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I've come across two different forms of a skewness-adjusted t-statistic, which was developed originally by Johnson (1978): $ J = t + \frac{gt^2}{3n} + \frac{g}{6n} $

and $ J = t + \frac{gt^2}{3\sqrt{n}} + \frac{g}{6\sqrt{n}}, $

where $t$ is the conventional t-statistic, $n$ is the number of observations, and $g$ is the skewness estimate. The null hypothesis is zero mean.

Could you advise me what's difference between the two forms?

Many thanks, Dave

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    Sorry, $g$ in my notation is equal to $\hat{\mu}_3/s^3$ in Johnson's notation.2012-10-30

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