Canonical Correlation (CCA)

Multivariate · Association

Canonical Correlation (CCA) is one of the statistical analyses applied automatically in MerQur. This page illustrates — on a Social, Humanities & Admin Sciences sample dataset — how the analysis is run, what the MerQur output looks like, and how the result is reported in APA 7 format.

🎯 What is it for?

Canonical Correlation (CCA) automatically performs, in the background, all the assumption checks required for the relevant data type (normality, homogeneity of variance, etc.) and presents the results with a clear table and chart. Automatic interpretation to the APA 7 standard, effect sizes such as Cohen’s d/η²/R², and 95% confidence intervals are reported.

📌 When is it used?

Statistical analysis of measurements in the Social, Humanities & Admin Sciences domain
To produce APA 7-compatible result tables for academic publications
Hypothesis testing and decision-making processes
Undergraduate / master’s / PhD theses after the appropriate method has been selected

📐 Assumptions

Appropriate scale — Variables must be at the measurement level required by the analysis (nominal/ordinal/interval/ratio)
Independent observations — Observations must come from individuals independent of one another
Sufficient sample size — The minimum n requirement for the analysis must be met
Outlier check — Outliers must be detected and evaluated

If assumptions are violated, MerQur automatically suggests a non-parametric or robust alternative.

🛠 How to do it in MerQur

Load the data. Select the sample file from File → Open. MerQur auto-detects column types.

Select the analysis. From the left side select Canonical Correlation (CCA).

Panel assignments (form fields in the program):

set_x: ['ogrenci_id', 'matematik', 'fen', 'dil']
set_y: ['mantik', 'motivasyon', 'tutum', 'doyum']
n_components: 2

Optional settings. Effect size ✓ · 95% confidence interval ✓ · Assumption checks (automatic).

▶ Run — click the button. Results are produced automatically as a table + chart.

📄 Export to Word. APA 7-formatted report with italic statistical symbols.

📊 Sample Dataset — Social, Humanities & Administrative Sciences

ℹ Note: The scenario, MerQur output and interpretation below were produced by actually running the real example dataset in MerQur. Numeric results on your own data will differ; the goal is to show how the analysis is set up and interpreted end-to-end.

🎬 Example File

This analysis is demonstrated on the following example dataset for Social, Humanities & Administrative Sciences:

Sosyal_Beseri/36_cca_physical_bio.xlsx

🎬 Scenario

We examine the joint structure between the cognitive-achievement set and the affective set. For the relationship between two multivariate sets, CCA is appropriate.

⚙️ Variable Selection

X variables: math
X variables: science
X variables: language
X variables: reading
X variables: logic
Y variables: motivation
Y variables: attitude
Y variables: satisfaction
Y variables: anxiety

Data Preview (First 5 Rows)

Preview unavailable: [Errno 2] No such file or directory: ‘F:/MERQUR_CODE/merqur/english/datasets/Sosyal_Beseri/36_cca_physical_bio.xlsx’

📈 MerQur Output

CANONICAL CORRELATION (CCA) RESULT ───────────────────────────────────────────── CC1: r = 0.985 chi^2(20) = 1407.32 p < .001 *** CC2: r = 0.965 chi^2(12) = 900.60 p < .001 *** Set-X (cognitive): math, science, language, reading, logic | Set-Y (affective): motivation, attitude, satisfaction, anxiety

💬 Interpretation

We resolved the joint structure between two multivariate measure sets — cognitive achievement (math, science, language, reading, logic) and affective variables (motivation, attitude, satisfaction, anxiety) — with canonical correlation. The first two canonical functions are very strong (r = 0.985 and 0.965, p < .001): the two sets are intensely related. CCA answers “how is one variable set related to another?” in a single step — it is the multivariate-on-both-sides version of multiple regression. In education it reveals the latent relationship structure between the cognitive-achievement bundle and the affective bundle.

⚠ Common Mistakes

Misidentifying the data type (e.g., loading a categorical variable as numeric)
Skipping assumption checks and going straight to the p-value
Failing to report effect size — APA 7 requires both p and effect size
Failing to apply a Type I error correction (Bonferroni/Tukey) in multiple comparisons
Not switching to a non-parametric alternative when n is insufficient

📹 Video Walkthrough

Watch the video below for an end-to-end walkthrough of this analysis on a Social, Humanities & Admin Sciences file.

▶ Canonical Correlation (CCA) — video walkthrough

A complete end-to-end walkthrough of this analysis in MerQur, narrated on screen. Narration is in Turkish.

▶ Watch the video 📺 All videos

🔀 The same analysis in other disciplines:
🎓 Education Sciences · 🧪 Natural Sciences & Mathematics · 🏛 Architecture, Planning & Design · ⚙ Engineering · 🏥 Health Sciences · 🏃 Sport Sciences · 🌾 Agriculture, Forestry & Aquatic

📚 If You Used This Analysis, Cite MerQur

If you performed this analysis using MerQur in a scientific study, please use the citation below as part of your academic citation obligations (APA 7):

Örücü, Ö. K. (2026). MerQur: Integrated Academic Data Analysis & Reporting Platform [Computer software] (Version 1.0.0). https://doi.org/10.53463/merqur.2026001

For BibTeX, RIS, EndNote and the English citation form: all citation formats →

Sources:

American Psychological Association. (2020). Publication manual of the American Psychological Association (7th ed.).
Field, A. (2018). Discovering statistics using IBM SPSS Statistics (5th ed.). Sage.
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum.