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View Full Version : Following up an F ratio test

D Man
12-22-2009, 02:23 AM
Hi guys,
This is my first post, so I'll start with an easy(?) one :)

I have two independent groups with identical mean scores but obviously different variance and range.
I need to produce a results section which is fine but I'm struggling to think what I can write up, except showing the descriptives, maybe a graph and report the F ratio, standard deviation range etc and explain in plain English that "yes the variances are different".
Is there another test that can explore the variances further?
As the means are identical, a T-test is redundant and I'm not sure if doing an ANOVA will yield anything.

Riverdale27
12-26-2009, 09:56 PM
You do an F-test for different variances... This test does suppose normally distributed populations though, so check if they kinda are...

Divide var1 by var2 and compare this to the critical F value with n1 and n2 degress of freedom... If you can reject equal variances (which you will probably can do), then conduct a t-test assuming inequal variances for the mean. This gives your "words" a little bit more background.

D Man
12-29-2009, 11:11 PM
Thanks Riverdale27,
Yes, I've done an F-test and the variances are significantly different.
I was wondering if there is anything else besides the F-test that I can do.
There doesn't seem any point doing a T-test as the means are absolutely identical (as can be seen from the descriptives output).
ANOVA is also based on a comparison of means, so I'm thinking there's no point doing that either....unless there's some useful output to be gained from doing a T-test or ANOVA anyway??
So...besides reporting descriptives and the results of the F-test, is there anything I'm missing?

Riverdale27
12-31-2009, 10:23 AM
Oh yes if the means are absolutely equal, then it just doesn't matter what you do... The T-statistic will always be 0 (since the numerator is zero) and you can never reject... ANOVA is also comparing means but for more groups, so no use for that either. By the way, if you do ANOVA for just two groups, your F statistic will equal tē. This is because your F-test basically reduces to an t-test, if you only have 2 groups.

So what you basically can conclude from this is that the means are equal, but the variances are not. It's kinda like the following strategies in roulette:

- always play red
- always play the number 20

Both strategies have exactly the same expected value or mean, but the variance of the second one is (obviously) much much more. I guess this is the same as what you found.

It is however very strange that you have exactly exactly exactly the same means... Isn't there a fault in the data?

Moreover, what is it that you are looking for in the data? Do you have a question you want answered? What is the meaning of the data? What do you want to accomplish, etc...

D Man
01-03-2010, 12:32 AM
Thanks again Riverdale27,
It's an exercise which has obviously been manipulated so that the means are identical. I guess the point is for the student (me) to analyse the data and choose an appropriate statistical test. I've written up a results section but it's very short! Not necessarily a bad thing, I guess...