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Can you take an average of correlations?
Correlations coefficients cannot be averaged in the arithmetic sense as they are not additive in the arithmetic sense. This is due to the fact that a correlation coefficient is a cosine, and cosines are not additive.
What is an average correlation?
The average correlation coefficient of a correlation matrix is a useful measure of the internal reliability of the set of variables in the matrix. Moreover, it is a (gross) measure of predictiveness of the variables – when the correlations are with respect to a target variable.
How to calculate the correlation between X and Y?
The dash lines in the graph above represent linear regression for each data series (experimental setup) and the numbers in the legend denote the Pearson correlation of each data series. I would like to calculate the “average correlation” (or “mean correlation”) between X and Y. May I simply average the r values?
Is the average correlation in a paper meaningul?
Here’s a paper and the wikipedia entry. The average correlation can be meaningul. Also consider the distribution of correlations (for example, plot a histogram).
When is the correlation with the stock market highest?
Correlation tends to be highest during periods of high inflation expectations. On the flip side, correlation is typically lower during periods of low inflation expectations or high stock market volatility. These factors contributed to negative correlation in 1998 during the Asian Financial Crisis.
Which is the best way to transform Pearson correlation coefficients?
For Pearson correlation coefficients, it is generally appropriate to transform the r values using a Fisher z transformation. Then average the z -values and convert the average back to an r value. I imagine it would be fine for a Spearman coefficient as well. Here’s a paper and the wikipedia entry.