Correlation Explorer & Correlation Stability

Explore different association measures and how sample size affects correlation estimates

Compare association measures

Correlation coefficients quantify the association between two variables, but not all coefficients capture the same thing. Pearson r measures linear association and is sensitive to outliers; Spearman ρ and Kendall τ use ranks and detect monotonic relationships; mutual information and distance correlation pick up arbitrary nonlinear dependencies.

Click to place points, drag to reposition, and watch all five measures update in real time. Use the presets to generate common patterns.

Preset N: 60

Signal strength: 0.80

Click to add · Drag to move · Shift-click to remove · N = 0

Pearson r linear

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Linear association. Sensitive to outliers.

Spearman ρ rank

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Monotonic rank-based. Robust to outliers.

Kendall τ concordance

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Pairwise concordance. Robust at small N.

Mutual Info nonlinear

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KNN estimator (k=3). Biased at small N.

dCor nonlinear

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Zero iff independent. Range [0, 1].

Pearson, Spearman, and Kendall range $[-1, 1]$. $MI \geq 0$ (nats); bar uses heuristic cap. $dCor \in [0, 1]$. MI uses Kraskov et al. (2004) KNN with $k=3$ — noisy and upward-biased at small $N$. Points live in $[0, 1]^2$. Click the ? buttons for detailed descriptions.

At what sample size do correlations stabilize?

Sample correlations converge to the population value as N grows, but estimates in small samples can be wildly inaccurate. In Schönbrodt and Perugini's own worked example, a correlation sitting at r = .69 with 20 participants had settled to r = .26 by the time the sample reached 274. The corridor of stability (COS) is a band of width ±w around the true ρ, and the point of stability (POS) is the sample size from which the running correlation never again leaves this corridor (Schönbrodt & Perugini, 2013).

Correlation trajectories

Trajectories

True ρ

Corridor of stability

True ρ .30

Corridor w ±.10

Trajectories 15

Median POS

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80th pctl POS

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Stable by N=250

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Corridor

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Each line is an independent random sample drawn from a bivariate normal population with the specified ρ. After each new observation the running Pearson r is recalculated. Notice how trajectories are erratic early on and then settle into the corridor.

Distribution

Where do trajectories stabilize?

The histogram below shows the POS for each of the simulated trajectories. The vertical line marks the 80th percentile — the N by which 80% of trajectories have stabilized.

Distribution of points of stability

Reference

Critical sample sizes (Table 1)

From the original paper. (A 2018 corrigendum corrected an r-to-Z metric issue; the r-metric values reproduced below are unchanged.) Each cell shows the sample size at which the stated percentage (80/90/95%) of simulated studies have entered the corridor of stability and never leave it again. It is a percentile of the point-of-stability distribution across many studies — not the point at which a single trajectory settles, and not a confidence interval. The row closest to your current ρ is highlighted.

	80% confidence			90% confidence			95% confidence
ρ	w = .10	w = .15	w = .20	w = .10	w = .15	w = .20	w = .10	w = .15	w = .20

Bottom line: For typical effect sizes in personality psychology (r ≈ .21), with a corridor of ±.10 and 80% confidence, you need roughly N ≈ 250 for a stable correlation estimate. There are few scenarios where going below N = 150 is justifiable.

Stability simulation based on Schönbrodt & Perugini (2013).

Citation

Persson, B. N. (2026). Correlation Explorer & Correlation Stability [Interactive visualization]. https://bjorn-persson.github.io/visualizations/correlation-stability/

@misc{Persson2026correlationstability,
  author = {Björn N. Persson},
  year = {2026},
  title = {Correlation Explorer \& Correlation Stability},
  note = {Interactive visualization},
  url = {https://bjorn-persson.github.io/visualizations/correlation-stability/}}