Can you show me how to find the F Crit without using an ANOVA Calculator or spreadsheet add-on?
ANSWER: YES!
It is quite similar to how we look up the area associated with a z-score!
Let’s say we are given the following to use in a single factor ANOVA test:
| group a | group b | group c | |
| option 1 | 582 | 580 | 524 |
| option 2 | 558 | 650 | 499 |
| option 3 | 525 | 600 | 521 |
| option 4 | 540 | 548 | 567 |
| option 5 | 560 |
We need to find the df (degrees of freedom) for two things.
- df1 or df Between Groups is the total number of groups – 1
- in this case we have three groups so,: 3 – 1 = 2 .
- df1 = 2
- df2 or df Within Groups is when we look at each group’s df and take the sum of those
- In each group we are looking at n -1 and then taking the sum for all the groups OR
- *** find the total sample size (n) and subtract how many samples there were (k) aka n – k ***
- in this example we have n = 13 and k = 3 since we have three samples and a total of 13 data values
- n – k and when we plug in we get 13 – 3 = 10.
- df2 = 10
Once we have this we consult a F-Distribution table and find the cell that has this! That gives us the F crit.
look up like we do with the area under the curve (df1 = 2 and df2 = 10):
I will give you an input for the final; you will not have to get the F-crit yourself.
As you can see, it is faster these days to use technology but always wonderful to understand how to do it without a spreadsheet!