What a correlation is

1. A correlation is a relationship between two variables, where a change in one tends to go with a change in the other.
2. Nothing is manipulated, so a correlational study measures both variables as they already are.
3. The hypothesis predicts a relationship between the two variables named in it.
4. The result is reported as one of three patterns: positive, negative or zero.

Co-variables

1. The two variables measured in a correlation are called co-variables.
2. There is no independent variable and no dependent variable, because the researcher changes nothing.
3. Each co-variable is operationalised, which means saying exactly how it will be measured.
4. "Sleep" becomes "hours slept last night", and "mood" becomes "a self-rating from 1 to 10".
5. Every participant supplies one value for each co-variable, so each person contributes a pair of numbers.

Use of quantitative data

1. Both co-variables produce numbers, so a correlation always runs on quantitative data.
2. Those numbers can come from a test score, a time in seconds, a tally from an observation or a rating scale.
3. Each set of numbers can be summarised on its own with a mean, a median, a mode or a range.
4. Strength: numbers are objective, so two researchers reading the same data set describe the same pattern.
5. Weakness: a number can be a poor stand-in for the behaviour, and a weak measure of "happiness" makes the pattern hard to trust, which lowers validity.
6. Qualitative data cannot be used, because words cannot be placed on the two axes of a graph.

Positive, negative and zero correlations

1. Positive correlation.
   1. As one co-variable rises, the other rises too.
   2. On a scatter diagram the points slope upwards from left to right.
   3. The more hours a pupil revises, the higher their test score tends to be.
2. Negative correlation.
   1. As one co-variable rises, the other falls.
   2. On a scatter diagram the points slope downwards from left to right.
   3. The more time a teenager spends on a screen after 10pm, the fewer hours they sleep.
3. Zero correlation.
   1. There is no relationship between the two co-variables.
   2. On a scatter diagram the points form a shapeless cloud with no slope.
   3. Shoe size and test score show no pattern.

Reading a scatter diagram

1. One co-variable goes on the x-axis and the other on the y-axis, each with a label and units.
2. Each participant becomes a single point, placed where their two values meet.
3. Points rising to the right show a positive correlation, and points falling to the right show a negative one.
4. The tighter the points sit to a straight line, the stronger the correlation that can be described.
5. A scatter diagram also needs a title, so the reader knows which two measurements are plotted.

Strengths and weaknesses of correlations

1. Strength: it can study variables nobody could ethically manipulate, such as hours of sleep lost or how much someone smokes.
2. Strength: behaviour is measured as it already is rather than in a set task, so ecological validity is good.
3. Strength: the two measurements can be taken again with a fresh sample, so the study is repeatable and reliability can be high.
4. Strength: it is a quick and cheap way to check whether a link exists before an experiment is designed.
5. Weakness: it cannot show cause and effect, because no variable is controlled and extraneous variables are left uncontrolled.
6. Weakness: a badly measured co-variable makes the pattern misleading, and a self-rating brings social desirability bias with it.
7. Weakness: a relationship that is real but not a straight line can look like zero, so a true link gets missed.

Why a correlation cannot show cause

1. A correlation shows that two variables move together, which leaves the direction of any influence unknown.
2. Less sleep might produce a lower mood, or a lower mood might produce less sleep.
3. A third variable could be driving both, so stress could be pushing the sleep figures down and the mood ratings down at the same time.
4. An experiment, where an independent variable is manipulated and other variables controlled, is what tests for cause.
5. A correlation therefore fits an objective about whether two measurements go together.

Turning this into marks

1. When a direction and a conclusion are both asked for, keep them as two separate points, one naming positive, negative or zero and one saying what that means for the two variables in the study.
2. Name both co-variables as they were measured, such as hours slept last night and a mood rating out of 10, because "sleep and mood are linked" does not secure the knowledge mark.
3. Describe the slope of the points before naming the pattern, since a scatter with no slope gives a zero correlation.
4. The mark most often lost is writing that the correlation proves one variable caused the other.