Data Handling » Scatter Diagrams for Correlation

What you'll learn this session

Study time: 30 minutes

What correlation means and the different types
How to create and interpret scatter diagrams
How to use scatter diagrams to identify correlations
The strengths and limitations of correlation studies
How to calculate correlation coefficients
Why correlation does not equal causation

Introduction to Scatter Diagrams for Correlation

In psychology, we often want to know if two variables are related to each other. For example, is there a relationship between the number of hours spent studying and exam scores? Or between social media use and anxiety levels? Scatter diagrams help us visualise these relationships and determine if a correlation exists.

Key Definitions:

Correlation: A statistical relationship between two variables.
Scatter diagram: A graph that shows the relationship between two variables by plotting data points.
Variables: Factors that can be measured and can change (vary).
Co-variables: The two variables being studied in a correlation.

📊 Types of Correlation

There are three main types of correlation:

Positive correlation: As one variable increases, the other also increases (e.g., study time and exam scores).
Negative correlation: As one variable increases, the other decreases (e.g., time spent gaming and homework completion).
Zero correlation: No relationship between the variables (e.g., shoe size and intelligence).

🔍 Strength of Correlation

Correlations can vary in strength:

Strong correlation: Points on the scatter diagram form a clear pattern.
Moderate correlation: Points show a pattern but with some variation.
Weak correlation: Points show a slight pattern but with lots of variation.
No correlation: Points show no pattern at all.

Creating Scatter Diagrams

A scatter diagram (also called a scattergram or scatter plot) is a visual representation of the relationship between two variables. Each point on the diagram represents one participant or case with measurements for both variables.

How to Create a Scatter Diagram

Collect data for two variables from the same participants or cases.
Draw a horizontal axis (x-axis) for one variable and a vertical axis (y-axis) for the other.
Label each axis with the variable name and units of measurement.
Plot each data point on the graph where the x and y values meet.
Add a title that describes what the scatter diagram shows.

👍 Positive Correlation

Points form a pattern from bottom-left to top-right. As x increases, y increases.

Example: Hours of revision and exam scores.

👎 Negative Correlation

Points form a pattern from top-left to bottom-right. As x increases, y decreases.

Example: Hours spent on social media and hours spent studying.

😐 Zero Correlation

Points are scattered randomly with no clear pattern.

Example: Favourite colour and reaction time.

Case Study Focus: Sleep and Academic Performance

A psychology researcher collected data from 30 GCSE students about their average hours of sleep per night and their recent exam scores. When plotted on a scatter diagram, the points showed a moderate positive correlation - students who got more sleep tended to achieve higher exam scores. However, some students with less sleep still performed well, showing that while there's a relationship, other factors also influence exam performance.

Interpreting Scatter Diagrams

When looking at a scatter diagram, consider these key aspects:

Direction: Is the pattern rising (positive) or falling (negative)?
Strength: How closely do the points follow a clear line or pattern?
Outliers: Are there any points that don't fit the general pattern?
Clusters: Are there groups of points that might suggest different patterns for different subgroups?

📈 Correlation Coefficient

The correlation coefficient (r) is a numerical measure of correlation strength, ranging from -1 to +1:

+1: Perfect positive correlation
0: No correlation
-1: Perfect negative correlation

Generally:

0.7 to 1.0 (or -0.7 to -1.0): Strong correlation
0.3 to 0.7 (or -0.3 to -0.7): Moderate correlation
0 to 0.3 (or 0 to -0.3): Weak correlation

⚠ Correlation ≠ Causation

A common mistake is assuming that correlation means one variable causes the other. Just because two variables are related doesn't mean one causes the other. There are three possible explanations for a correlation:

Variable A causes Variable B
Variable B causes Variable A
A third variable C causes both A and B

Example: Ice cream sales and drowning deaths both increase in summer. The correlation is due to a third variable: hot weather.

Strengths and Limitations of Correlation Studies

👍 Strengths

Allow researchers to study variables that can't be manipulated experimentally (e.g., age, gender)
Can identify relationships that might be worth investigating further
Often use naturally occurring data from real-life settings
Can study multiple variables at once
Usually more ethical than experiments as they don't manipulate variables

👎 Limitations

Cannot establish cause and effect relationships
May be affected by extraneous variables not being measured
Correlations can sometimes be coincidental or spurious
May oversimplify complex relationships
Outliers can significantly affect the apparent correlation

Using Scatter Diagrams in Psychological Research

Psychologists use scatter diagrams in many areas of research:

Developmental psychology: Studying relationships between age and cognitive abilities
Clinical psychology: Examining links between therapy duration and symptom reduction
Educational psychology: Investigating relationships between teaching methods and learning outcomes
Health psychology: Exploring connections between stress levels and physical health measures

Real-World Example: Screen Time and Mental Health

A 2019 study collected data on daily screen time and self-reported anxiety levels from 500 teenagers. The scatter diagram showed a weak positive correlation (r = 0.25), suggesting that higher screen time was somewhat associated with higher anxiety. However, the researchers noted that the relationship was complex - some teens used screens to cope with existing anxiety, while for others, excessive screen use might have contributed to anxiety. This highlights why correlation findings need careful interpretation.

Practical Application: Drawing Conclusions from Scatter Diagrams

When writing about correlations in psychology, follow these steps:

Describe the pattern: State the direction and strength of the correlation.
Support with evidence: Mention the correlation coefficient if available.
Interpret carefully: Discuss possible explanations but avoid claiming causation.
Consider limitations: Acknowledge other factors that might influence the relationship.
Suggest further research: Propose how the relationship could be investigated further.

Remember that correlation studies are valuable for identifying patterns and generating hypotheses, but experimental methods are needed to establish cause and effect relationships.

💡 Exam Tip

In your GCSE Psychology exam, you might be asked to:

Identify the type and strength of correlation from a scatter diagram
Explain why correlation doesn't prove causation
Suggest alternative explanations for correlational findings
Evaluate the strengths and limitations of correlational research

Always remember to use psychological terminology correctly and provide real-life examples to support your answers.

🧠 Test Your Knowledge!