2nd Sep, 2021

Catholic University of Applied Sciences Munich, Munich, Bavaria, Germany

Question

Asked 20th May, 2016

Are there any justifiable method/heuristic for assessing the rough effect size (e.g. small, medium or large) of standardized beta coefficients from multiple regressions and path analysis?

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Christian Young Christian, since I have a similar issue, which "rules of thumb" did you use in the end for the standardised regression coefficients?

I took a look at your paper but I could not find anything for the Betas. It says "We followed conventional rules of thumb for effect sizes [29] and deemed medium effect sizes as: Cohen’s d = .5, zero-order correlation coefficient r = |.3|, and odds ratios = 2 or .5; large effect sizes were defined as Cohen’s d = .8, zero-order correlation coefficient r = |.5|, and odds ratios = 5 or.2. All other statistics were interpreted within the context of the study."

Elissa J Hamlat Elissa, did you find a workable solution?

In that case you may want to look at

Standardised regression coefficient as an effect size index in summarising

findings in epidemiological studies; Epidemiology Biostatistics and Public Health - 2013, Volume 10, Number 4

6 Recommendations

Dear Christian,

"Cohen’s d is a good example of a standardized effect size measurement. It’s equivalent in many ways to a standardized regression coefficient (labeled beta in some software). Both are standardized measures-they divide the size of the effect by the relevant standard deviations. So instead of being in terms of the original units of X and Y, both Cohen’s d and standardized regression coefficients are in terms of standard deviations."

2 Recommendations

You may want to have a look at this current debate on how to compare effect size in regression in favour of unstandardized coefficients

1 Recommendation

Thanks for your answers. To clarify, I am conducting a systematic review and am hoping to give a rough approximation of effect size based on multiple types of statistics (r’s, odds ratios, beta’s, b’s, etc.) I have conventions for correlations, t and F tests, and odds ratios. But am struggling to find and effect size convention (small, medium, large) for standardised regression coefficients (beta) as reported using multiple regressions and path analysis. As I understand, beta is the standard deviation change in the DV with one standard deviation change in the change in the IV, holding all other IV’s constant. Is there a justifiable method for assessing the effect size of beta in this context? Thanks.

2 Recommendations

In that case you may want to look at

Standardised regression coefficient as an effect size index in summarising

findings in epidemiological studies; Epidemiology Biostatistics and Public Health - 2013, Volume 10, Number 4

6 Recommendations

Christian Young Did you ever find a satisfactory solution? I am conducting a meta-analysis and have a similar issue. Thanks.

Christian Young Elissa J Hamlat I've used Acock (2014) (see this post for details: https://stats.stackexchange.com/questions/235110/how-to-evaluate-effect-size-from-a-regression-output/235259)

"Acock (2014) also argues that they can be interpreted similar to correlations: *β*^∗<0.2β^∗<0.2 is considered a weak, 0.2<*β*^∗<0.50.2<β^∗<0.5 moderate, and *β*^∗>0.5β^∗>0.5 strong effect (p.272)"

Daniel P. Moriarity Thanks Daniel! I've also found an article that suggests a formula for conversion from *β to r. *However, it's not helpful in the case of large *β, *as some *β* can be over 1.

My goal is to ultimately convert all to Hedges g' for meta-analysis.

Elissa J Hamlat I never really did, though the paper Daniel P. Moriarity has linked to above looks useful and is very similar to rules of thumb that I used in the end.

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Article

Full-text available

- May 1983

The application of multiple regression and path analysis is discussed in regard to the exclusive use of the beta coefficients. Beta is one of the possible ways of controlling for the effects of the remaining predictors, others are part and partial correlation, part and partial covariance. A typology is developed for the difference between total and...

Article

- Oct 2020

Path analysis was developed almost a century ago by geneticist Sewell Wright as a way to understand the relations among variables that goes beyond their correlations. While this method largely stayed in genetics and closely‐related fields, it eventually found its way into psychology in the later part of the twentieth century. This entry describes t...

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