Thread: interpreting f-values within a n-way anova

1. interpreting f-values within a n-way anova

Hi,

f-value determines the statistical significance of a main effect. I would like to find out in if the following is valid: 2 f-values for the 2 main effects examined. f-value1 =400 and f-value2=5. Other than saying the 2 main effects are statistically significant, can one suggest that main effect 1 is "more" statistically significant than main effect 2. If not, can a tool be suggested? Thanks.

2. Re: interpreting f-values within a n-way anova

You could not say that one is more statistically significant than the other. They either are or are not statistically significant. You could, however, consider 1 to have a greater contribution toward the total variation than 2. Look up epsilon^2 as a metric of percent contribution.

3. Re: interpreting f-values within a n-way anova

Originally Posted by Miner
You could not say that one is more statistically significant than the other. They either are or are not statistically significant. You could, however, consider 1 to have a greater contribution toward the total variation than 2. Look up epsilon^2 as a metric of percent contribution.
Hi Miner, thanks for your advice. Can you please provide a searchable term or url that I can read more about the epsilon^2 metric? In particular, can you please advise how one can do this within SPSS if possible? Thanks.

4. Re: interpreting f-values within a n-way anova

I am not an SPS user, so I do not know whether SPSS will provide it automatically. However, it is easily calculated in Excel using the standard outputs of an ANOVA table. See BIAS AND PRECISION OF EIGHT MULTIVARIATE MEASURES OF ASSOCIATION FOR A FIXED-EFFECTS ANALYSIS OF VARIANCE MODEL, page 12, for the formula. Omega^2 is another option, but do not use Eta^2 as it is biased and overestimates the effect size.

5. Re: interpreting f-values within a n-way anova

Originally Posted by Miner
I am not an SPS user, so I do not know whether SPSS will provide it automatically. However, it is easily calculated in Excel using the standard outputs of an ANOVA table. See BIAS AND PRECISION OF EIGHT MULTIVARIATE MEASURES OF ASSOCIATION FOR A FIXED-EFFECTS ANALYSIS OF VARIANCE MODEL, page 12, for the formula. Omega^2 is another option, but do not use Eta^2 as it is biased and overestimates the effect size.
Hi Miner,

Thanks for the information. How does one know the "words" to search when a similar situation happens in the future? I am a beginner at using statistical tools but have problems going beyond for clinical research purposes. Would like to know how to find these info independently. Is it preferable to get advice from a statistician?

In saying so, I do notice that disagreements exist even within statisticians. For example, I previously asked a statistics professor the same question. He said it would be okay to suggest one main effect is more different than the other, by comparing the two f-values, albeit my uncertainty.

6. Re: interpreting f-values within a n-way anova

That is difficult to explain, Your biggest problem is you don't know what you don't know, so you have to start with what you want to do and what you do know. You might start by searching "How do I measure how much larger one effect is than another?" You will probably get a lot of garbage results, but see a few that say "Effect size", so you search again on effect size. This time you get a number of responses such as Cohen's d and Wikipedia's Effect size. After that you realize there are multiple measures of effect size and you start to research the advantages and disadvantages of each. The more you know the easier it is, but it can still be difficult. For example, I found very few good articles on epsilon^2 despite it being one of the better measures of effect size. On the other hand there were a lot of hits on eta^2 when it is know to be a biased estimate that overestimates the contribution. However, a lot of people still use it because it is still taught.

7. Re: interpreting f-values within a n-way anova

I would say that partial omega squared effect sizes could be considered - because they do not involve the non-relevant factors in the design. For example, if you have a 2 factor anova (AxB) design, then for factor A the partial omega squared would be:

w^2 (A) = [df(A) * (F(A) - 1)] / [df(A) * (F(A) -1 + a*b*n ]

where "a" is the number of levels of factor A and "b" is the number of levels of factor B and "n" is the cell sample size.

Do the same for factor B.

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