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# [ODP] The personal Jensen coefficient does not predict grades beyond its association

Journal:
Open Differential Psychology

Title:
The personal Jensen coefficient does not predict grades beyond its association with g

Authors:
Emil O. W. Kirkegaard

Abstract:
General intelligence (g) is known to predict grades at all educational levels. A Jensen coefficient is the correlation of subtests' g-loading with a vector of interest. I hypothesized that the personal Jensen coefficient from the subjects' subtest scores might predict grade average beyond g. I used an open dataset to test this. The results showed that the personal Jensen coefficient did not seem to have predictive power beyond g (partial correlation = -.02).

Keywords:

PDF.
All project files.
Cannot you use the difference between g score and IQ score? (g-IQ)?I guess it's very similar to the MCV but may produce slightly different results.
Correl. between iq-g and gpa should be negative.
If my memory is correct, "unit-weighted average" is just a simple average such as (a+b+c+d)/4. In general, I hate to read these terms. I know a lot of examples where the authors use different names to say the same thing. It's very confusing. By the same token, I'm not sure I will recommend you to use the term "Jensen coefficient". Even I, I don't appreciate "Jensen effect". As I said, adding more and more new terms can be very exhausting for those who read.

Quote:However, it's correlation with GPA is weak.

I think it should be "its correlation", no ?

Your syntax may have a problem, because at some point, it's said that the Omega function needs the package GPA rotation, which you didn't have in your list.

More important. Can you explain me this code ? I don't understand it (but I see that DFcompleteZ is the "subset" of the data).

Code:
```Jensen.coef = as.vector(rep(0, nrow(DF.complete.Z))) for (case in 1:nrow(DF.complete.Z)){   cor = cor(as.numeric(DF.paf\$loadings), as.numeric(DF.complete.Z[case,1:7]))   Jensen.coef[case] = cor }```

MH,

Quote: If my memory is correct, "unit-weighted average" is just a simple average such as (a+b+c+d)/4. In general, I hate to read these terms. I know a lot of examples where the authors use different names to say the same thing. It's very confusing. By the same token, I'm not sure I will recommend you to use the term "Jensen coefficient". Even I, I don't appreciate "Jensen effect". As I said, adding more and more new terms can be very exhausting for those who read.

Unit-weighted average just means that all the items have the same weight, i.e. a normal average. This is just to make it clear that one can weight averages in non-unit fashion as is done with factor scores.

It's linguistically inconvenient to use either "(anti)Jensen effeect" or the fully spelled out "MCV correlation with g-loadings". "Jensen coef." is pretty short and avoids the problems of the first.

Quote: I think it should be "its correlation", no ?

You were looking at an older revision. The newest one does already fixed that. :)

Quote: Your syntax may have a problem, because at some point, it's said that the Omega function needs the package GPA rotation, which you didn't have in your list.

The omega() function loads the required libraries itself. One does not need to load them beforehand. They need to be installed tho.

Quote:More important. Can you explain me this code ? I don't understand it (but I see that DFcompleteZ is the "subset" of the data).

Sure, here is a more annotated version.

Code:
```#Personal Jensen coefficient Jensen.coef = as.vector(rep(0, nrow(DF.complete.Z))) #set up an empty vector for personal Jensen coefs #same length as the others for (case in 1:nrow(DF.complete.Z)){ #loop over every number from 1 to the length of the dataset,  this needed since we need to refer to the indexes   cor = cor(as.numeric(DF.paf\$loadings), as.numeric(DF.complete.Z[case,1:7])) #calculate the personal Jensen coef.   Jensen.coef[case] = cor #insert it into the vector we created above } DF.complete.Z["Jensen.coef"] = Jensen.coef #put the results into the dataframe```

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I added a new revision with some changes changes as well as the metric Piffer suggested.
https://osf.io/gb3cy/
I want to be sure. The Jensen coefficient is calculated as follows : you take each person's z-score on all subtests (7) and the g-loading for these subtests as calculated for the entire group, and you correlate the z-score and g-loading for each person to get the Jensen coefficient. Am I correct ?

I don't see anything wrong in the article, and I want to approve, but I need to be sure about the above question.
Yes.

DF.paf is the factor analysis object. Using \$scores gets you the g-loading weighted scores per case. The DF.complete.Z object is the data.frame ("DF") with only complete data (hence "complete") which has been standardized (hence "Z"). The first 7 columns are the subtest scores, the 8th col is the GPA (hence "1:7").

A pity the metric doesn't work. We can try in project TALENT too, if that dataset has grades or some other criteria variable.
It's ok. I approve.

EDIT: it's really optional, but i think the article will gain much by explaining the implication of a positive correlation between Jensen coeff and other variables (g scores, GPA, full IQ, etc) and how it differs with g-loading. Most people do not know what is the Jensen coeff. And it's also new to me.
I approve
Jensen coef. is not new, it's just a new name. It is just to avoid awkward language when the ... eh (anti)Jensen effect goes in different directions or neither.

Positive Jensen coef. = Jensen effect.
Negative Jensen coef. = AntiJensen effect.
Null Jensen coef. = no Jensen effect.

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I ran one more analysis. Since people always call for research into the predictive power of non-g. I ran the partial correlations between subtests and GPA with g-factor partialled out. They were all pretty small.

ravenscore lretot nsetot voctot hfitot vantot aritot
-0.09 -0.06 -0.08 0.05 0.07 0.12 0.01

The largest is .12. N=289, so this has p=0.045. Likely a fluke.
New revision (#6) with the above results added in a new section. Nothing else changed.

https://osf.io/gb3cy/

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