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I am performing some meta-analysis and I came around some paper which says " The results of a meta-analysis of 72 studies encompassing 33,732 observations... etc" or "We conducted a meta-analysis of 52 empirical studies representing 10,066 observations to test relationships" What does this observations mean in the context of meta-analysis.

The below table was given as an hint for my work from my advisor, although I could not understand what it does imply. How can I make observations with three factors in multiple ways?

Example given

The below table is the example I have been trying. [![This is the example I have been doing][3]][3]

So comparing my work to the above given example I have two doubts. 1) 1 denotes presence and 0 denotes does not presence according to the 1st image.

2) Regarding sample size, its 175 for one study, and I read that in case I use the sample size for calculations as an estimate for the std err (i.e. precision) of the estimator (i.e. the effect size respective the correlation),I need to account for the fact, that the std error are not independent and I need to adjust the estimator for the precision of the estimator. If the sample size is 175 and you have 8 entries from the same study here database, so I have to devise the sample size by the number of entries... i.e 175/23 = 7.6

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3 Answers 3

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The observation in the meta-analysis is the unit of the study.

For example in a medical meta-analysis an observation is a patient, so you can have 20 studies comprising 12000 observations (patients).

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  • $\begingroup$ So you mean the observations are the patients or the observations made on that study? $\endgroup$
    – Karthik Sharma
    Commented Mar 13, 2016 at 11:12
  • $\begingroup$ I was making an example, in medicine your observations usually are patients. In a meta-analysis generally speaking the observation is the unit in the studied you are analyzing and this depends on the study you are considering, patients for medical ones, plants for study regarding plants... $\endgroup$
    – GGA
    Commented Mar 13, 2016 at 11:37
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Unless you have all the individual data from all the primary studies all you can do is to analyse the summary statistics which in your case seem to be correlations. The statements you see about studies having a total of X observations are intended to give the reader some background and are really redundant since the variability of the summary estimate from your meta-analysis already tells us about the precision with which you have estimated it. The table you show suggests that (a) your advisor wants you to do a meta-regression (you could I suppose always ask him/her) (b) you do not there have enough information to do even a simple meta-analysis as you do not have either the sample sizes for your r or some other measure of their variability. But perhaps you do have that and could not fit it in the table.

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  • $\begingroup$ For example I have 10 studies and each of them have 100 as sample size so 10 * 100 is = 1000 is going to be the observations? So I can say based on 1000 observations ... Yes, I can ask him, but he is out of reach for now and I have work to do so I was asking for help. Yes, I should do a meta-regression. That was an idea he gave me to build. I do have them but I did not add them here. Its totally confusing. $\endgroup$
    – Karthik Sharma
    Commented Mar 13, 2016 at 14:18
  • $\begingroup$ The table above he gave was a hint and I have the data with me but I am getting confused how to take the data and fill in. The above one is just a sample. $\endgroup$
    – Karthik Sharma
    Commented Mar 13, 2016 at 14:32
  • $\begingroup$ You can say 1000 yes but that is the only part it plays in the analysis. If each study has 100 then you can use that to form the standard errors. You probably need to transform the r values to z using Fisher's hyperbolic arcsine transformation. $\endgroup$
    – mdewey
    Commented Mar 13, 2016 at 15:56
  • $\begingroup$ I have edited the image, can you tell me now. My only confusion is for the correlation values. To make it simple I have totally 6 factors to be considered. So where should I enter the correlation value for each of it in this table is my doubt. $\endgroup$
    – Karthik Sharma
    Commented Mar 14, 2016 at 7:32
  • $\begingroup$ Without knowing what software you are going to use I do not think anyone can help you here. Just as an extra comment I would have thought that trying to use six moderators simultaneously was rather ambitious. $\endgroup$
    – mdewey
    Commented Mar 14, 2016 at 9:17
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As stated by GGA, typically in an aggregate meta-analysis you have multiple units of analysis. Typically the study is the unit at hand, but it refers to smaller units (such as patients in a medical meta-analysis, or animals in a veterinary meta-analysis).

It is particularly important what the focus of your work will be. You typically want to tell people how to treat their individual patients, rather than how to conduct further trials (even if this is also meaningful).

According, the atomic unit / observation remains, for instance, the patient.

Assuming that your outcome of interest is the correlation, then the best approach is to use the sample size to compute the variances of the correlation coefficients, and then pool them using appropriate methods.

You can find here recommendations for these steps:

https://stackoverflow.com/questions/16097453/how-to-compute-p-value-and-standard-error-from-correlation-analysis-of-rs-cor

https://www.meta-analysis.com/downloads/Meta-analysis%20Effect%20sizes%20based%20on%20correlations.pdf

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  • $\begingroup$ Regarding the example its a sample help I got. Its random structure and I am confused how to enter data or the value of r into my table. Observation means size of the sample right? $\endgroup$
    – Karthik Sharma
    Commented Mar 13, 2016 at 14:22
  • $\begingroup$ Effect size is the correlation i.e r value. Correlation value is the effect size right? $\endgroup$
    – Karthik Sharma
    Commented Mar 13, 2016 at 14:41
  • $\begingroup$ I have edited my entry. The effect of interest might indeed be there as correlation factor. What is missing is a measure of precision / weighting factor (e.g. its standard error). $\endgroup$
    – Giuseppe Biondi-Zoccai
    Commented Mar 13, 2016 at 22:27
  • $\begingroup$ Once we have the effect sizes, how do we calculate the measure of precision or weighing factor? $\endgroup$
    – Karthik Sharma
    Commented Mar 14, 2016 at 5:29
  • $\begingroup$ I have edited the image, can you tell me. The effect size and size of the study are given. I am still stuck at entering values into my database. Like my only confusion is for the correlation values. How do I enter into the sheet? To make it simple I have totally 6 factors to be considered. So where should I enter each of the correlation value in the table is what I am confused about. $\endgroup$
    – Karthik Sharma
    Commented Mar 14, 2016 at 7:34

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