I am running a one-way ANOVA to compare a numeric continuous variable between four groups, and getting a very high F-value. Below are the descriptives and code I used in R (I get similar values when trying a different package in Python):
> oneway.test(ideology_score ~ region, data = mydata) One-way analysis of means (not assuming equal variances) data: ideology_score and region F = 1270.6, num df = 3, denom df = 101578, p-value < 2.2e-16
Total N of observations = 262,267
The means and standard deviations of the variable are almost the same for each group, and the variance and distribution of scores within each group are quite similar as well.
Is there anything else that may be going wrong here to explain the high F value?