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Sample skewness and kurtosis are bounded by functions of sample size, but those limits don't bite here: for example, with 1000 values skewness can't exceed 31.606 (3 d.p.). … n = 1000 | mean SD skewness kurtosis (*) ----------------+-------------------------------------------------------- age | 35.542 11.353 1.023 …

So too with skewness. The first measure is moment-based skewness, made famous by Karl Pearson, even though he used other measures too, and T.N. Thiele used the same idea earlier. … The same bounds don't apply to moment-based skewness, although it is bounded according to sample size. …

The problems are definitely Extreme skewness and very likely Reported zeros Granularity of results, e.g. reporting to $2$ decimal places, i.e., $0, 0.01,$ etc. … To see any but the grossest skewness of the data, we need to think on what are likely to seem unconventional or unfamiliar scales. …

To summarize so far: Mild skewness in your data can be handled by a mild transformation. Your bigger problem is identifying what model makes sense for your data. …

So, I can imagine saying the skewness is such-and-such, but that's mostly a side-effect of a few outliers, as shown by the fact that the 5% trimmed skewness is such-and-such. … I don't think that trimmed skewness or kurtosis is very much used in practice, partly because If the skewness and kurtosis are highly dependent on outliers, they are not necessarily useful measures, …

By "the skewness" I guess you mean the moment-based skewness calculated from third and second powers of deviations from the mean. … So the distance between mean and median is pertinent to skewness and is made a measure of skewness (so unitless) by dividing by the SD. …

It could hardly be a (useful) measure of skewness otherwise. … Personally I often value sensitivity in measures of skewness (and kurtosis, which otherwise we will leave on one side here), as they alert me to what may be a problem, or even a feature: high skewness …

One answer is no transformation at all. Poisson regression in fact can give the best of both worlds, the ability to cope with observed zeros and a logarithmic link. The point is that the mean response …

I suggest a concordance correlation between $y$ and $x$. This measures agreement between $y$ and $x$, not correlation. http://en.wikipedia.org/wiki/Concordance_correlation_coefficient

A terminology that fits more generally is that positive skewness corresponds to right skewness and negative skewness to left skewness, where positive and negative are the signs recorded for measures of … skewness, such as the moment-based measure defined by T.N. …

The details that skewness can be sometimes positive, sometimes negative and that you are thinking of combining scores also hint that you would be better off leaving the data as they are. …

However, there aren't general relations available on just knowing the skewness or kurtosis. … Skewness and kurtosis don't pin down the form of the distribution in general, as higher moments can vary too. …

I think it helps here to be concrete, not abstract. Think about the support of such transformations. ln $x$ requires that $x > 0$, ln ln $x$ requires that $x > 1$, ln ln ln $x$ that $x > e = \exp(1) …

I am still sketchy on what you want but guess that you are over-thinking this, as the similarity of skewness calculation to your problem is less than it seems. Kurtosis seems even less relevant. …

By and large, with this kind of sample size marginal distributions hardly matter to comparisons of means (and the fact that you have paired observations helps too, as you are looking at the pattern of …