Data, Correlation & Causal Reasoning
How do data change what we are justified in claiming?
What does a number prove?
A study finds that students who report more sleep also tend to earn higher memory-test scores. Write one conclusion the data support and one conclusion they do not support.
When does an association become a causal claim?
By the end of today
- Interpret frequency, percentage, mean, median, range, distribution, and outlier at an introductory level.
- Recognize positive, negative, and near-zero associations.
- Explain why correlation does not establish causation.
- Identify third-variable and directionality problems.
- Evaluate graph integrity and distinguish descriptive from causal language.
correlation
Formal definition
A statistical relationship indicating the degree to which two variables vary together.
Student-friendly definition
A pattern showing that when one variable changes, another tends to change too—without automatically telling us why.
Related: association · directionality · third variable · scatterplot · causation
Reading a dataset
Frequency / percentage
Frequency counts how often something occurs; percentage expresses a part relative to 100.
Mean / median
Mean is the arithmetic average; median is the middle score when values are ordered.
Range / distribution
Range is highest minus lowest; a distribution describes how values are spread.
Outlier
A value unusually far from most others; it may be important, erroneous, or simply rare.
Third variable
An unmeasured variable that may help explain an observed association.
Random assignment
A procedure that gives participants an unbiased chance of entering experimental conditions, helping balance alternative causes.
Data discipline: say exactly what the evidence permits
Psychological research often begins with description. Researchers count behaviors, calculate percentages, summarize distributions, and compare groups. Descriptive statistics help us see patterns, but interpretation matters. A mean can be pulled by extreme values, while a median may better represent a skewed distribution. A range tells us spread but not where most scores cluster.
Researchers also examine whether two variables are associated. A positive correlation means higher values on one variable tend to occur with higher values on another. A negative correlation means higher values on one tend to occur with lower values on the other. A near-zero correlation means there is little linear relationship in the observed sample. Correlation can be scientifically useful because it can reveal patterns worth explaining and can support prediction.
But a correlation does not, by itself, show causation. Suppose sleep duration and memory scores are positively associated. More sleep might improve memory performance. But stronger time-management skills might increase both sleep and study quality. Health, workload, age, stress, device use, or other variables could influence both. It is also possible that students who are functioning better organize their schedules in ways that permit more sleep. The observed association cannot tell us the direction of causation by itself.
Experiments strengthen causal inference by manipulating an independent variable, comparing conditions, and controlling alternative explanations. Random assignment helps reduce systematic pre-existing differences between conditions. Even then, causal conclusions should match the exact manipulation, sample, task, and outcome measured.
Graphs can clarify evidence or distort it. A bar graph with a truncated axis may make a small difference look dramatic. Unequal intervals can disguise trends. Cherry-picking a narrow time period can hide the larger pattern. Responsible psychological science therefore treats graph design as part of evidence quality.
The strongest scientific language is proportional. “X caused Y” is stronger than “X was associated with Y.” “The groups differed by 4 percentage points in this sample” is more precise than “Group A was much better.” Precision is not timid writing; it is accurate writing.
Mean and median can tell different stories
Study-session minutes: 20, 22, 24, 25, 27, 120.
| Statistic | Value | Interpretation |
|---|---|---|
| Mean | 39.7 min | Pulled upward by the 120-minute outlier. |
| Median | 24.5 min | Closer to the center of the typical values here. |
| Range | 100 min | Shows a wide span but not the cluster. |
Causal claim audit
- Measure: Define social-media use, bedtime, sleep, and memory.
- Evidence: Is the source observational or experimental?
- Alternative: Could stress, workload, or sleep schedule affect both use and memory?
- Limitation: Was use self-reported? Was the sample narrow?
- Conclusion: Match the wording to the design.
Sleep & Memory Data Lab
| Participant | Sleep (hours) | Memory score / 20 |
|---|---|---|
| A | 5.0 | 11 |
| B | 5.5 | 12 |
| C | 6.0 | 13 |
| D | 6.5 | 15 |
| E | 7.0 | 15 |
| F | 7.5 | 17 |
| G | 8.0 | 16 |
Pattern: In this small fictional sample, more reported sleep is generally associated with higher memory scores. One participant at 8 hours scores slightly below the 7.5-hour participant, reminding us that correlations describe tendencies, not perfect rules.
“A strong correlation proves causation.”
Verdict
Incorrect. Strength of association does not solve directionality or third-variable problems.
What would help?
Experimental manipulation when ethical and feasible, longitudinal evidence, statistical controls, replication, and converging methods can strengthen causal reasoning.
Graph Integrity Mini-Lab
Two news graphics show the same percentages: Group A = 48%, Group B = 52%. Graph 1 uses a 0–100% axis. Graph 2 uses a 47–53% axis.
Data Claim Repair
Rewrite each overclaim into scientifically justified language: (1) “Students who sleep more are smarter.” (2) “This app boosts attention by 50%.” (3) “People who exercise are happier because exercise fixes mood.” Explain what data or design would be needed for a stronger causal conclusion.