Hello,
I have a run some meta-regressions using CMA software. Rather than analyze effect sizes, I have inputted and examined mean scores (cross-temporal). When looking at my regressions' data output, is the reported coefficient a standardized beta or rather an unstandardized B? I want to ensure I am accurately interpreting my data and want to ensure how it was calculated given this is slightly different than your usual meta-analysis. Does the software automatically standardize this or because these are raw means, does it simply report its unstandardized value (which would make sense based on my current results). Thank you very much for your consultation!
In meta-regression, the reported coefficient is typically an unstandardized coefficient (often denoted as B) unless you specifically standardized your variables before conducting the analysis. If you input and examined mean scores (cross-temporal) without standardizing them, the output from your meta-regression analysis would generally provide you with unstandardized coefficients.
To clarify:
If you want standardized coefficients, you would need to standardize your variables before running the meta-regression analysis. Some software packages might offer an option to request standardized coefficients in the output, but this doesn't mean your data was automatically standardized.
To ensure you are interpreting your results correctly, check the documentation of the software you are using or consult with someone familiar with the specific software's output format. Additionally, you can inspect the output directly to see if it mentions whether the coefficients are standardized or unstandardized. In most cases, if you didn't explicitly standardize your data, the coefficients will be unstandardized (B).
Hugo Assunção - a really good answer however, while "Standardized coefficients are helpful when comparing the relative importance of different predictors, especially when predictors are on different scales." is the common text book answer, I don't think this holds water.
Why would using the sample SD put variables on a common scale? You'd have to assume that the variables are measured with equal reliability, coarseness, without range restriction among other things. (This is rarely plausible). Its also debatable whether a beta statistic is a sensible measure of importance (there's other candidates).
I would argue if you know anything about the domain context the unstandardised coefficients are nearly always more interpretable.
Thom Baguley Interesting perspective. You are right, Beta coefficients are always a simplification and the evaluation of importance is more than simple comparison of these values. Thanks for the perspective.
I am reminded of John Fox's comments on standardized regression coefficients. Here is an note I wrote when I first read his book.
--- start of note ---
John Fox, author of "Applied Regression Analysis and Generalized Linear Models" (2008, Sage) is very cautious about the use of standardized regression coefficients. He gives this interesting example. When two variables are measured on the same scale (e.g., years of education, and years of employment), the relative impact of the two can be compared directly. But suppose those two variables differ substantially in the amount of spread. In that case, comparison of the standardized regression coefficients would likely yield a very different story than comparison of the raw regression coefficients. Fox then says:
"If expressing coefficients relative to a measure of spread potentially distorts their comparison when two explanatory variables are commensurable [i.e., measured on the same scale], then why should the procedure magically allow us to compare coefficients [for variables] that are measured in different units?" (p. 95)
That is an excellent question!
--- end of note ---
Bruce Weaver I suppose that if normality of distribution is assumed, then Z values have a similar meaning in both scales, at least in terms of relative frequency. Obviously this is not the case for every situation.
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