The strength of a correlation is given by its value; the closer the absolute value is to 1 the stronger it is.

You may also wish to test the reliability of the coefficients obtained. Benjamin's test will help you decide whether there is a significant difference between two correlation coefficients.

ANCOVA.

Also t-test.

T-test to figure out whether two correlations are significantly different. How ?

t = (coeff1-coeff2)/SE

Also see this: http://www.philippsinger.info/?p=347

"For the independent case, one basically uses Fisher's z-transformation for correlation coefficients [3] and then tests the null hypothesis that p1 - p2 = 0 using the Student t-test."

And this: http://core.ecu.edu/psyc/wuenschk/docs30/CompareCorrCoeff.pdf

Thank you everybody and particularly Benjamin for this useful and efficient link. My correlations do not differ from each other. Thank you again.

Vahid pointed you to a document on Karl Wuench's nice website. Karl and I actually wrote an article describing the common methods for comparing correlations and OLS regression coefficients. Those with institutional access to "Behavior Research Methods" can download it here: http://link.springer.com/article/10.3758/s13428-012-0289-7#close. (Note that there is also an Errata document: http://link.springer.com/article/10.3758/s13428-013-0344-z). The supplementary material includes SPSS syntax and SAS programs, which can be downloaded from the following pages:

https://sites.google.com/a/lakeheadu.ca/bweaver/Home/statistics/spss/my-spss-page/weaver_wuensch

http://core.ecu.edu/psyc/wuenschk/W&W/W&W-SAS.htm

I hope this helps.

Answer withdrawn

Answer withdrawn

Regression analysis gives you indication about the contribution of each factor on the formation of the formula for each variable. I believe this is what you want.

For those who down voted my answer, please remember that only by recognizing our weakness and our long-held but erroneous belief that we shall improve. Let us not continue and multiply this blunder to our students and among our peers. Please review your statistics please.

Answer withdrawn

Answer withdrawn

.

Alex is right, what I wanted was to figure out whether two correlations are SIGNIFICANTLY different from each other. One was .62 and the other .68. Given my limited number of participants, the outcome of the formula that was given first by Benjamin and commented by the others is that my two correlations do not differ from each other and that, consequently and unfortunately for me, the second is not stronger than the first one.

Thank you all for your help and thank you Ed for your comments.

Regarding this sentence of yours: "unfortunately for me, the second is not stronger than the first one"

Note that the absence of evidence is not the evidence of absence. Your case is the absence of evidence. So you cannot say "the second is not stronger". You should say "I don't know if the second is stronger or not (in real population)".

I agree with Eddie. The second correlation is obviously stronger than the first correlation. The lack of significance means that we cannot generalize the current answer (that correlation 2 is stronger than correlation 1) to the real population. It does not mean at all that the second correlation is not stronger.

Down-voting option is good, but it shouldn't be anonymous. I was surprised my correct answer was downvoted twice!

Hi Alex and thanks for upvoting me :-)

I completely agree with your point that we should not compare things without statistically verifying our comparison. I have actually a recent letter on this issue (among other points): https://www.academia.edu/5520280/On_automatic_landmarking

plus a recent (unpublished) letter, again pointing out the same thing: https://www.academia.edu/6329305/On_the_report_and_statistical_problems_of_a_metal_ion_release_study

So you can see I didn't make up this right now. I too am rather concerned about unsubstantiated comparisons that are clouding the science and even get cited or used later. They sometimes become dangerous especially in health sciences.

However, I saw Catherine is saying "...the outcome of the formula that was given first by Benjamin and commented by the others is that my two correlations do not differ from each other and that, consequently and unfortunately for me, the second is not stronger than the first one."

So I wanted to tell her that no, you shouldn't and technically can't say "my two correlations do not differ from each other", but should say "I don't know about the real population". This was why I brought it up.

edit: and found Eddie's answers in line with this issue. I think he was indicating that "comparison" differs from "statistical comparison". This is another subtle but important issue that is quite overlooked in many fields. Even at some points, the simple comparison (without any statistical verification) gets as important as or even more important than statistical comparisons. For example, in small or pilot studies, or when dealing with practical significance or clinical significance.

Catherine's study is a good example. Its result seems non-significant. But given its low test power, should we rely on it? Or should we also take into account the difference itself too? it is hard to tell without more detailed information regarding her study. But if it was real small, I would go with the second option and would count on the non-significant difference too.

We had a discussion on ResearchGate previously and many people agreed that P value and statistical significance (if treated blindly) is nothing but dangerous garbage.

I'm aware that I cannot draw definite conclusions from a null result. My analysis is just telling me : Given your results and the number of participants in your study, I cannot tell you that one of your correlation is stronger than the other.

And still I've got to say "Thank you dear analysis"

:-)

Answer withdrawn

Answer withdrawn

Consult

Kulback, S. Information theory and statistics (Wiley: NY, 1959), pp. 320-324.

For bivariate populations the test formula (Eq. 5.20, p. 321) is simple and is distributed as non-central chi-squared.

Donald Laming

Hi Catherine.

The easiest approach is to estimate confidence intervals for the two estimated sample correlation coefficients. if the two CI do not overlap, then the correlations are different. Otherwise, you do not have evidence to say that they are different.

Hi Jaime. The method you propose can mislead, because there can be a statistically significant difference (at the .05 level) between two point estimates despite overlap in the two 95% CIs. For example, see this short note from CMAJ:

http://www.cmaj.ca/content/166/1/65.long

That note talks about means, but the same point applies to correlations or any other statistic you might compare (e.g., odds ratios, etc).

If you want to use a CI method, you need a CI for the DIFFERENCE between the two correlations. If the CI for the difference does not include a value of 0, then the difference is statistically significant at the .05 level. The SPSS and SAS programs I mentioned earlier in this thread do compute the usual tests for comparing two correlations, but also compute CIs for the differences. The SPSS syntax and corresponding SAS programs can be downloaded at the links shown below.

https://sites.google.com/a/lakeheadu.ca/bweaver/Home/statistics/spss/my-spss-page/weaver_wuensch

http://core.ecu.edu/psyc/wuenschk/W&W/W&W-SAS.htm

I hope this helps!

?

Catherine,

Check this link, the describe an easy test for the equality of two sample correlation coefficient using Fisher's Z transformation

http://www.lesn.appstate.edu/olson/stat_directory/Statistical%20procedures/Correlations/a_test_of_the_equivalence_of_two.htm

Use the Fisher's Z-transformation when you are comparing correlation coefficients from 2 independent groups (e.g. between control and experimental groups). However, use Hotelling's t for comparing correlations within a sample.

A handy calculator can be found at http://psych.unl.edu/psycrs/statpage/ (click on computators link and download FZT application)

I am not sue If it is a master level project or a doctoral level dissertation. Depending on the research question analysis needs to be done. You could use mixed method.

You could also do triangulation to draw conclusion.

This is the page I use for doing Fisher's Z transformations to compare correlation coefficients http://vassarstats.net/rdiff.html 

Thank you!

You can apply the SPSS software in order to compute the correlation matrix.

Good Luck.