John,

Thanks for reviewing.

The item questions, answer options, sample sizes and pass rates has been added in a table in the appendix (after references). Furthermore, a plot of the distribution of scores has been added to the main text.

A factor is really just a common source of variance. In this case, all items share variance, so it is possible to estimate a common cause of this shared variance, i.e. a common or general factor.

A summed score would in fact be very similar to the factor score. A factor score is a kind of optimally weighted mean. Since standardized measures such as correlations are not concerned with mean levels, the distinction between sums and means is irrelevant. When all correlations are positive, the correlation between a weighted mean and an unweighted mean score would be high. The difference is that the weighted score weighs having been arrested or been to prison higher than having cheated on an exam, as common sense would have it. In general, the rarer crime, the more serious it is and the higher factor loading.

I calculated a summed score. The correlation to the crime score, r=.75, is shown in the attached plot. Note that this value is not suited for analysis because the sample size is reduced to a mere n=2240. This is because a sum like this cannot take into account missing data, so one has to use only complete cases. If this wasn't the case, one could have used this variable with something like ordinal logistic regression. Nonetheless, I attach some plots of interest: 1) cognitive ability by crime sum and 2) distribution of crime sum scores. As can be seen, there is also a fairly linear negative relationship to see here. The correlation is -.13. I have added a discussion of this alternative approach to the paper.

Given all this, I think it is best to choose a single variable that best measures this underlying criminal factor that we are unable to measure well given the nature of the data. Since arrest history has a loading of ~1, this variable is the most suited.

I computed the group means for each of the crime variables as well as the group difference, shown below.

(The cognitive data are standardized, the above 0 values are due to selection. No everybody answers all the questions, smarter people tend to answer more.)

The gaps are not large, but they are roughly in the size order one would expect: Largest for prison, next largest for arrest (often means violence) and violence. Low for non-violence.

I have added this table to the paper.

I agree. The point with the study was to see whether the relationship could be seen i yet another context and to add 1 (or 5) more datapoints towards an eventual meta-analysis.

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The files have been updated.

Thanks for reviewing.

Quote:The measurement of cognitive ability remains unclear. It would be helpful to know the actual 14-items used to create the scale, their content, and distribution. As the core variable in the analysis more detail is necessary.

The item questions, answer options, sample sizes and pass rates has been added in a table in the appendix (after references). Furthermore, a plot of the distribution of scores has been added to the main text.

Quote:The criminal behavior measure is, of course, a bit limited but prior research shows that even content limited measures usually have good statistical and content validity. Given the items included, which range form minor forms of deviance (cheating on tests), to more serious indicators of criminal behavior (arrest/prison), the expectation that a uniform factor would be extracted seems misplaced. Yes, criminals are generalists and this is confirmed with the inter-item correlations, but you really do not have a sufficient number of items to produce a reliable, single factor.

I would suggest creating a summated index and comparing the results against the results of found using only arrest. The additional variance in the index would allow you to more closely examine how cognitive scores perform across the index. Is a score of zero on the crime index associated with a cognitive score that is significantly higher than ascending index scores?

A factor is really just a common source of variance. In this case, all items share variance, so it is possible to estimate a common cause of this shared variance, i.e. a common or general factor.

A summed score would in fact be very similar to the factor score. A factor score is a kind of optimally weighted mean. Since standardized measures such as correlations are not concerned with mean levels, the distinction between sums and means is irrelevant. When all correlations are positive, the correlation between a weighted mean and an unweighted mean score would be high. The difference is that the weighted score weighs having been arrested or been to prison higher than having cheated on an exam, as common sense would have it. In general, the rarer crime, the more serious it is and the higher factor loading.

I calculated a summed score. The correlation to the crime score, r=.75, is shown in the attached plot. Note that this value is not suited for analysis because the sample size is reduced to a mere n=2240. This is because a sum like this cannot take into account missing data, so one has to use only complete cases. If this wasn't the case, one could have used this variable with something like ordinal logistic regression. Nonetheless, I attach some plots of interest: 1) cognitive ability by crime sum and 2) distribution of crime sum scores. As can be seen, there is also a fairly linear negative relationship to see here. The correlation is -.13. I have added a discussion of this alternative approach to the paper.

Given all this, I think it is best to choose a single variable that best measures this underlying criminal factor that we are unable to measure well given the nature of the data. Since arrest history has a loading of ~1, this variable is the most suited.

Quote:Prior research seemingly converges to show that average IQ differences between delinquents and non-delinquents is around .5sd. For adult offenders, average differences around 1sd are common. How much difference are we seeing with this sample of older, probably better educated and less criminal, men and women?

I computed the group means for each of the crime variables as well as the group difference, shown below.

Code:

`non offender offender d`

0.34 0.04 0.29

0.44 0.06 0.38

0.31 0.06 0.25

0.26 0.16 0.10

0.20 0.08 0.12

(The cognitive data are standardized, the above 0 values are due to selection. No everybody answers all the questions, smarter people tend to answer more.)

The gaps are not large, but they are roughly in the size order one would expect: Largest for prison, next largest for arrest (often means violence) and violence. Low for non-violence.

I have added this table to the paper.

Quote:Low cognitive ability has repeatedly been linked with antisocial and criminal conduct. The relationship appears to be robust and not conditioned by the measurement of cognitive ability or problem behavior. In this sense, the findings presented here converge with other studies.

Lastly, the sample is clearly highly selected but I don’t see this as a problem. Yes, the sample is composed of older people who use the internet and a case can be made that subjects may be a bit brighter than comparatively situated others......but the effect of this type of selection would be to minimize variance on crime and cognitive measures. The results would thus be more conservative compared to samples that contain more variance in these measures.

I agree. The point with the study was to see whether the relationship could be seen i yet another context and to add 1 (or 5) more datapoints towards an eventual meta-analysis.

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The files have been updated.

**Attached Files**

score_vs_sum.png (Size: 43.14 KB / Downloads: 530)

crime_sum_ca.png (Size: 36.48 KB / Downloads: 494)

crime_sum_hist.png (Size: 66.59 KB / Downloads: 526)