Correlation (Edexcel GCSE Statistics): Revision Notes
Correlation
What is correlation?
Correlation is a way of describing the relationship between two variables using scatter diagrams. When we look at correlation, we're trying to see if there's a pattern or connection between how two different measurements change together. Correlation shows us whether there's an association between variables, and this can reveal either increasing or decreasing trends.
A scatter diagram (also called a scatter plot) is the main tool we use to spot correlations. Each point on the diagram represents a pair of values, and by looking at how these points are arranged, we can identify different types of relationships.
Types of correlation
There are five main types of correlation you need to recognise:
Strong positive correlation
When one variable increases, the other variable also increases in a clear, consistent pattern. The points on a scatter diagram form a tight line that slopes upwards from left to right. For example, as hours spent revising increase, test results also increase significantly.
Weak positive correlation
Similar to strong positive correlation, but the relationship is less clear-cut. The points still generally trend upwards, but they're more spread out. There's still a positive relationship, but it's not as predictable. An example might be the relationship between height and shoe size - generally taller people have bigger feet, but there are plenty of exceptions.
No correlation
There's no clear relationship between the two variables at all. The points on the scatter diagram appear randomly scattered with no obvious pattern. For example, there's no correlation between the number of bracelets someone wears and their test results.
Weak negative correlation
As one variable increases, the other tends to decrease, but the pattern isn't very strong. The points generally slope downwards from left to right but are quite spread out. An example might be age and reaction time - as people get older, their reactions tend to slow down, but there's lots of variation.
Strong negative correlation
As one variable increases, the other decreases in a clear, consistent pattern. The points form a tight line sloping downwards from left to right. For example, as hours of TV watched per day increases, test results decrease significantly.
Reading scatter diagrams
When interpreting scatter diagrams, look at:
- Direction: Does the pattern go up (positive) or down (negative) from left to right?
- Strength: Are the points tightly clustered around a line (strong) or more spread out (weak)?
- Pattern: Are the points forming a straight line or a curve?
Non-linear correlation
Sometimes correlation doesn't follow a straight line pattern. Non-linear correlation occurs when there's still a clear relationship between variables, but the pattern forms a curve rather than a straight line.
For example, the relationship between a circle's radius and its area shows positive non-linear correlation. As the radius increases, the area increases too, but at an increasing rate, creating a curved pattern. This still shows correlation, but the trend line would be curved rather than straight.
Worked example: Temperature and coat sales
Let's work through a real example step by step.
Question: A shop owner recorded average monthly temperature and money made from coat sales. Here's the data:
| Temperature (°C) | 4 | 3 | 8 | 12 | 18 | 25 | 22 |
|---|---|---|---|---|---|---|---|
| Money made (£1000s) | 46 | 50 | 49 | 23 | 14 | 4 | 5 |
(a) Plot a scatter diagram to show this information
To create the scatter diagram:
- Draw your axes with temperature on the x-axis (horizontal) and money made on the y-axis (vertical)
- Scale your axes appropriately - temperature from 0 to 25°C, money from 0 to 50 (£1000s)
- Plot each pair of coordinates: (4,46), (3,50), (8,49), (12,23), (18,14), (25,4), (22,5)
(b) Describe and interpret the type of correlation shown
Looking at the plotted points, we can see they form a clear downward trend from left to right. This indicates strong negative correlation.
Interpretation: As the temperature increases, the money made from coat sales decreases. This makes perfect sense - when it's warmer, people buy fewer coats, so the shop makes less money from coat sales. When it's colder, people need coats, so sales increase.
Common exam tips
- Always look at the context when interpreting correlation - does the relationship make logical sense?
- Remember that correlation doesn't prove causation - just because two things are correlated doesn't mean one causes the other
- When describing correlation, always mention both the strength (strong/weak) and direction (positive/negative)
- For non-linear correlation, mention that there's still a relationship but it follows a curved pattern
- Practice identifying explanatory variables (the one you think might influence the other) and response variables (the one being influenced)
Remember!
- Correlation describes the relationship between two variables shown on scatter diagrams
- There are five types: strong positive, weak positive, no correlation, weak negative, and strong negative
- Positive correlation means both variables increase together; negative correlation means as one increases, the other decreases
- Strong correlation shows points close to a line; weak correlation shows points more spread out
- Non-linear correlation can still show clear relationships but follows curved patterns rather than straight lines
- Always interpret your findings in context - does the correlation make logical sense?