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like a homework question (and I could be wrong), I will start by only providing a hint: There is a concise relationship between the product of the $z$-scores for two variables (say $x$ and $y$) and the correlation …

In path model analysis, the correlation between two variables connected via a third variable is calculated in this fashion. … The total correlation would be this value added to the values from any other valid paths in the model. …

of $u$ and $v$ to calculate the partial correlation.  … If you take the correlation of $u$ with $s$, you obtain the semi-partial correlation.  …

I am not certain a correlation is the best approach. I am making a number of assumptions on the nature of your data, so this approach may not be correct. …

I believe you are referencing the Fisher's z-transformation (as if you were referring to a test statistic for the correlation, it would be a t-ratio). …

Let me provide my answer using the tetrachoric correlation (which is the polychoric correlation when you have two dichotomous ordinal variables). … Now, if we assume the same thing for our 2nd variable, say $y$ (with an underlying $\eta$ variable), then we call the correlation of $\xi$ and $\eta$ the tetrachoric correlation. …

The correlation you reference in your question is between the independent and dependent variable. … However, you could also reference the correlation between the dependent variable and the predicted values for this variable using the independent variable(s), $R= \text{cor}(y,\hat{y})$. …

But, Pearson's correlation is a defined quantity. As such, it is what it is, and the value itself does not have any assumptions. … But, the real reason people might argue that this is an assumption is because the correlation is often used as a measure of the linear relationship. …

If you wish to test if two correlations from two samples for independent pairs of variables are different from each other, the null hypothesis statistical test (NHST) appropriate for this would be the …

The reason for this is that the distribution of the correlation coefficient is nearly normal with the transform. …

It is possible to run a CFA where there is a non-zero correlation estimated between the two latent factors. … Assuming these values are all from a population with zero correlation, some positive and negative small values would be expected. …

If you look only at the direct effect of $x_3$ on $y$, you will see a strong positive correlation. However, this ignores the other variables that may/may-not be influencing $y$. … Conceptually, if you take the residuals from predicting $y$ form everything by $x_3$ and the residuals from predicting $x_3$ with everything (but $y$, of course), these residuals have a negative correlation …

(Not sure why you would want to test if the aggregated sample correlation matrix on its own...but if you did, multiple by 3 instead of 2.) … If you have three times points, then you probably would want to assess the correlation for each scale at each pair of time points. …

I am going to propose a very pragmatic protocol based on the following rationale: a high number of high average ratings should be ranked very high a low number of high average ratings probably should …