value d for method pwr.t.test()

[LonelyJerry]

I am wondering whether the d is actually dz rather than cohen'd when the type = c('paired'), because when I assigend the same value to 'effect size dz' in the G*Power software, the result is completely the same as the output of the pwr.t.test().

[heliosdrm]

Thanks for the comment.

The manual of pwr defines d as "Effect size (Cohen's d) - difference between the means divided by the pooled standard deviation". This receives different labels in Cohen's book, as d, d₃ (for one sample) or d_z (for one sample of differences between paired observations), but it's essentially the same concept.

Let aside the nomenclature given in G*Power, do you think that the way it is defined in the manual is misleading?

[LonelyJerry]

Thanks for the comment.

The manual of pwr defines d as "Effect size (Cohen's d) - difference between the means divided by the pooled standard deviation". This receives different labels in Cohen's book, as d, _d_3 (for one sample) or dz (for one sample of differences between paired observations), but it's essentially the same concept.

Let aside the nomenclature given in G*Power, do you think that the way it is defined in the manual is misleading?

Thanks for your reply.

I think there may be one potential confusion caused by the use of Cohen'd for paired t test. When one use the 'small', 'medium', 'large' criterion of the effect size, he will recognize the cohen'd value as 0.2, 0.5, 0.8 natrually. However, for the paired t test, the real cohen'd value (used in the power table in chapter 2 of the cohen's book) is sqrt(2)dz. If one doesn't know that, when he want to get the power for a paired t-test given a large effect size (cohen'd =0.8), he will set the d value of 0.8 to the pwr.t.test(). When he do that, he use the dz of 0.8 and cohen'd of sqrt(2)0.8 indeed. Consequently, he will overestimate the power.

Maybe I am wrong, but the mixed use of dz and cohen'd is often confusing for non-experts.

[heliosdrm]

Cohen used different symbols like d and d_z, as you say, because of the transformation needed to look into the power table. Anyway, in both cases the represented value is the one expressed in the manual: "difference between means divided by the pooled standard deviation".

If users may still be confused, it's ok to add a note in the documentation, but in such case, I think it would be also necessary to comment on the case of the "one sample test" - which is actually the same case.

If you have a specific proposal about how to explain this in a clear way for novice users, feel free to propose it --or better, to submit a pull request--. This should go into the file man/pwr.t.test.Rd.