When conducting a Welch's t-test on a ratio of measurements that are not normal(wing length divided by wing width) , should you log transform the ratio or use log transformed values of wing length and wing width to make the ratio? When I run the t test using those two options, I get different results. Can you please explain and advise as to the best course to take?
Although Wright is right ;) it is often the case for biological data that the log ratio is a "more meaningful" measure than the ratio. But it still depends on the context.
The distribution of the ratio of two variables can be quite weird, depending on the distribution of these variables. However, if the values for the denominator variable are all "far from zero" (relative to the width of their range), there is a good chance that the ratio has an approximate log-normal distribution, what means that the log ratios has an approximate normal distribution.
The ratio of logs is really hard to interpret in any meaningful way. The result would be a log to a base defined by the denominator, since
logD(A) / logD(B) = logB(A)
I have no idea where this should be meaningful (because "B" in the formula above would not be a constant). It could be that this has some meaning in some context, but I doubt it.
While the log is often used in this situation, more details (like the distribution and how meaningful the ratio is) before advising. I would have thought the ratio might be more meaningful for whatever theories you are exploring than the log of the ratio. The meaning changes when logging.
Article Football standings and measurement levels
Although Wright is right ;) it is often the case for biological data that the log ratio is a "more meaningful" measure than the ratio. But it still depends on the context.
The distribution of the ratio of two variables can be quite weird, depending on the distribution of these variables. However, if the values for the denominator variable are all "far from zero" (relative to the width of their range), there is a good chance that the ratio has an approximate log-normal distribution, what means that the log ratios has an approximate normal distribution.
The ratio of logs is really hard to interpret in any meaningful way. The result would be a log to a base defined by the denominator, since
logD(A) / logD(B) = logB(A)
I have no idea where this should be meaningful (because "B" in the formula above would not be a constant). It could be that this has some meaning in some context, but I doubt it.
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