Use this tool whenever you want to know how two sets of variables relate to each other at the same time, for example a set of predictors (motivation, self-efficacy, study time) against a set of outcomes (exam, course and project scores). It suits psychology and education, biology and plant science, ecology, and health research that reports canonical correlations in APA 7 format. Upload your data below (CSV or Excel, or paste it), assign the variables to Set X and Set Y, and run the analysis.
About canonical correlation analysis
Canonical correlation analysis (CCA) measures the association between two sets of variables. Instead of correlating single variables, it builds a weighted combination of the variables in each set, called a canonical variate, so that the two variates correlate as strongly as possible. This first pair forms the first canonical function. The next pair is built to be uncorrelated with the first and to correlate as strongly as what is left, and so on, until there are as many functions as variables in the smaller set.
When to use it
Use CCA when you have two groups of continuous variables and want one analysis of how they relate, for example learning behaviours and academic results, soil properties and plant traits, or symptom scales and functioning scales. With one variable in a set it reduces to multiple regression, and with one variable in each set to a simple correlation, so it is most useful when both sets have two or more variables.
What this calculator reports
Canonical correlations (Rc) and squared canonical correlations (Rc²) for every function.
Wilks’ Λ with Bartlett’s χ² test of dimensionality, so you can see how many functions are statistically significant.
Standardized canonical coefficients and structure coefficients (canonical loadings) for both sets.
Variance extracted and redundancy indices.
A bar chart of the canonical correlations and a plot of the first pair of canonical variates.
A ready-to-use APA7 results paragraph and APA7-style tables you can download as a Word file.
Assumptions to check
The relationships between variables are roughly linear and the variables are approximately normal, without extreme outliers.
Variables inside one set are not almost perfectly correlated (multicollinearity makes the coefficients unstable).
The sample is large enough. A common guideline is at least 10 to 20 cases per variable.
How to report it in APA7
State the two sets and the sample size, report the full-model test (Wilks’ Λ, χ², degrees of freedom and p), then give the canonical correlation and shared variance of each significant function, and interpret the variables using the structure coefficients. The calculator writes this paragraph for you and lays out the tables in APA7 style.
Frequently asked questions
Is the Canonical Correlation Analysis calculator free?
Yes. You can run the analysis and read the results without an account. Create a free account or log in only when you want to download the results.
Which functions should I interpret?
Interpret the functions that are statistically significant in the test of dimensionality and that explain a meaningful share of variance (Rc²). Use the structure coefficients, rather than the weights alone, to name what each function represents.
What is the difference between canonical correlation and multiple regression?
Multiple regression predicts one outcome from several predictors. Canonical correlation relates a whole set of predictors to a whole set of outcomes and finds the combinations of each that are most strongly related.
Is my data uploaded to a server?
The analysis runs in your browser. Your data stays on your device while you work with the calculator.
