No, Cohen d is not equal to z.
z = b / SE
d = b / SD
in words: the z-statistic is the estimate ("b") divided by its standard errer ("SE"), whereas Cohen's d is the estimate divided by the standard deviation ("SD").
Without further information, a conversion between d and z is not possible. At least the sample size ("n") is required, because
SE = SD / sqrt(n)
thus,
SD = sqrt(n)*SE
and, eventually
d = b / (sqrt(n)*SE) = b / SE * 1 / sqrt(n) = z/sqrt(n)
No, Cohen d is not equal to z.
z = b / SE
d = b / SD
in words: the z-statistic is the estimate ("b") divided by its standard errer ("SE"), whereas Cohen's d is the estimate divided by the standard deviation ("SD").
Without further information, a conversion between d and z is not possible. At least the sample size ("n") is required, because
SE = SD / sqrt(n)
thus,
SD = sqrt(n)*SE
and, eventually
d = b / (sqrt(n)*SE) = b / SE * 1 / sqrt(n) = z/sqrt(n)
No, Cohen d is a measure of the effect size of your study; it is something like the error standard of the difference between two groups because (it uses de difference between the means and the “pooled standard deviation” of the two groups). The effect size measures the strength (or magnitude) of the difference between the groups. If you performed a statistic test of hypothesis, it is required that you report a p-value and the effect size.
The Z scores gives you the “position” of a particular value in the Z scale, and gives you information about how far is that value from the mean.
Z statistics helps you to establish if the difference between means of two populations have or not statistical significance or not, it gives you a “p-value”. The difference with Cohen d is that in the first you use de error standar of each group and in Cohen d is the "pooled" standard deviation, without the correction for the sample sizes.
I think it depends on what kind of Z you mean. If you mean a Z from a Z-test then the answer is no it is not the same. Here is the question. Is what you are looking at based off basically the form of mean difference/sd this is basically what d is though you would want to make sure the sd being used is the same as the one you would want to use and remember in the case of paired data there are other considerations etc. If its in the form of mean difference/se this is your basic z-test and its not equivalent (though we could get it there with some math). Here is a site that's useful for converting between effect sizes http://www.psychometrica.de/effect_size.html .
Dear all,
I like to thank everyone who have contributed to my previous questions. your help has been a tremendous support for my meta analysis.
Thank you
It is worth adding that the calculation of Cohen's d for a data set can be calculated in several different ways depending on what sort of data it is, what sort of question you are interested in and what assumptions you want to make.
This becomes important in meta-analysis because applying the same formula to two different data sets might produce estimates of two different quantities.
Also, more generally, Cohen's d - as usually calculated - is a measure of the discriminability or detectability of an effect not a measure of how big it is. That is because it is scaled in terms of sample variability (the SD) and thus anything that influences the SD influences d (even if it doesn't change the size of the effect).
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