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Questions tagged [fisher-transform]

Fisher's z-transform is a transformation that is applied to the correlation coefficient, r, for use in hypothesis testing & constructing confidence intervals.

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Normality of $z$ transformation without preliminary assumption

Assuming data $X_1,...,X_n, Y_1,...,Y_n$ we have Pearson correlation $r=\frac{Cov(X,Y)}{\sigma_X\sigma_Y}$. Fisher's $z$ transform is then $$z=0.5\log\left(\frac{1+r}{1-r}\right)=\tanh^{-1}(r)$$ If $(...
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Fisher r-to-z transformation: comparing correlation coefficient of multiple samples

I am comparing the linearity of a regression model for two independent devices (n=10 each device group). The data is force (newtons) over time (seconds). The regression models show R^2 values of 0.9 ...
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Is Fisher transformation appropriate for magnitude squared coherence and phase locking value?

Fisher transformation, or hyperbolic arctangent, is recommend before performing arithmetic on correlation coefficients (e.g., estimating confidence intervals), because it makes their distribution ...
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Standard Error of Truncated Fisher's z Transform

I have a question regarding data following the truncated Fisher's z-transform. I currently understand that the correlation coefficient data, after the unbounded Fisher's z-transform, has a standard ...
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Polychoric Correlations to Fisher's Z Transformation

I'm interested in conducting a meta-analysis of polychoric correlation coefficients using metafor package in R. When performing a meta-analysis with Pearson ...
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Seeking Feedback on Mixed-Effects Model with Weighted Observations

I've been working on a project where I'm comparing different methods using a mixed-effects model, and I'd appreciate some feedback on my approach. Background: I have a dataset with several variables: ...
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Correlations can be compared with the Comparing Correlations ('cocor') package or R - but what if one of the variables is ordinal?

Let's say I want to compare the correlation of BMI and blood pressure in two independent groups and see, whether there is a difference between the correlations (whether the correlation is stronger in ...
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Can I compare Pearson's r and Spearman's rho with Fisher's r to z transformation?

I'm using the tool in the following website to compare correlation coefficients: http://vassarstats.net/rdiff.html The tool uses Fisher's r to z transformation to ultimately compare two correlation ...
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Fisher Z transformation still not normal

I have 18 different groups that I need to compare. I used the raw values from a neuroimaging file to represent synchronization between two brain regions (which ranged from 0 to 1) and Fisher Z ...
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I want to conduct some test on a large correlation matrix in r

The data I have is essentially the number of times two students were seen together. So student 1 and 3 were seen the most amount of times together, then 2 and 3, then 1 and 2. The correlation matrix ...
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Negative data for log transformation [duplicate]

I am analysing data on hourly electricity prices to try to do some forecasting, in my dataset I have mostly positive values, but some negative, around 20 per region for the two year duration. I want ...
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How to correctly compare 2 correlation values using the Fisher r-to-z transform?

In https://www.statisticshowto.com/fisher-z/, it is stated that “But it’s probably most commonly be used to test the significance of the difference between two correlation coefficients, r1 and r2 from ...
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Interpreting fisher’s Z transformation and correlations

Part of my planned analysis in a paper is testing the difference in strength of correlations between depression and other things like social relationships and quality of life. This test is set up with ...
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Z-transforming Pearson correlation vs. converting to mutual information: they seem to be related, but how?

EDIT: By noodling around a bit, I found that they can actually both be re-arranged into even more similar forms: $Z = -\frac{1}{2}(\ln(1-\rho) - \ln(1+\rho))$ $I =-\frac{1}{2}(\ln(1-\rho) + \ln(1+\rho)...
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A question about fisher's z transformation detail of his paper published in 1921

Typically, people will use Fisher's z-transformation (arctan) to turn the r into a variable that is approximately normally distributed. When I look though his paper published in 1915(https://www.jstor....
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How to meta-analyze latent correlations when r=1?

I compiled 11 correlations from k=11 studies. Let's just call the two variables $A$ and $B$. The correlations were very high and ranged in between $r=.54-.84$, but there is one study that reported a ...
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Confidence intervals for mean correlation

What is the correct way to define confidence intervals for the mean of multiple correlations? I understand how to calculate CIs for individual correlation coefficients, I also understand how to ...
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Significance test of Fisher z scores

There are 14 vectors given, each vector has approx 3000 components that take vast range of values. I'd like to determine how closely linked they are or whether an independence could be assumed. I ...
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In what order should I perform Fisher's r-to-z transformation and correction for range restriction and measurement error on correlation coefficients?

I have a two part question; both parts relate to correcting/transforming raw correlation coefficients for the purpose of a meta-analysis. Confirming my understanding of ...
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Fisher transformation for pearson allows building a different confidence interval than for spearman?

I'm confused by the wikipedia articles for Fisher transformation for spearman and pearson. It looks like for Pearson, the confidence interval is built around $\frac{1}{2}ln(\frac{1+\rho}{1-\rho})$ ...
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'rma.mv' function output- fisher Z or raw correlation

I would like to ask a question regarding the output of the rma.mv function. I had raw correlations which I transformed into Fisher's Z correlations using the 'escalc' function. Then, I performed a ...
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Fisher transformation

I am currently working with panel data, namely its correlations. The data is three-dimensional. I am looking for a way to aggregate the correlation coefficients. I found a model which uses the Fisher ...
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When testing Pearson's r, when should I use r-to-t transformation instead of [Fisher's] r-to-z' transformation?

At least two tests are common for testing the significance of a Pearson correlation coefficient. Comparing $t=\frac{\sqrt{r^2/(1-r^2)}}{\sqrt{\frac{1}{N-2}}}$ to Student's $t$-distribution with $N-2$ ...
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Why is fisher transformation necessary?

I read that the correlation coefficients have to be converted by using a fisher-transformation when one wants to test their significance (like here When is Fisher's z-transform appropriate? ). I ...
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Simple mean or weighted mean of Fisher z-transformed correlation coefficients

I need to perform the average of a set of correlation coefficients $\rho_i$ with $i=1,\ldots,m$. I follow the standard prescription: apply the Fisher z-transformation to my $\rho_i$ ($z_i$ are the z-...
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How to calculate Mean Sample-Based Reliability Estimates Used for Analyses

I am conducting a meta analysis of Pearson's r , of correlations presented between test scores and job performance ratings. I need to present an uncorrected effect size and an effect size corrected ...
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Average sample size of two fishers z correlations

I am conducting a meta analysis of Pearson's r correlations. As there are two correlations , sometimes three , for the same study and dependent variable I have averaged the correlations via fishers z ...
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Averaging of two or more standard erros

I have calculated two standard errors for two fishers z correlations from the same study , both measuring the same variable. Is it acceptable for me to average the two standard errors into one? If so ,...
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What is the name of this random variable?

Let $X \sim \text{Normal}(\mu, \sigma^2)$. Define $Y = \frac{e^X -1}{e^X+1}$. The inverse transformation is $X = \text{logit}\left(\frac{1+Y}{2}\right) = \log\left(\frac{1+Y}{1-Y} \right)$. By the ...
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Fisher Z transformation vs T-Test in cross sectional correlations

I want to compare the correlations of stock related measures. According to the paper referenced below, time series can be compared for statistically different correlations with the Fisher Z ...
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Fishers-R-to-Z - published study reporting value I can't replicate

I am reading a paper that reported a significant difference in correlation between age and some measure between groups. It looks like they calculated the Fisher's-R-to-Z wrong? I wonder if someone ...
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Fisher z test to compare correlations in a time series

I am running an analysis (in SAS, using proc corr fisher). http://core.ecu.edu/psyc/wuenschk/docs30/CompareCorrCoeff.pdf I basically want to know how different the correlations are on a daily basis ...
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Doing the equivalent of a dependent t-test on a sample of correlation coefficients

I’m doing an analogy of the following study. I take participants etc. and show them a picture of man 1 and have them rate his attractiveness and rate his intelligence just from his picture. I then ...
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fisher r to z test with different number of observations between variables.

Is there a way to test whether the correlation coefficient between two variables with a shard third variable is significantly different, if the sample sizes are different? Here is the case, ...
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Can someone explain the Fisher transformation and why it is used in layman's terms?

I am writing a paper on comparing different business cycles and have calculated bilateral correlation coefficients between individual countries and the overall aggregate. I have read in some of the ...
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Reporting Fisher-transformed Pearson's correlations when the magnitude of difference is relevant

My field regularly demonstrates a certain type of result with pairwise Pearson's correlation matrices between predicted and measured data. As soon as such correlations become high, Fisher-transforming ...
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Fisher R-to-Z transform for group correlation stats

I have independent correlation coefficient measures for each subject. I would like to test whether the correlation coefficient of the group is significantly different from 0. My understanding is ...
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Is Fisher's z transformation necessary when comparing the variances of correlation coefficients?

I am working on functional connectivity between brain regions, where functional connectivity is represented by the Pearson correlation coefficient between the time series (fMRI) of brain regions. I am ...
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Significance testing between two mean correlation values

I have collected 50 data points from 9 individuals for 4 variables, say, a,b,c,d. For each individual, I correlated ab and cd using a Pearson correlation. Aim: I would like to test whether across ...
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Difference Between Two Correlation Coefficients - questions

I’m working on an exercise to check if a difference between two correlation coefficients is significant. However, I have certain doubts after I did some reading about the topic. My data consists of 2 ...
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Averaging correlation coefficients

I am calculating Spearman correlations multiple times between individual data vectors that are not necessarily of the same length. So for example, ...
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Statistical significance test for averages of correlation coefficients

My setting looks like that I have several subjects $i$ (let's say 5) and for each subject I measure the lists/vectors $A_i$, $B_i$, $C_i$ and $D_i$. Then, for each subject $i$, I calculate the ...
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What is Bartlett's theory?

This neuroimaging paper has been cited thousands of times. In it, a method is proposed for computing the correlations among several seed regions and all other brain voxels. Part of this method ...
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Confidence interval for correlation

I know the confidence interval of an estimated correlation can be calculated after performing Fisher transformation. But I never figured out why. I also couldn't find the explanation online. Can ...
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Bootstrap confidence intervals

I write to you for 3 questions. I want to calculate confidence intervals on different measures of association (Pearson's correlation coefficient, Cramer's V and the Eta-square). I will make the ...
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Special case of Fisher Z for comparing two correlations

I'm a statistical consultant, one of my clients requested something I haven't heard of before: She wants to compare the correlation between X and Y (two ratio scaled variables) before an intervention, ...
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Fisher's z-transform in Python?

I want to test a sample correlation $r$ for significance ($n=16$), using p-values, in Python. As I have understood from this question, I can achieve that by using Fisher's z-transform. Is there a ...
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Calculating CIs for $\eta^2$ via Z scores - sample size?

In the thread Confidence Interval for $\eta^2$ it was proposed that if only limited statistics are available (in my case, F, df1, df2, means), one could calculate the 95% CI for $\eta^2$ by: ...
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Significance of average correlation coefficient

Disclaimer: if you find this question to be too similar to another one, I happy for it to be merged. However, I did not find a satisfactory answer anywhere else (and do not yet have the "reputation" ...
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Testing significant difference between two determination coefficients $R^{2}$ for two PLS-based structural equation models

Two structural equation models were tested (one was based on a sample with 199 individuals and the second one on a sample with 93 individuals). The aim was to test whether the results of the first ...
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