In R it's pretty easy (if you know R)

Here an example:

# A test if two correlation matrices are equal

# Correlation matries obtained from:

#

# Ryan, J. J., Paolo, A. M., Miller, D. A., & Morris, J. (1997).

# Exploratory factor analysis of the Wechsler Adult Intelligence Scale-Revised in a sample of brain-damaged women.

# Archives of Clinical Neuropsychology, 12(7), 683-689.

#

# and

#

# Allen, D. N., Huegel, S. G., Seaton, B. E., Goldstein, G., Gurklis, J. A., & Van Kammen, D. P. (1998).

# Confirmatory factor analysis of the WAIS-R in patients with schizophrenia.

# Schizophrenia research, 34(1), 87-94.

# load R structural equation modeling package lavaan

library( lavaan )

# Varible names

# Replace with yours (separated by a space, no tabs )

varnames

This can be soon through Confirmatory Factor Analysis to examine a "moderation" effect due to the variable that creates your two sub-samples. This technique is explicitly designed to test the equivalence of two correlation (co-variance) matrices.

Thanks, David. The samples are completely independent (and 35 years apart). And there may be several variables that created the discrepancy. Do you have a reference?

I addition to David L Morgan's opinion 

see the attached file, please 

good luck 

Thank you, Salam, The tekst is useful in its own right but not in answering my question.

Confirmatory Factor Analysis is a very widely used methods, and you will find a great many citations on the internet. Unfortunately, it typically reqires its own separate program such as M-Plus or the AMOS module in SPSS.

Hello David, Yes I know (see my critique on CFA: https://www.researchgate.net/publication/280077456_CFA_as_a_tool_in_research_using_questionnaires_a_critique). The latent factor model of CFA does not apply to my questionnaire (on OCD), nor does the common factor analysis method. Still, CFA may suggest a way to compare correlation matrices that can tell me something about statistical significance of te diferences. However, without a specific reference that would be searching for a needle in a haystack. So any sugestion would be welcome.

Article CFA as a tool in research using questionnaires: a critique

The reason that searching for an article on this topic is like looking for a needle in a haystack is that the original work was done in the early 1970's. By this point, the basic idea of using CFA to teat the equivalence of correlation matrices is so taken for granted that almost no one cites a specific source. Instead, I would look at an introductory textbook on CFA or Structural Equation Modelling.

Thanks, I have Brown: CFA for applied research in my cupboard and will have a closer look. However, what I have in mind is not the equivalent of the residual matrix in CFA / SEM / common factor analysis. But, perhaps, the GOF-indices can be of service in my special case as well.

More than GOF measures, the tests for differences in chi-sq will show you the improvement between fitting one matrix to the entire population, versus allowing for differences between the two subpopulations

Mantel Test?

Interesting suggestion. I understand that the Mantel test is about the (significance of the) correlation between two matrices. A correlation ignores the differences between the means and the SDs of two sets of values of variables - which is what I am presently interested in -, but not the other types of deviations between the two matrices. So, perhaps, for another occasion...

Randomization test? The appropriateness of this suggestion assumes that you have sufficient replication.

In R it's pretty easy (if you know R)

Here an example:

# A test if two correlation matrices are equal

# Correlation matries obtained from:

#

# Ryan, J. J., Paolo, A. M., Miller, D. A., & Morris, J. (1997).

# Exploratory factor analysis of the Wechsler Adult Intelligence Scale-Revised in a sample of brain-damaged women.

# Archives of Clinical Neuropsychology, 12(7), 683-689.

#

# and

#

# Allen, D. N., Huegel, S. G., Seaton, B. E., Goldstein, G., Gurklis, J. A., & Van Kammen, D. P. (1998).

# Confirmatory factor analysis of the WAIS-R in patients with schizophrenia.

# Schizophrenia research, 34(1), 87-94.

# load R structural equation modeling package lavaan

library( lavaan )

# Varible names

# Replace with yours (separated by a space, no tabs )

varnames

Thank you, Kees Jan,

I am not yet familiar with R, though I intend to become so soon. All my own programming is still in BASIC (amazing what you can do with basic). So it is simply a chi square comparison of the corresponding correlations?

Regards, Peter

In a sense, but you don't estimate correlation matrix 1 - correlation matrix 2 or something. It's more like you compare matrix 1 and matrix 2 with the pooled correlation, although that's also not 100% correct, I think. But if the correlation matrices would be the same, their pooled correlation matrix is also the same, so you would get perfect fit. That would agree with a chi-square value of 0 and a p value of 1.

Thanks again

Hi Peter,

I was wondering if you solved your question already? I also have a similar question regarding the significance of two correlations recently.

In my case, I administered two different questionnaires to one sample, and got two correlations between each of them with another variable (r1 and r2). Based on this, what I want to do is to compare whether the two correlations are significantly different or not? do you have some ideas on this issue? Thanks in advance!

Best, Qian

Kees Jan and some others above provided an answer.

About your question: The answer is easily to find on the internet. For instance, try this link: http://vassarstats.net/rdiff.html

Good luck

Kees- Jan Kan where can I find commands which revolve around programm R?

Hello,

I examined correlation between X and Y at Time 1 and Time 2. Can I use Z score test for understanding whether there is a significant difference? If so, could you please send me a formula or online calculator if you have?

Thanks