If two measurements vary together, they have an association. A correlation coefficient can summarize a particular kind of that association. A causal claim goes further: it says that changing one factor would change another outcome under specified conditions.
The extra claim needs extra evidence. A pattern can arise because one variable affects the other, because another factor affects both, because the direction runs the other way, or because of how observations were selected. Naming an association accurately is therefore a beginning, not a failure to reach a more exciting conclusion.
A community-event example
Imagine a fictional community center comparing ten events. Events with more reminder emails tend to have higher attendance. A chart shows an upward pattern, and someone concludes that sending more emails caused the larger audiences.
The observation may be useful, but the conclusion outruns it. Perhaps staff sent more reminders for events they already expected to be popular. Perhaps those events had larger rooms, more prominent speakers, or more advance registrations. Perhaps the reminders helped, but the chart alone cannot isolate how much.
The causal question is more specific: for comparable events or invitees, what would attendance have been with one reminder strategy rather than another? That comparison is not supplied merely by observing that email count and attendance move together.
All events and numbers in this article are invented to illustrate reasoning. They are not findings from a community program or a claim about email effectiveness.
What the scatter plot actually shows
NIST's scatter-plot guide describes plots as tools for identifying relationships, nonlinear patterns, and unusual observations. A plot is useful because it shows the paired data rather than only a headline coefficient.
For the fictional center, one point could represent one event, with reminders on the horizontal axis and attendance on the vertical axis. The chart can show that larger reminder counts tend to accompany larger audiences. It cannot show, by its shape alone, what would have happened to the same audience under a different reminder strategy.
Even the unit of observation matters. A chart of event-level totals differs from a chart of individual invitees. Ten events with a thousand invitees each are still ten event-level observations if the analysis uses one point per event.
A third factor can influence both variables
Suppose expected demand influences how much promotion staff plan. High-demand events receive more reminders and attract more attendees. Demand now provides an alternative explanation for the observed relationship.
OpenStax's research-methods explanation discusses confounding: another factor can help account for systematic movement in the variables of interest. The central issue is not whether the researcher can invent a story, but whether the design and evidence distinguish credible alternatives.
For the community center, recording event type, capacity, advance registration, timing, and other relevant features may improve the analysis. It does not automatically remove every difference between events. Some factors may be poorly measured or unobserved.
Adding a column to a spreadsheet is therefore not a magic act of control. A useful adjustment needs a reason that the variable matters and a method appropriate to the question. The adjusted result should retain the assumptions on which it depends.
The direction can run backward
Perhaps staff send extra reminders only after an event accumulates many registrations. In that case, early demand partly causes the higher reminder count. The final correlation can look similar to the one expected if reminders caused demand.
Time order helps investigate this possibility. A record of when reminders were sent and when registrations arrived is more informative than two totals collected at the end. It can show whether the supposed cause preceded the relevant outcome.
Precedence alone is still not enough. A reminder sent first can coincide with a popular speaker announcement or a change in venue. Establishing the order removes one ambiguity while leaving other explanations to examine.
A careful description might say, “Reminder count was associated with attendance, but the records do not separate the effect of reminders from the center's response to early demand.” That is a useful finding because it identifies the missing comparison.
Selection can create a misleading view
Suppose the center studies only events that sold at least 80% of their seats. Low-attendance events disappear from the dataset. The remaining relationship may differ from the relationship across all events, because inclusion depends on the outcome being studied.
Alternatively, suppose only attendees complete the follow-up survey. Their answers can describe respondents who attended, but they cannot automatically explain why invitees stayed away. The people absent from the data may be exactly the people needed for that question.
Our survey-question guide explains why the wording and response options also affect what is measured. A well-worded question cannot repair a dataset that excludes the relevant population, and a broad sample cannot repair an ambiguous question.
When reading a causal claim, ask who could have entered the dataset, who actually did, and whether the selection process is related to the variables being compared.
Random assignment creates a different kind of comparison
A well-designed randomized experiment assigns the intervention by chance rather than allowing participants or staff to choose it based on expected outcomes. For the fictional center, eligible invitees might be assigned to two clearly specified reminder schedules under an appropriate study plan.
The purpose is to reduce systematic differences between groups in how they receive the intervention. Random assignment does not guarantee perfectly identical groups in one finite experiment. Chance imbalance, missing outcomes, implementation problems, and measurement errors still need attention.
The intervention itself must also be defined. “More reminders” could change timing, wording, number, and delivery channel at once. If all those features change together, the experiment estimates the effect of that bundle, not automatically the separate contribution of each feature.
This is why the design should follow the question. A vague intervention produces a vague causal interpretation even if its assignment was randomized.
Blocking can make a comparison more informative
NIST's randomized-block discussion explains how known nuisance factors can be handled through the design. A block groups experimental units on a relevant characteristic, with randomization arranged within the design rather than left to an uncontrolled mixture.
In an invented event study, organizers might want reminder schedules compared within similar event types rather than having one schedule used only for music and the other only for lectures. The exact design depends on the units, intervention, and outcomes.
Blocking does not justify trying many groupings after seeing results until a favorable answer appears. Its value comes from a reasoned design that addresses known sources of variation. The report should explain the choices so readers can understand what was compared.
No procedural label replaces implementation evidence. A study described as randomized still needs to show what was assigned, how outcomes were measured, and which participants were included in the analysis.
Random assignment is not random sampling
Random sampling concerns how people or units enter a study from a population. Random assignment concerns how included units receive an intervention. The two processes answer different problems.
A carefully randomized experiment conducted among volunteers at one center may support an effect estimate for that study while leaving questions about other centers or populations. A broad probability sample that merely observes behavior can describe associations without automatically isolating an intervention's effect.
The distinction is between the comparison inside the study and the reach of the conclusion beyond it. Both matter, but neither should be inferred from the other.
Our margin-of-error guide discusses uncertainty in estimates. Precision within a defined sample or model does not itself prove that a causal explanation is correct or that the result applies everywhere.
A correlation coefficient is not a percentage explained by a cause
For a standard Pearson correlation, values summarize the direction and strength of a linear relationship on a scale from −1 to +1. A value of 0.8 does not mean that one variable caused 80% of the other, or that changing one by 1% changes the other by 0.8%.
It is also not a slope. A slope has units tied to the variables; a correlation is standardized. Changing a measurement from meters to centimeters changes the numerical slope while leaving the corresponding Pearson correlation unchanged when the conversion is a positive linear rescaling.
The coefficient should be read with the plot and definitions. Outliers, restricted ranges, and group structure can matter to the pattern. A single summary can hide distinctions that become obvious when the points are shown.
Zero linear correlation does not rule out a pattern
Consider the invented pairs where X is −2, −1, 0, 1, 2 and Y is X squared: 4, 1, 0, 1, 4. The relationship is perfectly systematic and curved. Its Pearson linear correlation is zero because the positive and negative sides balance around the center.
This is a mathematical example, not a measured social relationship. It demonstrates why “no linear correlation” should not automatically be rewritten as “no relationship of any kind.” NIST's scatter-plot examples include nonlinear forms precisely because a line is not the only possible structure.
Our mean and median guide makes a similar point about summaries: a number can be correct while omitting a feature important to the question. The solution is to choose the summary and visualization for the pattern being investigated.
Two trends can move together without one driving the other
If event attendance and the center's social-media following both grow over several years, they can be correlated partly because both change with time. The center may be expanding, the surrounding population may be growing, or other conditions may be changing.
Comparing raw levels across time without examining those patterns can overstate what the association establishes. Our seasonal-adjustment explanation describes one kind of recurring time pattern; long-term trends and irregular changes introduce additional issues.
The relevant analysis needs a reasoned comparison of changes, timing, and alternative explanations. Merely drawing two upward lines on the same chart does not identify which one caused the other.
Observational evidence can still be valuable
Some questions cannot be studied with a practical or ethical randomized experiment. Observational evidence can contribute to causal understanding through appropriate designs, explicit assumptions, timing, mechanisms, and convergence across different sources of evidence.
The warning that correlation alone does not establish causation is not a rule that every nonexperimental finding is useless. It is a boundary on what follows from one observed association by itself.
A stronger report explains why particular alternatives are less plausible, what assumptions remain, and how the design addresses the missing counterfactual comparison. It also distinguishes an estimated average effect from a promise about every individual case.
For the fictional center, the responsible conclusion might remain an association and a plan for a better comparison. That is progress: the evidence has identified a pattern and clarified what must be learned before changing the wording to “caused.”
Sources
- NIST: Scatter Plots
Scatter plots reveal linear and nonlinear relationships and outliers; an observed association does not by itself establish causation.
- OpenStax: Analyzing Findings
Correlation describes relationships; confounding and experimental controls matter when investigating cause and effect.
- NIST: Randomized Block Designs
Blocking handles known nuisance factors and randomization operates within the experimental design; design is distinct from simply observing associated variables.