What a correlation is
Correlation
A relationship between two variables, where a change in one tends to go with a change in the other. It does not on its own show that one variable causes the other.
- A correlation looks at whether two things you have measured tend to change together.
- Neither variable is manipulated, which is why a correlation is not an experiment and has no independent variable.
- You take a pair of scores from every participant and then look at the pattern across the whole set.
Positive and negative correlations
Co-variables
The two variables measured in a correlation, neither of which is manipulated by the researcher.
- Positive correlation means that as one co-variable goes up, the other tends to go up as well.
- Negative correlation means that as one co-variable goes up, the other tends to go down.
- No correlation means the two co-variables show no consistent pattern in either direction.
- The more hours a pupil spends revising, the higher their mock score tends to be, and that is a positive correlation.
- The more time a pupil spends on a phone after ten at night, the fewer hours they sleep, and that is a negative correlation.
- Shoe size and mock score show nothing at all, and that is no correlation.
Scatter diagrams
Scatter diagram
A graph that plots two variables against each other, with one point for each participant, used to show the correlation between them.
- A scatter diagram shows a correlation by putting one co-variable on each axis.
- Each participant contributes exactly one point, placed where their two scores meet.
- Points that climb from left to right show a positive correlation, and points that fall from left to right show a negative one.
- Points scattered with no slope show no correlation, and the closer the points sit to a straight line the stronger the relationship.
- Do not join the points up, because a scatter diagram is not a line graph.
- Do not call a relationship strong on the strength of a handful of points, because a small sample can look convincing purely by chance.
Correlation does not show causation
- A correlation tells you that two variables move together and it tells you nothing else.
- The relationship may run the opposite way round, so poor sleep could be driving the late phone use rather than the other way about.
- A third variable you never measured could be producing both, such as worry keeping a pupil awake and on their phone at the same time.
- Only an experiment, where you set the independent variable yourself, can properly test for cause.
Strengths
- It reaches relationships you could not create, since variables such as sleep and exam performance can be studied without interfering with anyone's life.
- It is a good first step, because it is quick and often uses data that already exists, so it shows whether a relationship is worth a full experiment.
Weaknesses
- Cause stays out of reach, because however convincing the pattern looks the design cannot tell you which variable acted on which, or whether either did.
- Both co-variables have to become numbers, so something like stress must be scored before it can be plotted, and that score may capture the real thing poorly.
When to choose a correlation
- Choose it when manipulating either variable would be impossible, impractical or unethical.
- Choose it when you want to check cheaply whether two variables are related at all before designing something larger.
- Choose an experiment instead the moment your question is actually about cause.
Turning this into marks
- Reading a scatter diagram, name the direction together with the two variables.
- A hypothesis here predicts a relationship between two named, measurable variables, not a difference between two groups.
- The mark most often lost comes from writing that a correlation proves one thing causes another.
- What is a correlation, and what are co-variables?
- Describe what positive and negative correlations look like on a scatter diagram.
- Give two reasons why a correlation cannot show that one variable causes the other.
- When would you choose a correlation over an experiment?