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How to Calculate the Effect Size at p=.05

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Johannes Reifenrath
Johannes Reifenrath el 12 de Oct. de 2023
Respondida: Jeff Miller el 14 de Oct. de 2023
Hello All,
Suppose I have caluclated the effect size for two different measurements (using the computeCohen_d(x1, x2, varargin) toolbox).
Now I want to determine the effect size, at which a measurement-difference becomes significant.
In other words: How to I calculate the effect size at p=.05?
Thanks in advance!
  2 comentarios
Jeff Miller
Jeff Miller el 12 de Oct. de 2023
'independent' or 'paired' ?
Johannes Reifenrath
Johannes Reifenrath el 13 de Oct. de 2023
Thanks for asking.
Independent.

Iniciar sesión para comentar.

Respuesta aceptada

Jeff Miller
Jeff Miller el 14 de Oct. de 2023
You can get an answer by computing a confidence interval for the Cohen's d. Specifically, at p=0.05, one end of the confidence interval for that d is right at 0 (well, epsilon above 0, I suppose). In the independent case, the half width (HW) of a 95% confidence interval for d is approximately the following (e.g., Bird, 2023, Eq. 2):
HW = tinv(0.975,n1+n2-2) * sqrt(1/n1 + 1/n2)
where n1 and n2 are the sizes of the two independent samples. So, plug in your sample sizes and the HW that comes out should be the d value that would be just significant at p=0.05.
Apparently this is only "approximately" the HW because the standard error of the d value depends on the true d value, but the references in Bird suggest that the approximation is pretty good unless the true d is greater than 1-1.5.

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