I am extracting data from RCT studies to see the effect of x intervention on y outcome. The effect will be measured by mean difference. Mean difference is determined from mean, SD and sample size. But, most of the researchers reported only mean and sample size of both arms (for instance mean for the control = -1.77, total size in the control group = 1132 and mean for the intervention group = -1.60 and total size = 1283). Can I calculate SD from mean and n?
No you can't derive SD with mean and N. SD shows the variation of data if data is normally distributed. Think about the bell shape of normal distribution, with same n and mean you can have many different bell shapes. Another example, 1,1,1 you have mean of 1, SD=0. But for -1 3 1 you have same mean, but SD=2.
I would have doubts about the methodological quality of a paper that does not provide a SD with the mean. Do they report something else? if so you could try
Estimating the sample mean and standard deviation from the sample size, median, range and/or interquartile range
https://doi.org/10.1186/1471-2288-14-135
No, you cannot get the SD from only mean and sample size. Stating only the mean and sample size is not enough for data presentation in a research paper. They cannot give the readers full picture about the data
You need in addition to the mean and sample size the p value, t statistics, standard error, or the confidence interval to be able to calculate the SD.
If you have th p value you can calculate the t, but you need to know the degree of freedom
df= N+N-2
Then, you can know the t from the table of t distribution or calculate it in excel using the following equation
= tinv(p value; df)
After knowing the t you can calculate the SE by the following equation
SE=MD/t
Where the MD is the mean difference
From SE you can calculate the SD
SD=SE/square root (1/N1 +1/N2)
The resulted SD is the average SD of the two groups and you should use it for the two groups (inserting it when doing a meta-analysis one time for experimental group and another for the control group)
E-mail the authors to get as much as possible missing SDs then
you can do pool their log together with the log of the means as a linear regression with scatter plot and get the missed log SD (y) from the regression equation such as (Y=a+bX), and don't forget to transform back to the normal scale. Also, cite some previous papers doing that method to support yourself.
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