You may not be able to get the desired results if you use T-Test for that type of data. The data you have right there is basically Ratio. Therefore, you may need to just make use of Hierarchical Cluster Analysis or Hierarchical Regression. You can as well try to get he data structure of the two periods' inter-item Correlation matrix and use it to explain the difference in the two periods. This coul be done using Factor Analysis.

Hello Jan,

The first question is, do you wish to make an omnibus comparison (is the set of correlations pre-covid equal to the set of correlations post-covid) or compare each of the 171 correlations individually?

In general, deriving an appropriate test for independent correlations (whether single values or matrices) is simpler than for dependent correlations.

Independent/matrix comparisons:

1. https://www.jstor.org/stable/2284596

2. Box's M test (though sensitive to non-normality)

3. Compute correlation of the correlations, or apply a permutation test.

(Examples: https://towardsdatascience.com/how-to-measure-similarity-between-two-correlation-matrices-ce2ea13d8231)

4. SEM-based: https://docs.tibco.com/pub/dsc-stat/14.0.0/doc/html/UsersGuide/GUID-61BA4549-6CB9-4797-93BE-B8AB4BE45390.html

Independent/single comparisons:

1. Fisher's method: https://garstats.wordpress.com/2019/06/17/compindcorr/

Dependent/single:

1. https://www.jstor.org/stable/2284252

2. https://www.jstor.org/stable/2529435

3.

Article Comparing Dependent Correlations

Good luck with your work.

This question was already on ResearchGate in 2017:

https://www.researchgate.net/post/Significance_of_the_difference_between_two_correlation_matrices

also in 2018:

https://www.researchgate.net/post/How_comparing_two_correlation_matrices

For comparing 2 covariance matrices:

https://www.researchgate.net/post/Does_anybody_know_some_good_metric_for_comparing_of_two_covariance_matrices

An alternative way is to use the goodness of fit chi-square. You have 171 corrlelations. As far as I can see (your jpg attachment is not very clear) all of them are larger druring pandemeic than before. The chi-square for the goodness of fit is obiously significant:

In R:

covid

covid

To test for a statistically significant difference in correlation coefficients between stock prices before and during the pandemic, you could use Fisher's z-test, the chi-squared test, or the bootstrap method. These tests are more appropriate for comparing correlation coefficients than a t test, as they account for the non-normal distribution and potential inequality of variances of correlation coefficients. However, it is important to consider the assumptions and limitations of each method, as well as properly interpret the results in the context of your data and research question(s). The following read might be helpful.

Wu, J., Zhang, C., & Chen, Y. (2022). Analysis of risk correlations among stock markets during the COVID-19 pandemic. International Review of Financial Analysis, 83, 102220. https://doi.org/10.1016/j.irfa.2022.102220

Good luck,