### How to interpret F- and p-value in ANOVA?

• I am new to statistics and I currently deal with ANOVA. I carry out an ANOVA test in R using

``````aov(dependendVar ~ IndependendVar)
``````

I get – among others – an F-value and a p-value.

My null hypothesis (\$H_0\$) is that all group means are equal.

There is a lot of information available on how F is calculated, but I don't know how to read an F-statistic and how F and p are connected.

So, my questions are:

1. How do I determine the critical F-value for rejecting \$H_0\$?
2. Does each F have a corresponding p-value, so they both mean basically the same? (e.g., if \$p<0.05\$, then \$H_0\$ is rejected)

Have you tried the commands `summary(aov(dependendVar ~ IndependendVar)))` or `summary(lm(dependendVar ~ IndependendVar))`? Do you mean all the group means are equal to each other and equal to 0 or just to each other?

yes, I did try the `summary(aov...)`. Thanks for the `lm.*`, did not know about this :-) I don't get what you mean by equal to 0. If that's short for my 0-Hypothesis than the Hypothesis would need a value, and I did not test on specific one, so in this case: just to each other!

For an intuitive explanation look at the Yhat blog on the topic of regression.

9 years ago

1. You find the critical F value from an F distribution (here's a table). See an example. You have to be careful about one-way versus two-way, degrees of freedom of numerator and denominator.

2. Yes.

It is not meaningful to talk about one- or two-way comparisons in an omnibus test such as the F-test.

Marcus Morrisey: I think you're confusing one vs two tails with one- vs two-way. The F-test doesn't have multiple "tails" to choose from, but one-way ANOVA vs two-way ANOVA needs to be considered when constructing the test statistic.