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This post states the formula to calculate the noncentrality parameter of a test statistic that has a standard normal distribution under the null hypothesis. For a t-test under an equal variance assumption, the mean is given by:

$\delta = \frac{\mu_1-\mu_2}{\sigma_{pooled}/\sqrt{n}}$

this is equivalent to

$\delta = d * \sqrt{n}$

with $d = \frac{\mu_1 - \mu_2}{\sigma_{pooled}}$ (Cohen's d)

G*Power appears to calculate the noncentrality parameter differently. More precisely it constantly reports half of the noncentrality parameter reported in the answer above.

For example, performing a post hoc power analysis in G*Power for a one-sided t-test with $d=0.5$, $α=0.05$ and $n_1=n_2=5$ ($n = 10$)

gives

$δ=0.7905=0.25∗\sqrt{10}≠d∗\sqrt{10}$

Can someone explain why that is or what I am doing wrong?

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You're right. My answer was missing a divisor of the degrees of freedom. In this case, there are two degrees of freedom for either of the means. The non-centrality parameter in a power calculation is off by a factor of 2.

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