Scattergrams and correlation coefficients | AQA A-Level Psychology Revision
- Revision Notes
- Aug 5
- 12 min read
Updated: 7 days ago
For 7182 specification, first teach in September 2025
AQA A-Level Psychology | Free Revision Notes
Estimated study time: 55 minutes
This Scattergrams and correlation coefficients A-Level Psychology revision page explains how psychologists display and interpret relationships between two co-variables. You will learn how to plot paired data on a scattergram, distinguish positive, negative and zero correlations, and interpret the direction and strength of a correlation coefficient. These skills form part of AQA Research Methods and build directly on correlations. Careful interpretation matters because a relationship between two co-variables does not necessarily show that one variable causes the other.
Learning Objectives 🎯
By the end of this revision page, you should be able to:
Construct a correctly labelled scattergram from paired data.
Interpret the overall pattern shown by a scattergram.
Distinguish positive, negative and zero correlations.
Identify the direction and strength of a correlation.
Interpret correlation coefficients between \(-1\) and \(+1\).
Explain why a correlation does not demonstrate a causal relationship.
Revision Notes 📚
Scattergrams and correlation coefficients in A-Level Psychology
A correlation investigates whether there is a relationship between two co-variables.
In a correlational investigation, both co-variables are measured for each participant or case. The researcher does not manipulate an independent variable or measure its effect on a dependent variable.
For example, a researcher could measure:
the number of hours each participant sleeps;
each participant’s score on a memory test.
The researcher could then investigate whether sleep and memory scores are related.
The results may be displayed using a scattergram and summarised using a correlation coefficient.
Co-variables
The two measured variables in a correlation are called co-variables.
For example:
Participant | Hours of sleep | Memory score |
A | \(4\) | \(7\) |
B | \(5\) | \(9\) |
C | \(6\) | \(11\) |
D | \(7\) | \(13\) |
E | \(8\) | \(16\) |
In this investigation:
the first co-variable is hours of sleep;
the second co-variable is memory score.
Each participant provides a pair of scores. Participant A provides the pair:
$$(4,7)$$
Participant B provides:
$$(5,9)$$
Each pair becomes one point on the scattergram.
What is a scattergram?
A scattergram, sometimes called a scatter diagram, displays the relationship between two co-variables.
Each point represents one pair of scores.
One co-variable is plotted on the horizontal axis and the other is plotted on the vertical axis. The overall arrangement of the points indicates the direction and possible strength of the relationship.
A scattergram should include:
a clear title;
a labelled horizontal axis;
a labelled vertical axis;
units where appropriate;
suitable and evenly spaced scales;
one accurately plotted point for each pair of scores;
no lines connecting the individual points.
Scattergrams are different from the displays covered in tables and graphs because they show the relationship between two numerical co-variables rather than frequencies for categories or intervals.
Constructing a scattergram
Use the following process:
Identify the two co-variables.
Decide which co-variable will appear on each axis.
Draw and label the horizontal and vertical axes.
Include units where required.
Select suitable, evenly spaced scales.
Plot each pair of scores as one point.
Check every plotted point against the original data.
Add a clear title.
Do not join the individual points.
Worked example: plotting paired scores
A psychologist records each participant’s weekly exercise and wellbeing score.
Participant | Hours of exercise per week | Wellbeing score |
A | \(1\) | \(8\) |
B | \(2\) | \(10\) |
C | \(3\) | \(13\) |
D | \(4\) | \(15\) |
E | \(5\) | \(18\) |
F | \(6\) | \(19\) |
A suitable scattergram would have:
horizontal axis: hours of exercise per week;
vertical axis: wellbeing score;
title: Relationship between weekly exercise and wellbeing score.
The points plotted would be:
$$(1,8)$$
$$(2,10)$$
$$(3,13)$$
$$(4,15)$$
$$(5,18)$$
$$(6,19)$$
As exercise increases, wellbeing scores generally increase. This indicates a positive correlation.
Choosing suitable scales
The scales should:
include every score;
increase in equal intervals;
use most of the available plotting space;
be easy to interpret.
For the exercise data, a suitable horizontal scale might be:
$$0,\ 1,\ 2,\ 3,\ 4,\ 5,\ 6$$
A suitable vertical scale might be:
$$0,\ 5,\ 10,\ 15,\ 20$$
A scale must not use unequal intervals.
For example, the following scale would be unsuitable:
$$0,\ 5,\ 10,\ 20,\ 25$$
The intervals do not increase consistently.
Plotting points accurately
To plot the pair:
$$(4,15)$$
Find \(4\) on the horizontal axis.
Move vertically until you reach \(15\) on the vertical scale.
Mark one clear point at that position.
Do not treat the two values as separate results. Together, they represent one participant’s paired scores.
If two participants have the same pair of scores, their points will appear in the same location. You may need to indicate clearly that more than one case is represented, depending on the information provided in the question.
Interpreting a scattergram
To interpret a scattergram:
Read the title and axis labels.
Identify the direction of the overall pattern.
Judge how closely the points follow that pattern.
Look for points that do not fit the general pattern.
State the relationship using the names of both co-variables.
Avoid making a causal claim.
A complete interpretation should identify both direction and strength where possible.
For example:
The scattergram shows a strong positive correlation between hours of exercise and wellbeing score. As hours of exercise increase, wellbeing scores tend to increase.
This is more precise than simply stating that there is a relationship.
Positive correlation
A positive correlation occurs when higher values of one co-variable are associated with higher values of the other co-variable.
Similarly, lower values of one co-variable tend to be associated with lower values of the other.
On a scattergram, the points generally rise from the lower-left area towards the upper-right area.
For example:
as hours of sleep increase, memory scores increase;
as revision time increases, test scores increase.
A positive correlation coefficient has a value greater than \(0\):
$$0<r\leq+1$$
A perfectly positive correlation has a coefficient of:
$$r=+1$$
This means that all points follow a perfectly consistent positive pattern.
Negative correlation
A negative correlation occurs when higher values of one co-variable are associated with lower values of the other.
On a scattergram, the points generally fall from the upper-left area towards the lower-right area.
For example:
as the number of hours without sleep increases, concentration scores decrease;
as stress scores increase, wellbeing scores decrease.
A negative correlation coefficient has a value below \(0\):
$$-1\leq r<0$$
A perfectly negative correlation has a coefficient of:
$$r=-1$$
This means that all points follow a perfectly consistent negative pattern.
Zero correlation
A zero correlation means that there is no consistent relationship between the two co-variables.
As the value of one co-variable changes, the other does not change in a predictable direction.
The points on a scattergram appear widely dispersed without a clear upward or downward pattern.
A zero correlation coefficient is:
$$r=0$$
For example, a researcher might find no consistent relationship between shoe size and memory-test performance.
Comparing the directions of correlations
Direction | Scattergram pattern | Meaning | Coefficient |
Positive | Points rise from left to right | Both co-variables tend to increase together | Between \(0\) and \(+1\) |
Negative | Points fall from left to right | One co-variable tends to increase as the other decreases | Between \(-1\) and \(0\) |
Zero | No clear pattern | No consistent relationship is shown | Around \(0\) |
The sign of the coefficient shows the direction:
\(+\) means positive;
\(-\) means negative;
a value close to \(0\) indicates little or no relationship.
The strength of a correlation
The strength of a correlation describes how closely the points follow a clear pattern.
A strong correlation has points that cluster closely around an imagined line of best fit.
A weak correlation has points that are more widely scattered, although an overall positive or negative pattern may still be visible.
The strength is shown by how close the correlation coefficient is to either:
$$+1$$
or:
$$-1$$
The closer the coefficient is to either end of the scale, the stronger the correlation.
The closer it is to:
$$0$$
the weaker the correlation.
The correlation coefficient
A correlation coefficient is a numerical value representing the direction and strength of a relationship between two co-variables.
It is commonly represented by:
$$r$$
A correlation coefficient must fall within the range:
$$-1\leq r\leq+1$$
The sign indicates direction, while the size of the value, ignoring the sign, indicates strength.
For example:
$$r=+0.82$$
shows a strong positive correlation.
$$r=-0.82$$
shows a strong negative correlation.
These correlations have the same strength because both have an absolute value of:
$$0.82$$
However, they have opposite directions.
Interpreting example coefficients
Correlation coefficient | Interpretation |
\(r=+0.94\) | Very strong positive correlation |
\(r=+0.71\) | Strong positive correlation |
\(r=+0.32\) | Weak positive correlation |
\(r=0\) | Zero correlation |
\(r=-0.28\) | Weak negative correlation |
\(r=-0.76\) | Strong negative correlation |
\(r=-0.97\) | Very strong negative correlation |
Descriptions such as weak, moderate or strong are judgements based on how close the coefficient is to zero or to either perfect correlation. The safest approach is to report the coefficient itself alongside a clear description.
For example:
There was a strong negative correlation between stress and wellbeing, \(r=-0.81\).
Comparing the strength of coefficients
Consider these coefficients:
$$r=+0.68$$
and:
$$r=-0.91$$
Ignore the signs when comparing strength:
$$|+0.68|=0.68$$
$$|-0.91|=0.91$$
Because:
$$0.91>0.68$$
the correlation of:
$$r=-0.91$$
is stronger.
The negative sign does not make a correlation weaker. It only shows that the relationship is negative.
Worked example: direction and strength
A researcher calculates the relationship between hours spent using a phone before sleep and sleep-quality scores:
$$r=-0.74$$
The sign is negative, so the relationship is a negative correlation.
The coefficient is reasonably close to:
$$-1$$
so the relationship is strong.
A suitable interpretation is:
There is a strong negative correlation between phone use before sleep and sleep-quality score. As phone use increases, sleep-quality scores tend to decrease.
This does not show that phone use caused lower sleep quality.
Reporting correlation coefficients
AQA identifies expressing a correlation coefficient to two or three significant figures as an example of using an appropriate level of numerical precision.
Suppose a calculated coefficient is:
$$0.783624$$
To three significant figures:
$$\boxed{r=0.784}$$
Suppose another coefficient is:
$$-0.45678$$
To three significant figures:
$$\boxed{r=-0.457}$$
Keep the negative sign when rounding a negative coefficient.
The use of significant figures is covered in percentages, ratios and numerical data.
Scattergram pattern and coefficient
The scattergram and correlation coefficient describe the same relationship in different ways.
Scattergram | Correlation coefficient |
Provides a visual representation | Provides a numerical summary |
Shows the arrangement of individual cases | Summarises direction and strength |
Makes unusual points visible | Allows precise comparison between correlations |
Requires visual interpretation | Gives a value between \(-1\) and \(+1\) |
A scattergram may show important features that are not fully communicated by a single coefficient. For example, it may reveal an unusual score that does not fit the main pattern.
Unusual scores
An unusual score is a point positioned away from the general pattern of the other points.
For example, most participants might show increasing memory scores as sleep increases, but one participant with high sleep may have a very low memory score.
This point may weaken the overall correlation because the scores follow the general pattern less consistently.
When interpreting a scattergram, you may describe an unusual point, but you should not automatically assume why it occurred.
Correlation does not show causation
A correlation shows that two co-variables are related. It does not demonstrate that one co-variable caused a change in the other.
Suppose a researcher finds a positive correlation between exercise and wellbeing.
It would be appropriate to conclude:
Higher levels of exercise were associated with higher wellbeing scores.
It would not be appropriate to conclude:
Exercise caused the increase in wellbeing.
There are several possible explanations for a correlation:
The first co-variable may influence the second.
The second co-variable may influence the first.
Another variable may influence both.
For example, social support might influence both exercise levels and wellbeing.
This is one of the key differences between correlational and experimental research.
Correlations and experiments
Correlation | Experiment |
Measures two co-variables | Manipulates an independent variable |
Investigates a relationship | Investigates the effect on a dependent variable |
Does not establish cause and effect | May support a causal conclusion when sufficiently controlled |
Can study variables that cannot be manipulated | Requires manipulation or naturally occurring differences |
Often presented using a scattergram | Results may be presented using tables or graphs |
A correlational investigation is useful for identifying relationships, but its findings must be interpreted carefully.
Writing a precise interpretation
A strong answer should include:
the direction;
the strength;
the names of both co-variables;
a description of how the variables are associated;
cautious language that avoids claiming causation.
For example:
The data show a strong positive correlation between revision time and examination score. Participants who reported more revision time tended to achieve higher examination scores.
Avoid writing:
Revision time definitely causes examination scores to increase.
Selecting a suitable statistical test
The appropriate inferential test for a correlation depends partly on the level of measurement.
The specification requires students to know when to use Spearman’s rho and Pearson’s \(r\). These tests are covered in Spearman’s rho and Pearson’s r.
Understanding whether data are nominal, ordinal or interval will support the selection of an appropriate test. This is covered in levels of measurement.
Key Words 🔑
Key word | Student-friendly definition | How it may be used in an exam |
Correlation | A relationship between two measured co-variables. | You may need to identify, describe or interpret a relationship. |
Co-variable | One of the two variables measured in a correlational investigation. | You may be asked to identify the co-variables in a research scenario. |
Scattergram | A graph on which each point represents a pair of scores for two co-variables. | You may need to construct or interpret one. |
Paired scores | Two related values obtained from the same participant or case. | Each pair is plotted as one point on a scattergram. |
Positive correlation | A relationship in which higher values of one co-variable are associated with higher values of the other. | You may identify this from an upward scattergram pattern or a positive coefficient. |
Negative correlation | A relationship in which higher values of one co-variable are associated with lower values of the other. | You may identify this from a downward pattern or a negative coefficient. |
Zero correlation | An absence of a consistent relationship between the co-variables. | You may identify this from a scattered pattern or a coefficient near zero. |
Correlation coefficient | A value between \(-1\) and \(+1\) showing the direction and strength of a correlation. | You may be asked to interpret or compare coefficients. |
Direction | Whether the relationship is positive, negative or zero. | The sign of the coefficient indicates direction. |
Strength | How closely the paired scores follow a consistent relationship. | The closer the coefficient is to \(-1\) or \(+1\), the stronger the relationship. |
Perfect positive correlation | A completely consistent positive relationship. | It is represented by \(r=+1\). |
Perfect negative correlation | A completely consistent negative relationship. | It is represented by \(r=-1\). |
Unusual score | A point that is positioned away from the general scattergram pattern. | You may identify how it affects the apparent strength of a correlation. |
Causation | A relationship in which one factor directly produces a change in another. | You should explain that correlation alone does not demonstrate causation. |
Hints from the Examiner Reports 💡
No lesson-specific examiner guidance was identified in the provided reports.
Common Mistakes ⚠️
Mistake: Plotting the two scores from one participant as separate points.
Why this is incorrect:
Each participant provides one pair of scores, so both values must be represented by a single point.
How to improve:
Write each pair as a coordinate before plotting it:
$$(x,y)$$
Mistake: Joining the individual points on a scattergram.
Why this is incorrect:
The points represent separate participants or cases rather than a continuous sequence.
How to improve:
Plot each point clearly but do not connect the points.
Mistake: Failing to label both axes.
Why this is incorrect:
The reader cannot determine which co-variable is represented by each axis.
How to improve:
Write the full name of each co-variable and include units where required.
Mistake: Describing a negative correlation as weak because it has a minus sign.
Why this is incorrect:
The minus sign indicates direction, not strength.
For example:
$$r=-0.92$$
is a strong negative correlation.
How to improve:
Ignore the sign when judging strength and consider how close the value is to \(1\).
Mistake: Interpreting a coefficient close to zero as strong.
Why this is incorrect:
Values close to zero indicate a weak or absent relationship.
How to improve:
Remember:
$$r\approx0$$
means little or no consistent correlation.
Mistake: Giving only the direction of the correlation.
Why this is incorrect:
A complete interpretation should usually describe both direction and strength.
How to improve:
Use a phrase such as:
There is a strong positive correlation between the two co-variables.
Mistake: Describing only the graph without naming the co-variables.
Why this is incorrect:
An answer such as “the points go upwards” does not explain the psychological relationship.
How to improve:
State how one named co-variable tends to change as the other changes.
Mistake: Claiming that one co-variable caused the other.
Why this is incorrect:
Correlation measures an association and does not establish cause and effect.
How to improve:
Use cautious language such as:
associated with;
related to;
tends to increase;
tends to decrease.
Mistake: Reporting an impossible coefficient.
Why this is incorrect:
A correlation coefficient cannot fall outside:
$$-1\leq r\leq+1$$
Values such as:
$$r=1.24$$
or:
$$r=-1.08$$
are not valid correlation coefficients.
How to improve:
Check that the value lies between \(-1\) and \(+1\).
Mistake: Rounding away the negative sign.
Why this is incorrect:
The sign communicates the direction of the correlation.
How to improve:
Retain the sign when rounding:
$$-0.7462\rightarrow-0.746$$
to three significant figures.
Exam-Style Questions ✍️
Question 1
Define the term co-variable.[1 mark]
Question 2
State the possible range of values for a correlation coefficient.[1 mark]
Question 3
A researcher records the number of hours each participant sleeps and their score on a concentration task.
Participant | Hours of sleep | Concentration score |
A | \(4\) | \(8\) |
B | \(5\) | \(10\) |
C | \(6\) | \(13\) |
D | \(7\) | \(15\) |
E | \(8\) | \(17\) |
F | \(9\) | \(18\) |
Construct a fully labelled scattergram to display these results.[4 marks]
Question 4
Using the data in Question 3, identify the direction of the correlation and explain your answer.[2 marks]
Question 5
A psychologist calculates the following correlation coefficient between stress scores and wellbeing scores:
$$r=-0.83$$
Interpret the direction and strength of this correlation.[2 marks]
Question 6
A researcher obtains the following three coefficients:
$$r=+0.24$$
$$r=-0.91$$
$$r=+0.68$$
a) Identify the strongest correlation.[1 mark]
b) Identify the weakest correlation.[1 mark]
c) Explain how you reached your answers.[2 marks]
Question 7
A researcher calculates a correlation coefficient of:
$$r=-0.74628$$
Report this coefficient to three significant figures.[1 mark]
Question 8
A study finds a strong positive correlation between the number of hours students revise and their examination scores.
Explain why the researcher cannot conclude that additional revision caused the higher examination scores.[3 marks]
Question 9
A researcher investigates the relationship between daily social-media use and sleep-quality scores.
Participant | Social-media use in minutes | Sleep-quality score |
A | \(30\) | \(18\) |
B | \(45\) | \(16\) |
C | \(60\) | \(15\) |
D | \(90\) | \(12\) |
E | \(120\) | \(9\) |
F | \(150\) | \(7\) |
a) Plot the data on a scattergram.[4 marks]
b) Describe the relationship shown by the data.[2 marks]
c) Explain one reason why the researcher should not make a causal conclusion.[2 marks]
Question 10
The descriptions below were written by students interpreting correlations.
Student A:“There is a negative correlation, so the relationship must be weak.”
Student B:“The coefficient is \(r=+0.89\), so increasing one variable definitely causes the other variable to increase.”
Student C:“The coefficient is \(r=-0.06\), which indicates little or no consistent relationship between the co-variables.”
Identify which student has given the most accurate interpretation. Explain why the other two interpretations are incorrect.[6 marks]
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