A spurious relationship is a statistical association between two variables that is not produced by either variable directly affecting the other. The numbers move together — sometimes strikingly so — but the connection runs through something else entirely: a shared cause, a selection process, an artefact of how the data were collected or aggregated, or plain chance. Spuriousness is a claim about mechanism, not about the size of a correlation coefficient: a spurious relationship can be r = 0.95, and a genuinely causal one can be r = 0.2. See Correlation Coefficient for how association itself is measured, and Correlation vs. Causation for the baseline reason association never implies causation on its own. This guide is about the specific mechanisms that generate false associations and how to tell them apart from real ones.
What makes a relationship “spurious” rather than merely non-causal
Every spurious relationship is non-causal, but treating “spurious” as a synonym for “not causal” undersells the term. A relationship is spurious when there is an identifiable process — confounding, selection, chance, or an artefact of measurement or aggregation — that explains why the variables appear connected even though neither one drives the other. Naming that process is the actual analytical task: “it’s spurious” is a diagnosis, not a stopping point, and different mechanisms call for different fixes. The sections below work through each one with a worked example.
Confounding: a shared cause
The most familiar mechanism. Two variables, X and Y, are both affected by a third variable, Z, which is not measured or not adjusted for. X and Y move together purely because they share a cause, with no arrow running between them at all.
Worked example: across regions, ice cream sales and drowning deaths are positively correlated. Neither causes the other; both rise with a third variable — warm weather, which increases both swimming exposure and ice cream purchases. Adjust for season or temperature and the association between ice cream sales and drownings collapses. This is why CASRAI’s confounding variable entry treats confounding as a distinct, identifiable structure (a common-cause fork in a causal diagram), not a vague caveat — see Causal Analysis for how DAGs represent this formally and how adjustment sets are chosen.
Selection bias and collider stratification: the subtlest mechanism
This is the mechanism most likely to be missed, because it does the opposite of what intuition expects: instead of a shared cause creating an association, conditioning on a shared effect creates one where none existed in the source population.
A collider is a variable that two other variables both causally influence — visually, two arrows point into it. Leaving a collider alone, out of the analysis, is harmless: it doesn’t distort the relationship between the two variables that cause it. But if the dataset is restricted, filtered, or stratified on the collider — even unintentionally, by how the sample was recruited — an association between its two causes can appear, or a real association can be reversed or hidden.
Worked example (illustrative, a standard statistics-teaching device, not a specific study): imagine talent and physical attractiveness are completely unrelated in the general population. Now look only at people who work as actors — a group selected partly on the basis of talent, partly on attractiveness, since either trait alone can be enough to get hired. Within that selected sample, talent and attractiveness will appear negatively correlated: an actor who was hired mainly for their looks, on average, needed less talent to clear the same hiring bar, and vice versa. Restricting attention to “people who got the job” — the collider — manufactured an association between two traits that are independent in the full population.
The same structure has a specific, well-documented name in epidemiology: Berkson’s bias (Berkson, 1946), where an association between a disease and an exposure appears spuriously among hospitalized patients because hospitalization itself is a collider — both the disease and the exposure (or a different condition linked to the exposure) increase the chance of being admitted, distorting associations estimated within the hospitalized sample compared to the general population. Any analysis restricted to survivors, volunteers, respondents, or admitted patients is at risk of the same distortion whenever the restriction is itself a common effect of the variables under study.
Reverse causation
The association is real and even causal, but the arrow runs the opposite direction from the one assumed. A cross-sectional or poorly time-ordered dataset often cannot distinguish “X causes Y” from “Y causes X.”
Worked example (illustrative): a cross-sectional survey might find that people who exercise less report more symptoms of depression, and be read as “inactivity causes depression.” But depressive symptoms — low energy, anhedonia, poor sleep — plausibly reduce exercise, so the same data are equally consistent with “depression reduces activity.” Without a time-ordered design (activity measured before the onset of symptoms) or a study design that can rule out reverse causation, the direction is genuinely ambiguous. Firefighter count and property damage at a fire is a cleaner illustrative version of the same trap: more firefighters correlates with more damage, not because firefighters cause damage, but because fire size (the common cause) determines both how many firefighters are dispatched and how much damage results — this example is also, more precisely, a case of confounding rather than reverse causation, and the two are easy to conflate without a diagram.
Chance: why testing enough variable pairs guarantees a “finding”
At a conventional significance threshold of p < 0.05, roughly 1 in 20 truly unrelated variable pairs will show a “statistically significant” association by chance alone. Test hundreds of variable pairs — as an exploratory correlation matrix across a large dataset routinely does — and some will clear that bar even if nothing in the underlying data-generating process connects them. This is the multiple-comparisons problem, and it is the mechanism behind most of the pairings in the popular “spurious correlations” genre discussed below.
See P-Value for what the threshold actually represents, and How to Report P-Values for reporting practice. Corrections such as Bonferroni or false-discovery-rate adjustment exist specifically to control the chance of a false positive when many tests are run against the same dataset — but the more durable fix is distinguishing, on the page and in the analysis plan, which comparisons were specified in advance and which were found by search (see the research-integrity section below).
Ecological fallacy and aggregation artefacts: Simpson’s paradox
An association measured at one level of aggregation (countries, hospitals, departments) does not necessarily hold — and can outright reverse — at the individual level. Assuming it does is the ecological fallacy: attributing a group-level pattern to the individuals inside the group.
Simpson’s paradox is the sharpest version of this: a trend that appears in several groups analyzed separately reverses when the groups are combined, or vice versa, because a lurking variable is unevenly distributed across the groups. The best-known documented case is the University of California, Berkeley graduate admissions data from 1973 (Bickel, Hammel & O’Connell, Science, 1975): aggregate admission rates appeared to favor male applicants, but when broken down by department, most individual departments showed no bias or a slight bias toward female applicants — women had disproportionately applied to more competitive departments with lower overall admission rates for everyone. The aggregate comparison was confounded by department; the disaggregated, department-level comparison told a different story. The lesson generalizes well beyond that case: any comparison pooled across a variable that itself affects both the grouping and the outcome is a candidate for a Simpson’s-paradox reversal, and the fix is checking whether the association holds within, as well as across, the relevant strata.
Time-series artefacts: trends, seasonality, and non-stationarity
Two time series that are both trending — rising or falling steadily over time for entirely unrelated reasons — will show a very high correlation coefficient even if nothing connects them causally or through any confounder in the ordinary sense. This is sometimes called a “nonsense regression” or non-stationarity problem: standard correlation and regression assume the series are stationary (roughly constant mean and variance over time), and violating that assumption inflates apparent relationships between series that share no real connection beyond both moving with time. Seasonality creates a related artefact: two series that both cycle annually (retail sales and ambient temperature, say) will correlate strongly over a period covering multiple cycles purely because of the shared cyclical pattern, independent of any direct link.
Tyler Vigen’s widely circulated “Spurious Correlations” project (tylervigen.com) catalogs dozens of real, extremely high correlation coefficients between unrelated time series (found by mining large public datasets for coincidental matches) — it is a genuinely useful teaching device for exactly this artefact, and is referenced again below. The statistical fix is testing for and, where appropriate, differencing or detrending non-stationary series before correlating them, rather than reading a high raw correlation between two trending series as evidence of a relationship.
Measurement artefacts
Three more mechanisms are worth naming individually because they are easy to build into a study design by accident:
- Shared method variance: when two variables are measured with the same instrument, rater, or self-report method, part of any observed correlation between them can reflect shared measurement error or response style rather than a real relationship between the underlying constructs.
- Regression to the mean: extreme measurements — the highest scorers, the sickest patients, the worst-performing sites — tend to be closer to average on a second measurement, simply because extreme values are partly the product of transient noise that is unlikely to repeat. Interpreting that natural reversion as an “effect” of an intervention applied between the two measurements is a specific, well-known error. Francis Galton first documented the phenomenon in the 1880s, in the height of children relative to their parents’ height.
- Mathematical coupling: correlating a ratio with its own numerator or denominator (or with another quantity that shares a term algebraically) can produce a strong correlation that is a mathematical near-certainty rather than an empirical finding — for example, correlating a rate (events per person-year) with the same person-year denominator used to compute a related rate, or correlating body mass index with weight, where weight is literally one of the two terms BMI is calculated from.
How to investigate a suspected spurious relationship
- Draw the DAG. Making causal assumptions explicit — which variables plausibly cause which, and which are colliders versus confounders — is the single most effective way to catch selection bias and confounding before they distort an analysis, because the correct adjustment strategy (what to control for, and what not to control for) depends entirely on the diagram. See Causal Analysis for how DAGs are constructed and used to select an adjustment set.
- Stratify and adjust. Check whether an association holds within relevant subgroups (as the Simpson’s-paradox check above requires), and adjust statistically for identified confounders — while being careful not to adjust for a collider, which can introduce bias rather than remove it.
- Run a sensitivity analysis. Ask how strong an unmeasured confounder would need to be to fully explain the observed association (an E-value or similar bound). A relationship that would require an implausibly strong confounder to explain away is more credible than one that a modest, plausible confounder could account for.
- Replicate in an independent sample. A genuine relationship should reappear in new data; most chance findings and many artefacts of a particular sample’s selection process do not.
- Pre-register the confirmatory analysis. Separating which comparisons were specified before looking at the data from which were found by searching the data afterward is what keeps an exploratory correlation matrix honest — see the research-integrity section below.
The research-integrity dimension
Spuriousness is not only a statistical hazard; it is a well-documented route into research misconduct territory when it is not disclosed. Running a large correlation matrix across many variables and reporting only the pairs that cleared a significance threshold — without disclosing how many comparisons were actually tested — is a form of data dredging, one of the practices catalogued under questionable research practices. Presenting a correlation found this way as though it had been the study’s original, specified hypothesis is HARKing (Hypothesising After the Results are Known): the exploratory origin of the finding is erased from the write-up, and readers have no way to judge how much multiple-comparisons risk it carries.
The fix is disclosure, not avoidance — exploratory correlation analysis is a legitimate and often necessary part of research, particularly at the hypothesis-generating stage. What integrity requires is labelling it as such: reporting the full set of comparisons tested (not just the significant ones), stating plainly that a finding was exploratory rather than confirmatory, and, where feasible, pre-registering the confirmatory follow-up test in an independent sample or dataset before running it. See Preregistration of a Study Protocol for how that separation is formalized in practice.
The “spurious correlations” genre: useful teaching device, not the main event
A genre of internet-famous charts — pairing, for instance, per-capita cheese consumption with the number of people who died tangled in their bedsheets, built by mining large datasets for high-correlation coincidences (Tyler Vigen’s tylervigen.com project is the best-known example) — has done real public-understanding work by making the “correlation isn’t causation” point memorable. They are almost all instances of the chance mechanism above (search enough variable pairs and some will match by coincidence) or the time-series trend artefact. They are a useful way to build intuition for why a high correlation coefficient alone proves nothing. But they should not anchor how researchers think about spuriousness in their own work: the cases that actually undermine published findings are rarely absurd coincidences that a reader would laugh off — they are confounding and collider bias, which look entirely plausible on their face and require a diagram, not a raised eyebrow, to catch.
Frequently asked questions
What is a spurious correlation, in plain terms?
A statistical association between two variables that shows up in the data but is not caused by either variable affecting the other — it’s produced instead by a shared cause, a selection process, chance, or an artefact of how the data were measured or aggregated.
Is a spurious correlation the same thing as a confounding variable?
No — confounding is one specific mechanism that produces a spurious relationship, not a synonym for the whole category. Selection bias, collider stratification, reverse causation, chance, ecological aggregation, and time-series or measurement artefacts can all produce a spurious relationship without any confounder being involved at all.
Can two variables be very strongly correlated with genuinely no real-world relationship?
Yes. Two non-stationary time series that are both trending over time, or two variables tested among hundreds of pairs in an exploratory matrix, can produce very high correlation coefficients — sometimes above 0.9 — purely through the mechanisms described above, with no substantive connection at all.
How do you test whether a correlation is spurious?
There is no single test that labels a relationship spurious; it is an investigative process. Draw a causal diagram to make the candidate mechanisms explicit, check whether the association holds after adjusting for plausible confounders and within relevant subgroups, run a sensitivity analysis for unmeasured confounding, and check whether the relationship replicates in an independent sample.
What is collider stratification bias in one sentence?
It is the association that appears between two variables purely because the analysis has been restricted (deliberately or through how the sample was selected) to a group defined by a variable that both of the original two variables causally influence.
