Correlation, Causation and the Vocabulary of Association
What Is Correlation?
When two variables tend to change together, we say there is a correlation between them. Correlation is about pattern, not proof. Statisticians have a precise vocabulary for describing correlations, and using the right term in the right context is one of the most reliable ways to pick up marks in interpretation questions.
Direction: Positive, Negative and Zero
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 from the city centre and house price often show negative correlation: properties further from the centre tend to cost less (though this depends heavily on context).
Zero correlation (no correlation) means there is no consistent relationship between the two variables. The points on a scatter graph are scattered randomly with no discernible pattern.
The three directions: positive correlation (both variables increase together), negative correlation (one increases as the other decreases), zero correlation (no consistent pattern). The word “moderate” for correlation strength is NOT used in this specification — use strong, weak, or no correlation only.
Strength: Strong, Weak and No Correlation
The strength of a correlation describes how closely the points cluster around a straight line. The specification defines precise thresholds for strength based on the value of the correlation coefficient \(r\):
- Strong correlation: \(|r| \geq 0.6\) (i.e. \(r \geq 0.6\) or \(r \leq -0.6\))
- Weak correlation: \(0.2 \leq |r| < 0.6\) (i.e. between 0.2 and 0.6 in magnitude)
- No correlation: \(|r| < 0.2\) (i.e. between \(-0.2\) and \(0.2\), not including these endpoints)
These thresholds are fixed by the specification. Do not use the word “moderate” — the specification explicitly excludes this term. Do not make up your own thresholds. Use strong, weak, or no correlation as described above.
Interpolation and Extrapolation
Interpolation means using the line of best fit to estimate a value that falls within the range of the data you collected. If your data covers ages 20 to 60 and you estimate for age 35, that is interpolation. Interpolation is generally considered reliable when the correlation is strong.
Extrapolation means extending the line beyond the range of your data to estimate a value. If your data covers ages 20 to 60 and you try to estimate for age 80, that is extrapolation. Extrapolation is much less reliable — the relationship seen within the data range may not continue outside it. The line of best fit might predict a negative house price if extended far enough, which is obviously impossible.
Interpolation (within the data range) is generally more reliable. Extrapolation (beyond the data range) is risky because the relationship seen in the data may not continue outside it. The further you extrapolate, the less reliable the estimate.
Causation vs Association
This is the most important idea in this lesson — and one of the most commonly examined. Finding a strong correlation between two variables does NOT mean that one causes the other. The specification explicitly states: correlation does not necessarily imply causation.
Consider this: there is a strong positive correlation between ice cream sales and drowning incidents over time. Does ice cream cause drowning? No. Both variables share a common cause: hot weather. People buy more ice cream in hot weather, and more people swim in hot weather, leading to more drowning incidents. The ice cream and the drowning are both responses to the temperature — they did not cause each other.
The hidden factor that explains both variables is called a lurking variable (also called a confounding variable). The specification says you should know that there are multiple factors that may interact. Any time you see a strong correlation, a good statistician asks: “Is there a third variable that could explain this?”
This is one of the most tested misconceptions in GCSE Statistics. Students see a correlation of 0.8 and write “the increase in X causes an increase in Y.” This will cost marks.
The correct language is: “There is a strong positive correlation between X and Y. This suggests X and Y are associated, but this does not mean X causes Y. There could be a lurking variable that explains both.” Using the word “associated” rather than “causes” shows you understand the distinction.
Interpreting Correlation Coefficients
At Foundation and Higher tier, you need to interpret a given Spearman's rank correlation coefficient. It measures the strength and direction of correlation between the rank orders of two variables — not the raw values. It works for any data that can be ranked, including ordinal data.
Pearson's PMCC (Higher): Pearson's product moment correlation coefficient (PMCC) measures the strength and direction of a linear relationship between two quantitative variables. The key distinction: Spearman's measures correlation of rank orders, whereas Pearson's measures the linear relationship itself. For a straight-line relationship between continuous variables, Pearson's is more appropriate; for ranked or ordinal data, Spearman's is preferred.
For questions that use Spearman's rank formula, it will be given. You do not need to memorise it. Interpret the resulting value using the same thresholds above: \(|r_s| \geq 0.6\) = strong, \(0.2 \leq |r_s| < 0.6\) = weak, \(|r_s| < 0.2\) = no correlation.
A researcher finds a Spearman's rank correlation coefficient of \(-0.72\) between students' daily screen time and their reading test scores.
Step 1: Direction — the value is negative, so this is a negative correlation. As screen time increases, reading scores tend to decrease.
Step 2: Strength — \(|-0.72| = 0.72\), which is \(\geq 0.6\), so this is a strong negative correlation.
Step 3: Causation caution — this does not prove that screen time causes lower reading scores. Other factors (e.g. time available for reading, parental education) might explain both variables.