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I have previously asked this question but should have provided more detail on the question.

I have been presented with multiple choice test results relating to intelligence and overall job performance test scores. I have been asked to test significance and strength of the link between scores on the first test and subsequent job performance scores.

I first checked for assumptions for correlation and decided that a Pearson r was most appropriate.

Results show r(25) = +0.33, p = 0.11 , which means a moderately strong correlation but not significant.

I am also required to relate the results to the test author's claims that the test user is able to make excellent predictions about the future job performance of the test taker. It has been designed to be sensitive to differences in intelligence within a graduate population and the test is free from adverse impact and has superb test-retest reliability.

Am I correct in thinking that the results of a Pearson r would not allow me to relate to the test user's claims as it would not be permissible to comment on any causality between the variables and that I should only report the results from the test stating a correlation and non significance?

Also are there any further tests I should conduct as a result of there being non-significance please?

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    $\begingroup$ Minimally posting a revised question requires an explicit cross-reference so that people can easily see what has already been said. stats.stackexchange.com/questions/257468/… (Usually, it is better to rewrite the original.) $\endgroup$
    – Nick Cox
    Commented Jan 28, 2017 at 16:00

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With that small a sample size it is not possible to provide a firm answer about the strength of the link. You could compute a confidence interval and you probably will conclude that both a strong link and even a slight negative link are consistent with the data. As far as significance is concerned, it looks like you computed that correctly.

As far as the quality of predictions, r is only an indirect measure of that because it is also sensitive to the variance of X and slope. Better would be the standard error of the estimate or perhaps the average absolute error of prediction.

P. S. This is probably not the answer your instructor is looking for.

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  • $\begingroup$ thanks David , all I need to do is report the significance and strength of the link between the two scores and , if relevant , comment on how these relate to the claims of the test author $\endgroup$
    – laboh
    Commented Jan 28, 2017 at 22:37
  • $\begingroup$ So , does this result mean that I can report there is a link between the two sores but this has happened by chance , and so this means that the first test is not a good predictor of overall job perfromance? $\endgroup$
    – laboh
    Commented Feb 1, 2017 at 19:25
  • $\begingroup$ also , I have been asked to describe any additional analysis that I think needs to be carried out in order to provide a more rigorous examination of the claims made by the test publisher, Including my opinion on the suitability of the test for graduate recruitment , with which I am struggling $\endgroup$
    – laboh
    Commented Feb 1, 2017 at 19:28
  • $\begingroup$ You can't say the correlation in the sample was due to chance but rather that that size correlation could easily have happened by chance. The data provide no evidence for a strong relationship. As far as other analyses, I would mention the confidence intervals I referred to earlier. Also, it is always wise to plot the data to see if the relationship is approximately linear and/or whether any observations have undue influence. $\endgroup$
    – David Lane
    Commented Feb 1, 2017 at 20:09
  • $\begingroup$ Thanks David , so if I am stating that there is a positive correlation between the first test and overall performance then this means that the first test is a good predictor of overall job performance $\endgroup$
    – laboh
    Commented Feb 1, 2017 at 20:57

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