42

If the authors use a statistical test and present the value of the test statistic (t or z, for example) or an exact p-value, it is also possible to reverse-engineer the SD. Since the p-value is a transformation of the test statistic you can recover the test statistic. And since test statistics are the effect size divided by the standard error, you can recover the standard error using the mean as the effect size. The standard error, in turn, is related to the SD by sqrt(n).

Tedious, but it might retrieve a couple of the SDs you need.

Actually, the obvious solution (which is always the second thing I think of) is to write to the authors.

No, if all that is reported is a mean, then you have no other data that you could use.

This is a rather academic comment: If you would know, by chance, the distribution of which the mean is given, and that for this distribution the variance is not independent from the mean (e.g an exponential or Poisson distribution), then knowing the mean would also mean knowing the variance (i.e. the standard deviation).

Thank you both for your help! Much appreciated.

42

If the authors use a statistical test and present the value of the test statistic (t or z, for example) or an exact p-value, it is also possible to reverse-engineer the SD. Since the p-value is a transformation of the test statistic you can recover the test statistic. And since test statistics are the effect size divided by the standard error, you can recover the standard error using the mean as the effect size. The standard error, in turn, is related to the SD by sqrt(n).

Tedious, but it might retrieve a couple of the SDs you need.

Actually, the obvious solution (which is always the second thing I think of) is to write to the authors.

Thank you everyone. Diana - that's a great paper and might be what I've been looking for.

I'm afraid the best you can get is variance. However many times the variance can get close enough to the standard deviation itself.

Hi Avi Biswas :

I hope the answer is not too late. I found my self with the same problem today.

The answer comes from Cochrane Handbook for Systematic Reviews of Interventions https://www.radioterapiaitalia.it/wp-content/uploads/2017/01/cochrane-handbook-for-systematic-reviews-of-interventions.pdf (pg 173 - 175)

Example:

A paper from 1994 which just reported the p value for a clinical trial comparing the use of postbiotics and placebo. They found that in the intervention group the average duration od diarrhoea in group 1 was 49,7 (n=38) h vs group 2 64,7 h (n=33), with p=0,04.

The first step is to find the difference between groups. In this case is 15.

Step two. T value. You should find the t value of that p value. In Excel it can be carried out in this way = TINV(0,04; 69) = 2,09330243 . Please, note that 69 comes from (38+33) -2. Two from liberty grades

Step three, estimate the standard error. It is possible to estimate the standard error in this way: ((38 -33)-2) /2,09330243 . Standard error = 7,16.

Step four, SD. It is possible to find this out by dividing the SE into the square root of (1/ n group 1 + 1/ n group 2). In this case is (1/38 + 1/33).

The value of SD is 30,1.

Also, there is a nice video from Cochrane here: https://www.youtube.com/watch?v=19gdqj-4VAI

Regards,

Thanks Dear Jeadran N Malagon-Rojas , I had a same problem. Much appreciated!