I am working on a meta-analysis that assesses the relationship between amount of substance A in the diet and the concentration of substance A in the blood. In the identified studies, this relationship is shown as a Pearson r in the majority and as beta coefficients in a large minority. However, a few studies report

*P*values for ANOVA. Instead of looking at the relationship between the two continuous variables, they categorized the amount of substance A in the diet into tertiles or quartiles, then provided the average concentration of substance A in the blood for those tertiles or quartiles.

For example, this leads to results like:

Lowest tertile of amount of substance A in the diet: concentration of A in the blood of 1g/L

Middle tertile: concentration 1.5g/L

Highest tertile: concentration 2.0g/L

They then provide n = X and a

*P*-value for the ANOVA. Let’s say for this study: n = 350 and

*P*<0.001. This study also provided an F-value, which is not that common in medicine, which in this case was 158.

I am looking for a way to convert the

*F*-value for the ANOVA into a Pearson r – if this is possible of course.

Based on this online lecture, it is possible:

However, I cannot find the formula for an ANOVA with 3 groups, nor do I know if my reasoning above is correct. I have looked at tables to convert F-values into

*P*-values, but I only found “Critical value tables”. I found online converters, but they don’t seem to match what I want (besides, I’d like to understand). Can anyone help me with the formula to convert an ANOVA with 3 groups into a Pearson r, and can anyone confirm whether I can use it this way – or explain to me if I cannot?

Thanks in advance!

Best,

Martin