Dear Ishrat Sharmin

Read the following stuff as the authors provided the table about the population and sample size.

Krejcie, R. V., & Morgan, D. W. (1970). Determining sample size for research activities. Educational and Psychological Measurement, 30(3), 607–610. https://doi.org/10.1177/001316447003000308

Fleiss, J. L., Cohen, J., & Everitt, B. S. (1969). Large sample standard errors of kappa and weighted kappa, Psychological bulletin, Vol. 72 No. 5, pp. 323.

https://doi.org/10.1037/h0028106

Best of luck

Best regards

Dr. Muhammad Yousaf

This seems to be a least squares regression problem. If so each combination of DV and the IVs is what you use in G*power. NOT all of them individually. Best wishes David Booth

As David Eugene Booth wrote, for multiple linear regression, you would typically want to know the optimal sample size for the entire model including all predictors. In G*Power, the relevant effect size measure is f-squared, which can be directly computed from the overall R-squared in G*Power by clicking on the "Determine" button. See the screenshot above. You would compute f-squared only once (for the entire model with all predictors), not for each predictor separately.

Is nobody bothered by the fact that there are 22 predictors?

Yes Rainer Duesing, that caught my eye too. And if one were to follow Frank Harrell's 20:1 rule of thumb (to avoid over-fitting), that would require a sample size of 440 even if G*Power suggested a smaller n was needed to detect an f2 of a certain size.

https://discourse.datamethods.org/t/author-checklist/3407

Dr During, we don't know the name of the student or of the school or the subject area.where the question arises. It would be presumptuous of us to say how many predictors are too many. In my current area, of work, disease risk risk factors it's common to see the possible factors are every factor they could possibly think of and then they run backward elimination to name the actual risk factors. As long as I don't know what the student is doing or what the advisor suggested I'm not going to criticize the number without knowing more about the what the plan is. Best wishes to all, David Booth.

Here's a reference that discussed that issue. Best wishes David Booth

David Eugene Booth I did not criticize the approach per se, but I this is something that bothered me and I felt that this should be pointed out and considered. I can only talk about my experiences in psychology and social sciences and in this area, I can hardly come up with an example, which used 22 unique, nearly uncorrelated predictors. The OP did not tell us what these variables are, but maybe "only" single items for the same factor? And as I said, it's not critique, but a hint that there may be other problems than how to use G*Power.

And I think your example with lots of predictors and a selction approach does not hit the nail on the head, since the OP specifically asked for a multiple regression approach and not selection. Therefore, I think he wants to estimate all predictors simultaneously.

David, you can view the original poster's profile here:

• https://www.researchgate.net/profile/Ishrat-Sharmin-3

Also, I am trying to work out whether or not you are endorsing old-fashioned backward elimination. I don't think you are, given other statements you have made in the past. And the article you attached does not seem to me to be giving it a ringing endorsement as a general variable selection method either. E.g., here are a couple paragraphs from the Discussion section (with boldface added).

Our simulation results show that, compared to estimating a model with all prespecified confounders, application of backward elimination was unlikely to reduce the MSE of the exposure effect estimator (defined as the cOR and the mRR), while introducing a bias. We identified some settings in which the MSE of the effect estimators was lower with backward elimination than without, yet the reduction in MSE was small. The results are driven by two antagonist effects: an MSE-reducing effect of omitting weak confounders, and an MSE-increasing effect caused by additional uncertainties incurred by applying automated selection as explained by Heinze et al (2018).

And later...

We conclude that backward elimination for confounder selection is unlikely to have added value when an initial set of covariates related to the exposure and/or outcome can be specified based on background knowledge. If researchers choose to perform backward elimination of potential confounders, selection should be justified, for example, because a large number of potential confounders are anticipated to function as (near-)instruments, and the approach should be prespecified in a statistical analysis plan. Covariate selection based solely on statistical criteria should be avoided due to the possible selection of mediators and colliders. Irrespective of whether or not covariate selection strategies are being applied, we recommend to always provide information about the assumed causal structure, ideally by a depiction of assumed causal dependencies, but at least by excluding mediators and the possibility of unmeasured confounding.

The most positive statement I know of about backward elimination is in this excerpt from Babyak (2004).

Automated selection algorithms that do make the appropriate corrections, such as the lasso method by Tibshirani (17), have been developed, but they are not yet widely available. If you absolutely insist on using a stepwise algorithms, simulations by Steyerberg et al. (14) showed that the least harmful of the approaches is probably backward selection using a very liberal p value criterion, say .50, again paying careful attention to the guidelines for sample size and the number of predictors. The authors argue that this is probably because when we have too many candidate predictors for the sample at hand, there is not much power to detect important predictors. The liberal criterion p value compensates by making it more likely that truly important predictors will be retained in the model. However, there is still the problem of many unimportant variables being included in the final model, but these simulations suggest that, under these particular circumstances, the inclusion of true predictors via the liberal entry criterion outweighs the problem of including unimportant variables.

https://people.duke.edu/~mababyak/papers/babyakregression.pdf

PS- In case you are not familiar with Babyak, note what he says about his article in one of the opening paragraphs.

The ensuing text is taken from a workshop I recently presented to the members of the American Psychosomatic Society (2) and was intended for a nontechnical audience. I have purposely retained this nontechnical flavor and the informal language here so that these often esoteric ideas may be more accessible to a wider audience. Virtually none of the ideas I present here are my own. I am reporting the work of many others, explaining them in a way that I hope is understandable to readers of varying backgrounds and levels of expertise in data analysis. Specifically, the vast majority of this article is based on a relatively new statistical text by Harrell (3), who was responsible for my initial exposure to these ideas, and who continues to be a source of clarification and encouragement in my own pursuit of understanding these issues. Virtually all of the ideas presented here are discussed in much greater detail in the Harrell text (3).

Dr Duesing, Thanks for the reply. But If I recall the now discredited backward elimination method the first fit is with the full model which if used with the discussed data would have all 22 predictors in it which I believe is your assumption and thus essentially your model would be run. Thus it would seem that my comment was appropriate by your criteria. But my point was really that it's not good science to criticize a research design on anything but the actual design not our assumptions about it. The key thing is the research proposal. Best wishes David Booth