minus parameters?

• What exactly did you learn about degrees of freedom and where? It definitely is not the case that "always more is better", so the claim is not correct.
– Tim
Commented Feb 16, 2022 at 14:13