# Calculating effect size for a study with no groups

I am working on a meta analyisis of the effects of e-learning in an organizational context. I have prepared a list of about 25 studies to analyze and I have organized all the path coefficients based on the TAM theory for the standard TAM constructs, i.e. Perceived ease of use -> Perceived usefulness etc.

Research that I did on calculating effect size always mentions having 2 groups which are used to calculate effect size. Problem is, in the studies which I singled out there are no control/treatment groups, but only path coefficients are calculated for TAM contructs and other additional factors which authors researched.

Is there some way to calculate an effect size for a study which has no groups?

Example study with available full text

• Do you want to meta-analyse the betas from Table 7 for instance? – mdewey May 14 '19 at 8:30
• @mdewey Exactly that – EldarGranulo May 14 '19 at 8:38

If you have a statistic from each study, in this case a $$\beta$$ and its standard error, then you just use them in the meta-analysis model. Software to do this is widely available in R and Stata and doubtless in other packages as well. In R you can use several different packages. I use metafor (available from CRAN) but meta also has many users. The relevant function in metafor is rma.uni. In Stata the metan command is the relevant one. If you want to do it by hand I starting from the Wikipedia article on inverse variance weighting which I think is the search term you were looking for.

In this case as so often you have the problem that the standard errors are not available but the $$p$$ values are. So you can back-calculate the value of $$z$$ from $$p$$ and then use the fact that $$z = \frac{\beta}{se}$$ to get the standard error. In a more complex model you could do all the $$\beta$$s from that table in one analysis but this would demand having the covariances between the $$\beta$$s which will be hard to find. It also might not correspond to your scientific question either.

The situation is not different from the two group case where you compute the effect size (odds ratio, standardised mean difference, etc) and its standard error and plug that in

• Could you point me to the formula or function in R to calculate effect size given the value of 𝛽 and the standard error? Is standard error = standard deviation? Please answer this and I will accept the answer right away. – EldarGranulo May 14 '19 at 11:06
• From what I read in your edit it seems that the functions demand effect sizes as an argument, but that is the very thing I need to calculate per study. Any instructions for that? – EldarGranulo May 14 '19 at 12:25
• Use the $\beta$ values. They are the effect size. – mdewey May 14 '19 at 12:29
• In the studies it is marked as path coefficient. Is this equivalent to effect size? – EldarGranulo May 14 '19 at 12:32
• I think you are getting confused about the multiple meanings of effect size. In meta-analysis it refers to the statistic which you are going to summarise. It could be a proportion, a correlation coefficient, a regression coefficient, or many other things. – mdewey May 14 '19 at 12:49