Correlation, Causation and the Vocabulary of Association
What Is Correlation?
When two variables tend to change together, statisticians say there is a correlation between them. A scatter graph is the standard way to spot a correlation — each point plots one individual’s pair of values, and the overall pattern of points tells you whether a relationship exists. Correlation is about pattern, not proof, which is the single most important idea in this lesson.
Direction: Positive, Negative and Zero Correlation
Positive correlation means that as one variable increases, the other tends to increase too. Hours of revision and exam score typically show positive correlation — students who revise more tend to score higher.
Negative correlation means that as one variable increases, the other tends to decrease. Distance travelled to school and time left for breakfast often show negative correlation — the further the journey, the less time remains.
Zero (no) correlation means there is no consistent relationship between the two variables. On a scatter graph, the points are scattered with no visible pattern — knowing one variable tells you nothing useful about the other.
The three directions of correlation are positive (both variables increase together), negative (one increases as the other decreases) and zero (no consistent pattern). Always state the direction first when describing a scatter graph.
Judging Strength by Inspection
The exam board expects you to describe the strength of a correlation as strong or weak by looking at how closely the points cluster around a line — this is an informal, visual judgement, not a calculation. If the points sit tightly along a clear line, the correlation is strong. If the points are loosely scattered but still show a general drift in one direction, the correlation is weak. There is no fixed number that divides strong from weak at this level — you are expected to make a reasonable judgement by inspection and justify it in context.
Strength is judged by how tightly the points cluster around a line of best fit — tightly clustered points mean strong correlation; loosely scattered but directional points mean weak correlation.
Interpolation and Extrapolation
Interpolation means using a line of best fit to estimate a value that falls within the range of data you actually collected. If your data covers ages 20 to 60, estimating a value for age 35 is interpolation, and this is generally considered reasonably reliable.
Extrapolation means extending the line beyond the range of your data. Estimating a value for age 80 from data that only covers ages 20 to 60 is extrapolation. This is much less reliable, because the relationship seen inside the data range might not continue outside it.
Correlation Does Not Imply Causation
Finding a strong correlation between two variables does NOT mean that one causes the other. The exam board’s specification states this explicitly: correlation does not necessarily imply causation, and you need to be alert to spurious correlation — an apparent relationship that is really caused by something else entirely.
A classic example: car ownership and birth rate across a number of cities can show correlation. This does not mean owning more cars makes people have more babies. Both variables are affected by a shared factor — the population size of the city. Bigger cities tend to have more cars registered and more births overall, simply because they have more people. The population size here is a lurking variable that explains the apparent link without either variable causing the other.
A common error: seeing a strong correlation and writing “X causes Y.” This is a statistically incorrect claim, because strength of correlation says nothing about cause.
The safer wording is: “There is a strong positive correlation between X and Y. This suggests X and Y are associated, but does not prove that X causes Y — a lurking variable could explain the pattern.” Writing “associated with” rather than “causes” keeps your answer statistically accurate.
Multiple Interacting Factors (Higher)
At Higher tier, the exam board expects you to recognise that more than one factor may interact to produce an apparent correlation. Real situations are rarely explained by a single lurking variable — several factors can combine. In the car ownership and birth rate example, population size is one shared factor, but wealth, urban planning and average family size could all interact with population size as well. Naming just one lurking variable is often not the full picture.
Interpreting Given Correlation Coefficients (Higher)
At Higher tier you may be given a Spearman’s rank correlation coefficient and asked to interpret it in context. Its value always lies between \(-1\) and \(+1\). A value close to \(+1\) shows strong positive correlation, a value close to \(-1\) shows strong negative correlation, and a value close to \(0\) shows little or no correlation. The exam board does not give a formal numerical boundary between “strong” and “weak” — you interpret closeness to the limits by inspection, just as you would with a scatter graph.
At Higher tier you also meet Pearson’s product moment correlation coefficient (PMCC). The key distinction: PMCC measures the strength of a specifically linear relationship, while Spearman’s rank measures the correlation between rank orders and can pick up any consistent increasing or decreasing pattern, not just a straight-line one. If two variables have a strong non-linear but consistently increasing relationship, both coefficients will be positive, but Spearman’s rank will usually be greater than the PMCC.
A researcher calculates a Spearman’s rank correlation coefficient of \(-0.82\) between students’ daily screen time and their reading test scores.
Step 1 — Direction: the value is negative, so as screen time increases, reading scores tend to decrease.
Step 2 — Strength: \(-0.82\) is close to \(-1\), so by inspection this is a strong negative correlation.
Step 3 — Causation caution: this does not prove screen time causes lower reading scores. A lurking variable, such as time available for reading, could explain both.