Was performing a meta-analysis, and data from a few studies were reported as mean and SE instead of the raw data of counts. Instead of excluding these studies from the analysis, is there a logical method by which we can infer back these values into the counts?
Perhaps - more information is required. You need to find out how the standard error is computed and this may allow you to infer N from then mean in situations where the variance is a function of N (such as logistic or Poisson regression).
Sorry, I don't understand the question. Usually meta-analysis uses aggregate data presented in studies. I think you need to say what the outcome is, how it's measured, what the estimate is that you want to pool, that sort of thing.
If it's a proportion you're wanting, most studies will hopefully give numerator and denominator, but if they just give the proportion and SE, then you should be able to re-arrange the formula for the SE of a proportion to give you the numbers you want (look in any basic stats textbook or wikipedia), or else convert all the studies with raw data to proportions and SE. I can't think why you would need to exclude any studies here, but it may be that there's some detail I've missed.
No.
If sample size is provided, you can figure out the standard deviation from SE.
However, the mean and standard deviation is not even sufficient to uniquely characterize a distribution let alone the original observations.
If there is a great deal of data (N in the thousands) then you could assume a normal distribution (or at the very least a symmetric distribution) and then use a random number generator to get values that come from the same distribution. You could do this even if the data came from only 3 observations, but the error in the method would make the result meaningless. Every time you sample you introduce error (uncertainty). So you have the underlying distribution in the original study. This is sampled to get the population of interest. The population is sampled by the researcher who publishes a mean and standard deviation. These are then used to build a new distribution, that is then sampled to simulate the original data that is subjected to statistical analysis. There is just a huge opportunity for error in this process and it gets worse as sample sizes decrease. You could improve things by doing this process over and over to get an idea of the range in outcomes from randomly drawing n values from a distribution with a given mean and standard deviation.
If the raw data were plotted, you could get an approximate value from that figure if there is sufficient resolution that few of the data points overlap. If many overlap, then you could use the data that you can recover and then use mean and SD to simulate the hidden values.
Timothy - I don't think that is in general true. For example a Poisson distribution has a single parameter (lamda) that is both mean and variance and thus SE is (lambda/n)^0.5. It follows that mean and SE is sufficient to derive n. The OP needs to provide more information about the situation for a more useful answer than "maybe".
@Thom
Ok, it depends on how you interpret the question.
It seems that you are reading the question to be "Is it possible to infer sample size from mean values and their standard errors?" If that was the intended question then your example is valid.
I interpreted the question to be "Is it possible to infer raw data from mean values and their standard errors?" If that was the intended question, then the answer is no. However, one could work around the problem through simulation or imputation (http://www.missingdata.org.uk/) if the original study was robust enough to support such activities.
Maybe this is a taxonomic work and they want to infer nightly counts of specific moth species given the mean nightly capture and the standard error.
I wonder which interpretation is correct.
It would be better to have the raw data, however the meta-analysis could be performed with mean and SE. Check the the quality of the studies: designs, measures and so on.
@Seile: have you find a method to recover raw data in the meanwhile?
@all: I have a similar question: my sample size is n= 3 and I have mean, SEM, SD and a scatter plot indicating the sum of two unknown values. Any help, any hope?
@Claudia,
With only the information that you have provided, this is not possible. You cannot recover the raw data from only the mean and standard deviation.
I am not sure what you mean by a scatter plot indicating the sum of two unknown values. Often scatter plots are of the raw data, and it is perfectly reasonable to recover the raw data from a scatter plot. There will be some error based on the resolution of the scatter plot, but that is ok.
If the goal is to make these values part of a large data set with data from many sources (meta-analysis), you could use the mean and SD and then do simulations. However, I would suggest consulting a statistician who was good at modeling/meta-analysis to help with this task.
Tim anticipated my reply. I'll just add that with n = 3 df = 2 and hence by definition the mean is insufficient to recreate raw data (unless the scatter plot provides another datum or equivalent).
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