Correlations. Analysis of the relationship between co-variables. The…

The idea

A correlation measures how two co-variables move together. Both are measured, neither is manipulated and nothing is controlled, separating it from an experiment and explaining why it cannot show cause. The coefficient runs from minus one to plus one: the sign gives the direction and the size gives the strength, so -0.76 is stronger than 0.31. Plot the pairs on a scattergram and the pattern is visible at a glance. Because nothing was manipulated, an untested third variable may be driving both, and a curved relationship can produce a coefficient near zero even where the link is strong. The pay-off is a quick, ethical first look at variables nobody could manipulate, and a source of hypotheses for future experiments.

What earns the marks

• Co-variables: both are measured as they are found, neither is manipulated, so there is no independent or dependent variable.
• Direction read from the sign and strength read from the magnitude, on a scale running from minus one through zero to plus one.
• The scattergram as the display, with one co-variable on each axis and one point per participant.
• No causal conclusion: without manipulation and control of extraneous variables, the association may run either way or come from a third variable.
• The third-variable problem named with a plausible example from the scenario rather than as an abstract caution.
• A curvilinear relationship can give a coefficient near zero, so a weak coefficient does not prove the variables are unrelated.
• Strengths: uses existing data economically, is ethically possible where manipulation is not, and generates hypotheses for later experimental work.

Common mistakes and how to put them right

• Reading a negative coefficient as a weak one, so -0.8 is ranked below 0.4 when it is the stronger relationship.

• Writing the hypothesis as a difference between conditions instead of a relationship between two operationalised co-variables.

• Sliding into causal language in the conclusion, saying the data show that one variable causes the other.

• Labelling one co-variable as the independent variable, which throws away the very distinction the question is testing.

Exam tips

• Phrase a directional hypothesis as "there will be a positive correlation between" the two co-variables, each operationalised as it was measured.
• When asked why a conclusion is not justified, name a specific third variable that fits the scenario rather than saying correlation is not causation.
• On a scattergram question, label both axes with the co-variables and their units, and plot one point per pair of scores.
• State the level of measurement before choosing between the correlation tests available in the statistical tables.