Search Results

One thing that could be done is to use Fisher's $z$-transformation as described on MathOverflow, i.e. $$ \bar\rho = \tanh \left(\frac{\sum_{j=1}^K \tanh^{-1}(\rho_j)}{K} \right) $$ It reduces the skewness … Averaging Correlations: Expected Values and Bias in Combined Pearson rs and Fisher's z Transformations, The Journal of General Psychology, 125(3), 245-261. …

If I understand the question, you can compare Pearson correlations with a Fisher transform, also called a "Fisher's r-to-z", as follows. … A Fisher's r-to-z comparison indicated that the Pearson correlation for I. Setosa (r = 0.28) was significantly lower (p = 0.02) than I. Versicolor (r = 0.55). Similarly, the correlation for I. …

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. …

Considering the question of distance matrix transform it is also useful to inquire about how this or that clustering criterion reacts to transforming of matrix elements. … Clustering criteria based on ideology of “cophenetic” correlation (correlation between likeness of objects and their falling into same cluster). Point-biserial correlation is usual Pearson r. …

Well, it's different in that it's bound between -1,1, it doesn't have the proper distribution, so you need to Fisher transform it before doing inference (and back transform it afterwards, if you want to … And you do not even know the exact difference, even if you do some inference, e.g. by calculating the CI for the differences between the two correlations. …

There is actually quite a bit of a debate in the literature whether one should conduct a meta-analysis with the raw correlation coefficients or with the r-to-z transformed values. … On the other hand, the sampling variance of an r-to-z transformed correlation is approximately equal to: $$\text{Var}[z] = \frac{1}{n-3}$$ Note that this no longer depends on any unknown quantities. …

In a nutshell, a 95% confidence interval is given by $$\tanh(\operatorname{atanh}r\pm1.96/\sqrt{n-3}),$$ where $r$ is the estimate of the correlation and $n$ is the sample size. … Explanation: The Fisher transformation is atanh. …

Wikipedia has a Fisher transform of the Spearman rank correlation to an approximate z-score. Perhaps that z-score is the difference from null hypothesis (rank correlation 0)? … use the Fisher transform to get the 95% confidence interval? …

Note that this transform is non-linear. … It does, however, distort correlations and distances within and across features. …

I want to test a sample correlation $r$ for significance, using p-values, that is $H_0: \rho = 0, \; H_1: \rho \neq 0.$ I have understood that I can use Fisher's z-transform to calculate this by $ … My question is: how large $n$ should be for this to be an appropriate transformation? Obviously, $n$ must be larger than 3. …

My null hypothesis is that in the general population, this correlation is equal to zero. … coefficient (and let's assume we've obtained this using Fisher's transformation on the per-subject coefficients first) and $n$ the number of observations. …

Yes, it can be done, if you use Fisher's R-to-z transformation. Other methods (e.g. bootstrap) can have some advantages but require the original data. … The logical conclusion is that you probably don't even need a test at all (especially not a test of the so-called ‘nil’ hypothesis that the correlation is 0). …

This expression for $Z$ is recognizable as the Fisher transformation of $\rho$, and therefore is equivalent to $\rho$ for assessing linearity. … One can go further and demonstrate that, among all the possible invertible monotonic transformations of $Z$, $\rho = \tanh(z)$ enjoys a special relationship to measures of linearity in simple ordinary …

Let $z_A$ = the Fisher transform of the observed correlation of set $A$, $z_B$ = the Fisher transform of the observed correlation of set $B$. … For $i = 1,\dots,n$, let $y_{A_i} = nz_A- (n - 1)z_{A'i}$, where $z_{A'i}$ is the Fisher transform of set $A$ of the one-left-out correlation obtained by deleting $(x_i,y_i)$, re-ranking, and re-computing …

Maybe some additional remarks about the comment of @chl The Spearman correlation can be seen as a Pearson correlation of the ranks. … Ranks clearly do not follow a normal distribution, with the consequence that the variance of the Fisher transformation ($\zeta$) is not well approximated by $(n-3)^{-1}$ especially at large absolute values …