If two variables move together, we say they are correlated. If they move in the same direction, we call it positive; opposite direction, negative. The number that summarises all of this — how strongly, and in which direction — is Pearson’s r.

r is bounded between -1 and +1. But knowing that is not enough to interpret it responsibly.

What r actually measures

r is a scaled version of covariance. It measures the linear relationship between two continuous variables. Its full name — the Pearson product-moment correlation coefficient — is worth remembering because every word matters.

• Linear. r only detects straight-line relationships. A perfectly curved relationship (U-shape, quadratic) can produce r ≈ 0.
• Product-moment. it is built from the joint deviations of both variables from their means.
• Coefficient. it is a one-number summary — not a full picture. Always plot the data.

Interpreting r’s magnitude

Cohen’s benchmarks (1988) are the most widely cited:

• **

  r

  ≥ 0.10** → small

• **

  r

  ≥ 0.30** → medium

• **

  r

  ≥ 0.50** → large

These are field-specific. In physics, r = 0.90 is common. In social psychology, r = 0.30 might be the strongest effect you will ever see. Compare to your field’s typical effect sizes, not to the benchmarks alone.

Four things r does not tell you

1. Causation. Perhaps the most-repeated caveat in statistics. A high r between ice cream sales and drowning deaths does not mean ice cream causes drowning — a third variable (summer weather) drives both.

2. Non-linear relationships. A dataset with a perfect U-shape can have r = 0. Always inspect a scatterplot before trusting r. If the relationship is non-linear, transform the variable (log, square root, quadratic term) or use a non-parametric measure like Spearman’s ρ.

3. The magnitude of change. r = 0.80 means the variables move together strongly, but it does not say by how much y changes when x changes by one unit. For that, you need the slope of a regression (β), not r.

4. Robustness to outliers. A single extreme point can pull r from 0.10 to 0.60. Always compute r with and without any influential outlier, and report both — or use a robust correlation (Spearman, Kendall’s τ) if outliers are theoretically meaningful and should stay in.

What to report

• The value of r to two decimal places, e.g. r = 0.42.
• The exact p-value, e.g. p = .003 — but read the P-values post first.
• The 95 % confidence interval for r (via bootstrap or Fisher’s z-transformation).
• The sample size n.
• A scatterplot showing the actual data.

Doing this in AnalyVa

A realistic workflow: many correlations in applied research are not between two raw variables but between two composite scale scores (e.g. the mean of six items measuring a construct). This tutorial covers the whole path — data import → build two composites via Transform → Compute Variable → run Correlate → Bivariate → read the result and the heatmap.

Step 1 — Click Import. Launch AnalyVa on an empty canvas. Click the Import button in the top toolbar.

Step 2 — The import dialog opens. An overlay appears asking for a file (.xlsx, .csv, or .tsv).

Step 3 — Load and preview. Drop your file. AnalyVa parses it and reports the shape (here: 361 rows × 53 columns, 49 numeric, 0 missing). Click Import.

Step 4 — Open Transform → Compute Variable. Every variable now appears in the sidebar. Before correlating, build the two composite scores. Open the Transform menu → Compute Variable….

Step 5 — Name the first composite. The Compute Variable dialog opens. In Target Variable, type a short, meaningful name — here Variable1 — this becomes a new column in your dataset.

Step 6 — Move to the Expression field. Click into the Expression field. Below it, AnalyVa shows every available variable as a clickable chip and the full list of supported functions and operators.

Step 7 — Enter the composite formula and click OK. Type or click-to-insert the arithmetic that produces the composite — here the mean of six items: (GP_1+GP_2+GP_3+GP_4+GP_5+GP_6)/6. Click OK. The header confirms “Computed ‘Variable1’ for 361 cases”.

Step 8 — Repeat for the second composite. Open Transform → Compute Variable… again to build the second composite. Same dialog, same flow.

Step 9 — Name Variable2. In the new dialog, type Variable2 in Target Variable.

Step 10 — Build the expression by clicking chips. Instead of typing, click the variable chips (PA_1, PA_2, …) below the expression box — AnalyVa inserts them at the cursor. Add the + between each and wrap in parentheses.

Step 11 — Confirm the second composite. The full formula: (PA_1+PA_2+PA_3+PA_4+PA_5+PA_6)/6. Click OK. The header confirms “Computed ‘Variable2’ for 361 cases”.

Step 12 — Open Analyze → Correlate → Bivariate. With both composites in the dataset, open the Analyze menu → Correlate → Bivariate….

Step 13 — Select the two composites and choose Pearson. The Bivariate Correlations dialog opens with every numeric variable listed. Ctrl/Cmd-click Variable1 and Variable2 to select just the two composites. Leave Method on Pearson. Click OK.

Step 14 — Read the results. The right pane switches to Results and shows a Bivariate Correlations (Pearson) table:

• Variable1 ↔ Variable2 = -0.332 ***

Below the table, a Correlation Heatmap visualises the magnitude and direction (red = negative, blue = positive). Significance stars follow the convention * p < .05, ** p < .01, *** p < .001.

In plain reporting: the two composites correlate r = -0.33, p < .001 — a small-to-moderate negative association. To also inspect whether the relationship is linear (Cohen’s caveat #2 above), open the scatterplot from the same panel before writing up.

Further reading

• Rodgers, J. L., & Nicewander, W. A. (1988). Thirteen ways to look at the correlation coefficient. The American Statistician, 42(1), 59–66.
• Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Erlbaum.