4.2.3.2 - Interpreting correlation coefficients
A correlation coefficient condenses both direction and strength into a value from -1 to +1. You will interpret the sign, magnitude and context of coefficients, distinguish strong negative relationships from weak positive ones, and translate values into careful conclusions. The lesson keeps association separate from causation and considers how outliers, restricted ranges and nonlinear patterns can make a single coefficient misleading.
What the coefficient adds
You already know that a correlation investigates the relationship between two measured co-variables. This lesson goes one step further: how to analyse and interpret the number that summarises that relationship.
Correlation coefficient
A correlation coefficient is a numerical value between -1 and +1 that shows the direction and strength of a relationship between two co-variables.
The coefficient is usually written as a decimal, such as +0.72, -0.48 or +0.03. In A-level Psychology, you may see it labelled as r for Pearson's r or as rho for Spearman's rho. The exact statistical test is covered later in inferential testing; here, the key skill is interpretation.
Every coefficient gives two pieces of information:
| Feature | What to read | Example |
|---|---|---|
| Direction | Look at the sign: + or - | +0.66 is positive; -0.66 is negative. |
| Strength | Look at how close the number is to 1, ignoring the sign | +0.84 and -0.84 are both strong. |
The number 0 sits in the middle. Pearson's r close to 0 shows little or no straight-line relationship; Spearman's rho close to 0 shows little or no monotonic rank relationship. A coefficient close to +1 or -1 shows a strong relationship. The endpoints are perfect correlations:
| Coefficient | Basic interpretation |
|---|---|
| +1.00 | Perfect positive correlation |
| 0.00 | No linear correlation for Pearson; no monotonic rank association for Spearman |
| -1.00 | Perfect negative correlation |
For Pearson's r, a perfect correlation means the paired scores fall exactly on a straight line. Spearman's rho instead summarises how consistently ranks move together: a perfect result means perfectly matching or reversed rank order, even if the original scores form a curve. A relationship that consistently increases or consistently decreases is called monotonic. Both coefficients range from −1 to +1, but Pearson describes a linear pattern while Spearman describes a monotonic rank pattern.
Direction: reading the sign
The sign tells you whether the co-variables tend to move in the same direction or in opposite directions.
Positive correlation
A positive correlation occurs when, as one co-variable increases, the other co-variable also tends to increase.
Negative correlation
A negative correlation occurs when, as one co-variable increases, the other co-variable tends to decrease.
The sign is about direction, not quality. A negative correlation is not a "bad" correlation, and it is not automatically weak. A value of -0.86 shows a much stronger relationship than +0.21.
| Coefficient | Direction | Good AQA-style wording |
|---|---|---|
| +0.62 | Positive | As self-esteem score increases, resilience score tends to increase. |
| -0.62 | Negative | As anxiety score increases, number of hours slept tends to decrease. |
| +0.04 | Very weak positive / near zero | There is little or no relationship between shoe size and memory score. |
| -0.04 | Very weak negative / near zero | There is little or no relationship between age in months and questionnaire score in this sample. |
For AQA, avoid vague phrases such as "one goes up" if the scenario gives named co-variables. State the actual relationship:
| Vague | Better |
|---|---|
| "It goes up." | "As daily caffeine intake increases, alertness score tends to increase." |
| "It is negative." | "As hours of sleep increases, tiredness rating tends to decrease." |
| "There is no effect." | "There is little or no correlation between handwriting neatness and recall score." |
The word tends matters. Correlations describe patterns across paired scores. They do not mean every single participant follows the pattern exactly.
Strength: reading the size
Strength is shown by the absolute value of the coefficient: the number without its sign. The closer this value is to 1, the stronger the relationship. The closer it is to 0, the weaker the relationship.
Absolute value
The absolute value of a number is its size without the positive or negative sign. For example, +0.80 and -0.80 both have an absolute value of 0.80.
This means +0.80 and -0.80 are equally strong. They differ only in direction.
| Coefficient | Strength judgement | Full interpretation |
|---|---|---|
| +0.94 | Very strong | Very strong positive correlation |
| +0.51 | Moderate | Moderate positive correlation |
| +0.18 | Weak | Weak positive correlation |
| -0.18 | Weak | Weak negative correlation |
| -0.51 | Moderate | Moderate negative correlation |
| -0.94 | Very strong | Very strong negative correlation |
There are no universal AQA cut-off points where "weak" suddenly becomes "moderate" or "strong". In an exam, use sensible comparative language based on closeness to 0 or 1. If two coefficients are compared, explain the comparison directly:
| Pair of coefficients | Stronger relationship | Why |
|---|---|---|
| +0.72 and +0.31 | +0.72 | It is closer to +1 and further from 0. |
| -0.72 and +0.31 | -0.72 | It has the larger absolute value, so it is stronger despite being negative. |
| -0.05 and +0.08 | +0.08 is numerically stronger | Its absolute value is larger, although both associations are very weak. |
Do not turn a coefficient into a percentage. A correlation of +0.60 does not mean "60% of participants had a positive relationship" or "one variable caused 60% of the other". For this lesson, treat the coefficient as a summary of direction and strength.
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