Chapter 21 Correlation
A correlation coefficient is an estimation of the degree to which two variables have a linear association, and is the square root of their mutual proportions of explained variance.
21.1.1 Example dataset
From this dataset, this example uses variables
highDose_AttDesirable_euphoria; these are a number of expressions of which effects people prefer when using MDMA (see Chapter 1).
21.2 Input: jamovi
In jamovi, use the ‘Regression’ menu, choose ‘Correlation matrix’, and select the variables you want to include.
You can check the checkbox for confidence intervals to order confidence intervals.
21.3 Input: R
Many analyses can be done with base R without installing additional packages. The
rosetta package accompanies this book and aims to provide output similar to jamovi and SPSS with simple commands.
21.3.1 R: base R
A basic correlation matrix can be produced with
cor(), passing argument
use="complete.obs" if there are missing values in the dataset (otherwise, missing values result in a correlation estimate that it also missing).
To obtain confidence intervals for a correlation,
cor.test() can be used. However, this function only works for one correlation.
21.3.2 R: rosetta (
A correlation matrix function has not yet been made available in the
rosetta package, but it is available in the
ufs package that comes installed with
rosetta. Therefore, if you have
rosetta installed, you can use the following command.
This function provides the confidence intervals (the confidence level, by default \(95\%\), can be set with argument
conf.level) as well as the point estimates and associated \(p\)-values. The \(p\)-values are corrected for multiple testing (using the false detection rate approach by default; this can be set using the
correction argument; for example, pass
correction="none" to not correct the \(p\)-values), and sample sizes are printed as well if they differ for each comparison (and omitted if they are the same for all correlation coefficients).
21.4 Input: SPSS
For SPSS, there are two approaches: using the Graphical User Interface (GUI) or specify an analysis script, which in SPSS are called “syntax”.
21.4.1 SPSS: GUI
Click the “Analyze” menu, then select the “Correlate” submenu, and then select “Bivariate”. Then specify the variables you’re interested in.
21.4.2 SPSS: Syntax
CORRELATIONS /VARIABLES = highDose_AttDesirable_long highDose_AttDesirable_intens highDose_AttDesirable_intoxicated highDose_AttDesirable_energy highDose_AttDesirable_euphoria .
21.5 Output: jamovi
21.6 Output: R
21.6.1 R: base
A correlation matrix (note: the variable names have been manually shortened, and the resulting correlations have been rounded to four decimal places, to make this example fit in the book):
long intens intoxi energy euphor long 1.0000 0.5724 0.3737 0.3885 0.4663 intens 0.5724 1.0000 0.5843 0.3476 0.3441 intoxi 0.3737 0.5843 1.0000 0.3519 0.1474 energy 0.3885 0.3476 0.3519 1.0000 0.4772 euphor 0.4663 0.3441 0.1474 0.4772 1.0000
The results of
cor.test() including the confidence interval:
Pearson's product-moment correlation data: dat$highDose_AttDesirable_long and dat$highDose_AttDesirable_intens t = 10.068, df = 208, p-value < 2.2e-16 alternative hypothesis: true correlation is not equal to 0 95 percent confidence interval: 0.4737307 0.6568901 sample estimates: cor 0.5724077
21.6.2 R: rosetta (ufs)
Note: the variable names in the first column have been adjusted to make the table fit, and make the labels consistent with those in Chapter 22.
|Prefer long effects|
|Prefer intense effects||r=[0.47; 0.66], r=0.57, p<.001|
|Prefer more intoxication||r=[0.25; 0.48], r=0.37, p<.001||r=[0.49; 0.67], r=0.58, p<.001|
|Prefer more energy||r=[0.27; 0.5], r=0.39, p<.001||r=[0.22; 0.46], r=0.35, p<.001||r=[0.23; 0.47], r=0.35, p<.001|
|Prefer more euphoria||r=[0.35; 0.57], r=0.47, p<.001||r=[0.22; 0.46], r=0.34, p<.001||r=[0.01; 0.28], r=0.15, p=.033||r=[0.37; 0.58], r=0.48, p<.001|
21.7 Output: SPSS
21.8 Read more
If you would like more background on this topic, you can read more in these sources:
- More options for creating scattermatrices in R are available here: http://www.sthda.com/english/wiki/scatter-plot-matrices-r-base-graphs