Correlation test calculator

Use a correlation test when you have two measurements on the same units and want to know whether they move together, and how strongly. Weekly ad spend and weekly revenue, session count and day-30 retention, page speed and bounce rate. Both variables are observed rather than assigned, which separates this from every other calculator here: nothing was randomised, so the analysis describes co-movement and stops. Pearson's r measures a straight-line relationship; Spearman's rho does the same on the ranks, which suits ordinal data and cases where a couple of extreme points would otherwise write the answer.

"Correlation is not causation" is true and almost useless, because it says nothing about how to read the number in front of you. Three failure modes are more actionable. Attenuation: measurement error in either variable pulls r toward zero, capping it at roughly the square root of the product of the two measures' reliabilities, so 0.45 between two noisy proxies can reflect something far stronger. Restriction of range: r shrinks when the sample is filtered on either variable, so correlating spend against return among campaigns that cleared a spend threshold understates the relationship. And non-comparability: r is a covariance rescaled by the sample's own standard deviations, so an identical slope gives different r values in two markets whose spend varies differently.

Use something else when the question is causal or the data is a different shape. To know what happens to revenue when you change spend — not whether the two drifted together — you need a design that breaks the confounding: a geo test, a randomised experiment, or an explicit causal model. Two categorical variables want a chi-square test; comparing groups rather than tracking co-movement wants the t-test or ANOVA; time-to-event data wants the log-rank test.

Computing r requires nothing — it describes whatever numbers you feed it. The p-value and the interval carry the assumptions, and one of them fails constantly in marketing data:

• The pairs are independent observations. Two weekly time series are not: both trend, both carry seasonality, and both are autocorrelated, so 104 weeks contain far fewer than 104 independent observations and the interval comes out much too narrow. Unrelated trending series routinely correlate above 0.9. Difference or deseasonalise first — one reason marketing mix modelling is a discipline, not a spreadsheet.
• Linearity, for Pearson. An r near zero means no linear component, not no relationship: a clean inverted-U — the shape diminishing returns actually takes — can produce r = 0.02. Plot the scatter first. Spearman relaxes this to monotonicity but still cannot see a curve that turns around.
• Approximate bivariate normality, for the inference only. Mild departures matter little at reasonable n; heavy tails matter a great deal, because they make the Fisher-z interval too narrow. It constrains neither r itself nor Spearman's rho.
• No single point is doing the work. One leverage point can create an r of 0.6 in a cloud with no relationship, or destroy a real one. Recompute without the extreme points and report both if they disagree — outliers bite harder here than in any test of means.
• That testing r against exactly zero is worth doing. Usually it is not: no relationship whatsoever is rarely plausible for two business metrics, and with a few thousand rows almost any r clears significance.

Before committing to a full media model you want to know whether weekly paid-search impressions and weekly branded organic sessions move together at all. Anything below r = 0.30 would not be worth carrying into the model, so that is what the study has to detect, at 80% power and 5% two-sided.

Two things fall out, and the second matters more. First, the interval at n = 40 spans everything from no relationship to a strong one, so "we saw a correlation of 0.3" from forty weeks is not a finding — it is a prompt to collect more data. Second, 85 weeks of weekly data does not contain 85 independent observations: both series trend and both are seasonal, so the effective sample is smaller than the row count and the real interval is wider than the one above. That gap between rows and information is the commonest way marketing analyses overstate their own precision.

Read the interval before anything else. An r of 0.42 from 30 observations carries a 95% interval of roughly 0.07 to 0.68 — technically significant, and consistent both with a relationship too weak to matter and with one strong enough to build a plan around. Small-sample correlations are among the least stable statistics in routine use, and the interval is the only thing on the output that says so — the argument for intervals over asterisks we make about reporting results.

Square r if you like, but be careful what you claim. r = 0.42 gives r² = 0.18, and "18% of the variance" is a statement about variance in this sample, biased upward — not 18% of revenue, or of anything a stakeholder will hear. Note too how modest the benchmarks are: an r of 0.30, widely called moderate, is under 10% of shared variance.

Before concluding a relationship is weak, work through the three biases. Is either variable measured with noise — survey responses, modelled attribution, a proxy for the thing you care about? Then r is attenuated and its ceiling may be well below 1. Has the sample been filtered on either variable, to active accounts or campaigns above a spend floor? Then the range is restricted and r is biased toward zero. And a difference in r across markets can reflect spread rather than relationship; compare regression slopes instead.

Finally, resist the pull from association to action. A strong correlation between spend and revenue is what you would see if both simply rose with demand, and what you would see if spend worked; the data cannot separate them and no sample size will. The only reliable route is a design where something was assigned rather than observed: a geo test turning spend up in some markets and not others, or a causal model stating its assumptions out loud — the longer version being why test lift differs from the real world.