# What should I enter as n when doing a meta analysis involving correlation coefficients- the number of observations or the sample size?

The r package and function (metafor; escalc) I am using to calculate effect sizes asks for n's (the sample sizes). Should I put the sample sizes of the study or the number of observations that went into calculating the correlation? A little more detail: in some of the studies each participants' score was correlated with the a variable of interest and therefore the number of observations equals the sample size. Yet, in other studies, several participant's scores were averaged to get a summary score for text A, text B, etc., and then those texts score summaries of performance were used to determine the correlation coefficient. In this latter case, the sample size could have been 100 but then only 20 texts were used to get the correlation coefficient. I'm assuming I still use sample sizes but wanted to check because I am new to meta analysis.

You use the sample size.

The sample size is used to calculate the standard error of the (transformed) correlation.

It's possible that the studies used some other method to get the standard error (or the variance) of the (transformed) correlation. If they did, and they report a standard error (or confidence intervals) you can use that.

The sample is the number of units of analysis that the correlation is comparing. That's often, but not always, people. A way to think about it: If you were to represent the correlation in a scatterplot, each unit of analysis is a dot. How many dots are there? That's the sample size to use.

Is it possible to point us to one of the papers that you are wondering about? I feel like I'd have more confidence in my answer then.

• +1 to asking for an example paper, because my initial intuition was the opposite of Jeremy's, but I might not be properly understanding your text A/B example. – jsakaluk Apr 25 '18 at 22:21
• In the paper (below) there are 88 people but the number of correlations is 50 (the performance of the 88 people were averaged for each of 50 passages and those 50 passages were correlated with the variable of interest). When you say sample size you mean the number of people? Because it sounds like sample size could also refer to the sample of 50 correlations. Ardoin, S. P., Williams, J. C., Christ, T. J., Klubnik, C., & Wellborn, C. (2010). Examining readability estimates' predictions of students' oral reading rate: Spache, lexile, and forcast. School Psychology Review, 39(2), 277. – sahanm Apr 26 '18 at 1:18
• I would have thought $n$ was 50 here as that is the number of observations making up the correlation. – mdewey Apr 26 '18 at 11:58
• @sahanm - I don't have access to the article. – Jeremy Miles Apr 26 '18 at 17:02
• @mdewey - from the abstract, I agree - I will edit the answer. – Jeremy Miles Apr 26 '18 at 17:02