Hello,
I was wondering if it is different to use a ratio or a percentage in ANOVA analysis.
Let's say we have two distinct continuous normal variables (A & B) and our factor independent variable. Therefore, we can express B in relation to A as follows (I suppose there are more methods):
- 1) A/B.
- 2) A/(A+B).
- 3) Construct an ANCOVA model.
Considering that:
A>0
B>0
A may be > or < than B.
I have read that option 1) may be non-linear (perhaps I am wrong), while 2) may be linear in the range between 0 and 1. Therefore, option 1) may be more likely to violate Anova assumptions?
I imagine that the best option is 3) when we want to correct the effect of B in the relationship between our factor and A (again, perhaps I am wrong). However, it is usual to use ratio or percentages in biomedical research.
In those cases, is there any difference between to use 1) or 2) formulas? What do you recommend?
Thanks in advance! =)
What are you suggesting for the covariate (B also?). You should look up generalized linear models, which can be well suited for proportions, but from the information more info would be useful.
What are your variables; how are they distributed; are A and B on the same scale; etc.?
If considering Ancova v Anova, the following might be useful. Preprint Allocation to Groups: Examples of Lord's Paradox (British J ...
(this is out online. If your workplace has a BPS subscription it will be available, otherwise this is the final submitted version).
Hello Daniel,
Thanks for your answer.
This is just a theoretical question, currently I do not have a problem which I need to fit. It's just that I usually see Anova models with percentages or ratios (specially in basic science) and I was wondering whether both methods are different (perhaps no situation is correct).
"What are your variables; how are they distributed; are A and B on the same scale; etc.?"
As an example (a common situation):
A is a normal distributed variable in cm^3 (e.g., a lesion volume).
B is a normal distributed variable in cm^3 (e.g., intracranial cavity).
A>0; B>0; A may be > or < than B.
In my previous analyses I have used GLM to deal with percentages (e.g., beta regression or binomial). But in the case we want to run an Anova (this is not my case, but is very common in basic science) is different to calculate a ratio (A/B) or a percentage [A/(B+A)]? As I said, perhaps no scenario is correct.
Thanks again! =)
Joan Jiménez-Balado , note that neither A nor B is normally distributed (since A>0 and B>0). They may be approximately gamma-distributed. The ratio of two gamma distributed variables is beta-prime distributed. The percentage is beta-distributed.
For a practical case (depending on the actual distributions of A and B and on the sample size), the approximation by the normal distribution may be sufficient.
- Badges
- Science method
- Similar topics
- Mathematics
- Statistics
- Statistical Modeling
- Analyses of Variance
- ANOVA