We have conducted a systematic review to investigate the effectiveness of a treatment for a psychological disorder. We aim to report effect sizes and p values of the reviewed studies but one study has only reported CI 95, p value and t score regarding the effect of the treatment on a variable between baseline and post-treatment. Given that the used t test was from a paired t test, is it possible to determine the Cohen's d based on the available information?
I'd very much appreciate it if you help me with this problem.
I had to calculate this once a long time ago. If I am not wrong, you can determine Cohen's d if you first use the CI to estimate the mean difference and the standard error of the mean difference. The margin of error (ME) is half the width of the CI, so the SE can be derived from the ME using the t-value if you know the the sample size.
With the SE, you can then calculate the SD of the differences (SD_diff). You'll get a Cohen's d dividing the mean difference by SD_diff.
You probably can compare the result with an on-line cohen's d calculator and check whether it is consistent.
I AM NOT AN EXPERT, but you can try and see if this helps.
Well, it's complicated. Cohen's d was originally defined as a population quantity for two independent groups:
(mu1 - mu0)/sigma0
where sigma0 is the control group population SD and the mu's are the population means of the groups. Its usually estimated with pooled SD of the groups on the assumption that sigma0 = sigma1.
Can you get an estimate of this quantity from a paired design? If you make certain assumptions. You can use the SD of the sample at one time point (often pre or baseline seems sensible but it depends on things like ceiling and floor effects and whether treatment impacts the variance as well as mean) and calculate it that way.
Can you get it from the CI, t statistic and p value? No, because the t statistic depends on the correlation between the paired measures. You ideally need the SD at both time points and the difference in means.
Note there are other ways to calculate a d-type statistic, but in my view they don't estimate Cohen's d (or rather what Cohen's d would be in a two group design assuming the two designs are otherwise comparable). Some of these other options might be useful (e.g., for power analysis) because they tend to account for the increase in power from taking account of the usually positive correlation between time points (assuming you want to estimate power for a paired design not an independent groups one). In any case I'd not call the statistic from a paired design Cohen's d ...
Hello Mohammad Hossein Ghaedamini Asadabadi
I think it is very easy to work with this formula
Cohen's d = 2t / √(df)
I appreciate the answers i have received so far. As one of the answers suggested, here's how you can calculate Cohen's d with CI 95 and t value from a paired sample t test: Step 1: Calculate Standard Error (SE) from CI 95. SE = (upper limit - lower limit)/ 3.92 Step 2: Convert the calculated SE to Standard Deviation (SD) using the sample sizes. Step 3: Calculate Mean Difference (MD) from SE and the t value. SE = MD/t so MD = SE*t Step 4: We have MD and SD now, therefore we can easily calculate the Cohen's d. Cohen's d = MD/SD It's worth mentioning that i calculated the Cohen's d for a made up dataset this way and it worked really well!
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