## Solved – Correlation between two Likert items with a non-monotonic relationship

One of the assumptions for Spearman correlation is that there is a monotonic relationship between the two variables. I've created a scatterplot for two Likert item variables, but it seems impossible to get the desired monotonic plot. Must the monotonicity assumption be met for me to calculate the Spearman correlation? My second question is, can … Read more

## Solved – How to convert \$eta^2\$ to Pearson’s r

I am doing a meta-analysis of associations between sets of variables that are essentially all continuous. However, many studies operationalised them at 'lower' levels, and I have (converted to) most effect sizes you can think of (Cohen's \$d\$, Pearson's \$r\$, Cramer's \$V\$, \$eta^2\$, \$omega^2\$, and \$OR\$'s). Converting between most of these is no problem (that … Read more

## Solved – Determining trend significance in a time series

I have some time series data and want to test for the existence of and estimate the parameters of a linear trend in a dependent variable w.r.t. time, i.e. time is my independent variable. The time points cannot be considered IID under the null of no trend. Specifically, the error terms for points sampled near … Read more

## Solved – Permutation test for multiple correlation test statistics

I read some great discussions about using permutation tests on correlation matrices to deal with Type I errors that arise from the multiple comparisons; however I have a question about the correlation test statistic. Specifically, what do you think about running a permutation test on a correlation matrix using multiple correlation test statistics? Can it … Read more

## Solved – Why does \$r^2\$ between two variables represent proportion of shared variance

Firstly, I appreciate that discussions about \$r^2\$ generally provoke explanations about \$R^2\$ (i.e., the coefficient of determination in regression). The problem I'm seeking to answer is generalizing that to all instances of correlation between two variables. So, I've been puzzled about shared variance for quite a while. I've had a few explanations offered but they … Read more

## Solved – Is it allowed to use averages on a dataset to improve correlation

I have a dataset with a dependent and an independent variable. Both are not a time series. I have 120 observations. The correlation coefficient is 0.43 After this calculation, I have added a column for both variables with the average for every 12 observations, resulting in 2 new columns with 108 observations (pairs). The correlation … Read more

## Solved – Mahalanobis distance via PCA when \$n<p\$

I have an \$ntimes p\$ matrix, where \$p\$ is the number of genes and \$n\$ is the number of patients. Anyone whose worked with such data knows that \$p\$ is always larger than \$n\$. Using feature selection I have gotten \$p\$ down to a more reasonable number, however \$p\$ is still greater than \$n\$. I … Read more

## Solved – invariance of correlation to linear transformation: \$text{corr}(aX+b, cY+d) = text{corr}(X,Y)\$

This is actually one of the problems in Gujarati's Basic Econometrics 4th edition (Q3.11) and says that the correlation coefficient is invariant with respect to the change of origin and scale, that is \$\$text{corr}(aX+b, cY+d) = text{corr}(X,Y)\$\$ where \$a\$,\$b\$,\$c\$,\$d\$ are arbitrary constants. But my main question is the following: Let \$X\$ and \$Y\$ be paired … Read more

## Solved – invariance of correlation to linear transformation: \$text{corr}(aX+b, cY+d) = text{corr}(X,Y)\$

This is actually one of the problems in Gujarati's Basic Econometrics 4th edition (Q3.11) and says that the correlation coefficient is invariant with respect to the change of origin and scale, that is \$\$text{corr}(aX+b, cY+d) = text{corr}(X,Y)\$\$ where \$a\$,\$b\$,\$c\$,\$d\$ are arbitrary constants. But my main question is the following: Let \$X\$ and \$Y\$ be paired … Read more

## Solved – How to quantify correlation stability

In many financial models we are interested in measuring the correlation between variables, returns etc. However, research shows that during crises times we observe "Correlation Breaks" where previously un-correlated variables become correlated. What is the best way to quantify "stability of correlation" by examining the historic time series of the variables on which I am … Read more