Correlation in Psychology

Correlation means association – more precisely, it measures the extent to which two variables are related. There are three possible results of a correlational study: a positive correlation, a negative correlation, and no correlation.

Types of Correlation

• Positive Correlation: relationship between two variables in which both variables move in the same direction. Therefore, one variable increases as the other variable increases, or one variable decreases while the other decreases. An example of a positive correlation would be height and weight. Taller people tend to be heavier.

• Negative Correlation: relationship between two variables in which an increase in one variable is associated with a decrease in the other. An example of a negative correlation would be the height above sea level and temperature. As you climb the mountain (increase in height), it gets colder (decrease in temperature).

• Zero Correlation: exists when there is no relationship between two variables. For example, there is no relationship between the amount of tea drunk and the level of intelligence.

Scatter Plots

A correlation can be expressed visually. This is done by drawing a scatter plot (also known as a scattergram, scatter graph, scatter chart, or scatter diagram).

A scatter plot is a graphical display that shows the relationships or associations between two numerical variables (or co-variables), which are represented as points (or dots) for each pair of scores.

A scatter plot indicates the strength and direction of the correlation between the co-variables.

 

When you draw a scatter plot, it doesn’t matter which variable goes on the x-axis and which goes on the y-axis.

Remember, in correlations, we always deal with paired scores, so the values of the two variables taken together will be used to make the diagram.

Decide which variable goes on each axis and then simply put a cross at the point where the two values coincide.

Uses of Correlations

Prediction

• If there is a relationship between two variables, we can make predictions about one from another.
• Occupational Success: Self-report personality tests demonstrate predictive validity when traits measured early in life (like conscientiousness) are shown to be significantly correlated with future job performance, occupational attainment, and even physical health and well-being.

Validity

• Concurrent Validity: Correlation between a new measure and an established measure.
• When a new psychological test is developed, it is often compared against an existing, proven standard. For instance, scores on a newly developed depression questionnaire should be highly correlated with scores on the established Beck Depression Inventory (BDI).

Reliability

• Test-Retest Reliability: If a psychological test (like a personality inventory) is reliable, a person taking it on a Tuesday should get a nearly identical score if they take it again on Friday. The correlation between the two sets of scores should be very high and positive.
• Inter-rater Reliability: When multiple professionals (like mental health diagnosticians or observational researchers) are assessing the same person or data, their judgments must be consistent. Ensuring that two different raters are in agreement is established by correlating their assessments.

Correlation Coefficients

Instead of drawing a scatter plot, a correlation can be expressed numerically as a coefficient, ranging from -1 to +1. When working with continuous variables, the correlation coefficient to use is Pearson’s r.

Correlation coefficients are standardized statistical measures used to quantify the strength and direction of the relationship between two variables.

The correlation coefficient (r) indicates the extent to which the pairs of numbers for these two variables lie on a straight line. Values over zero indicate a positive correlation, while values under zero indicate a negative correlation.

A correlation of –1 indicates a perfect negative correlation, meaning that as one variable goes up, the other goes down. A correlation of +1 indicates a perfect positive correlation, meaning that as one variable goes up, the other goes up.

Spearman’s Rho for Ranked Data

Pearson’s r assumes both variables are measured on an interval scale and that their relationship is roughly a straight line. When a variable is ordinal, such as ranks or ratings, a different coefficient is needed.

Spearman’s rho is the answer. Denoted ρ or rₛ, it was introduced by the English psychologist Charles Spearman (1904) as part of his work on general intelligence. It works by converting each score to its rank within its own variable, then correlating the ranks.

Spearman’s ρ is useful in three situations. It suits data that are already ordinal, such as class rankings.

It also copes better than Pearson’s r with a curved but steadily rising relationship. And it blunts the effect of a single extreme outlier that would otherwise distort the coefficient.

Spearman’s ρ shares Pearson’s −1-to-+1 scale. It says nothing about causation either. Researchers often report both together as a check. When the two diverge sharply, it is a sign the scatter plot deserves a closer look.

Interpreting Effect Size: Cohen’s Guidelines

There is no single rule for what counts as a strong, moderate, or weak correlation. Interpretation depends on the field and what is being studied.

The most widely used benchmarks come from psychologist Jacob Cohen. He proposed treating an effect size of r ≈ 0.10 as small, r ≈ 0.30 as medium, and r ≈ 0.50 as large.

• Small effect (r ≈ 0.10): about 1% of the variance explained.
• Medium effect (r ≈ 0.30): about 9% of the variance explained.
• Large effect (r ≈ 0.50): about 25% of the variance explained.

Cohen intended these bands as a rough guide for planning studies, not fixed rules. More recent research has challenged them directly.

Funder and Ozer (2019) argue that Cohen’s benchmarks undervalue small correlations in personality and social psychology. Small effects still matter. A modest per-encounter effect, they note, can accumulate into something meaningful across repeated exposures.

Their re-analysis suggests r ≈ 0.10 is already a typical small effect in personality research, and r ≈ 0.30 is unusually large outside controlled experiments. The gap is striking.

A separate review of published correlations found that the 25th, 50th and 75th percentiles of reported effects sit at roughly 0.11, 0.19 and 0.29 (Gignac & Szodorai, 2016). Cohen’s “medium” band therefore already sits near the top of what researchers typically find.

Correlation vs. Causation

Causation means that one variable (often called the predictor variable or independent variable) causes the other (often called the outcome variable or dependent variable).

Experiments can establish causation. An experiment isolates and manipulates the independent variable to observe its effect on the dependent variable. It also controls the environment to eliminate extraneous variables.

A correlation between variables does not automatically mean that one causes the other. It only shows that a relationship exists.

“Correlation is not causation” means that just because two variables are related it does not necessarily mean that one causes the other.

An experiment can predict cause and effect because it manipulates the independent variable directly. A correlation can only show a relationship, since an unknown extraneous variable may still explain it.

Third-Variable Problem

Variables are sometimes correlated because one causes the other. But often some other factor, a confounding variable, is actually driving the systematic movement in both.

This is called the third-variable problem: two variables appear systematically related, but no direct causal link connects them. Instead, an unseen or unmeasured third variable is independently influencing both, creating the illusion of a direct connection.

For example, being a patient in a hospital is correlated with dying. This does not mean one event causes the other, since a third variable, such as diet or exercise levels, might be involved.

This problem is the primary reason why researchers constantly emphasize that correlation does not imply causation.

Even when cause and effect seems intuitive, a correlational study cannot rule out a confounding third variable behind the pattern.

Examples of the third-variable problem

To understand how deceptive this can be, consider these examples from the sources:

• Ice Cream and Crime: Ice cream sales and crime rates rise together, but ice cream does not cause crime. Warm weather drives both, drawing people outdoors to buy treats and interact more.
• Spa Salons and Criminals: Cities with more spa salons also tend to have more criminals. City size explains this: a larger population naturally means more of both.
• Breast Implants and Suicide: Breast implants correlate with suicide, but implants do not cause it. Low self-esteem may independently drive both cosmetic surgery and suicide risk.
• TV Violence and Aggression: Children who watch violent television tend to be more aggressive. Neglectful parenting may explain both, since unsupervised children watch more violent TV and go uncorrected.
• Generosity and Happiness: Spending on others correlates with happiness, but wealth may be the real cause, enabling both greater generosity and greater happiness.

How researchers handle the third-variable problem

Because correlational studies cannot use experimental manipulation to completely isolate variables, researchers must be proactive to ensure their findings are credible.

The best way to combat the third-variable problem is to anticipate potential confounding variables in advance and include them in the research study.

By actively measuring these third variables, researchers can use advanced statistical techniques such as partial correlations. This lets them mathematically “remove” or hold constant the third variable’s effect.

If the correlation survives after the third variable is factored out, researchers gain more confidence the relationship is genuine and not spurious.

Strengths of Correlational Research

Correlational research offers several unique advantages that make it an indispensable tool, particularly when exploring complex or naturally occurring phenomena.

• Studying Unmanipulable or Unethical Variables: Correlational methods let researchers study variables that cannot ethically or practically be manipulated, such as trauma, stress, or genetics, as in twin and adoption studies.
• Predictive Value: A strong correlation lets researchers predict one variable from another. Universities use SAT scores to predict college GPA, for example.
• Numerical and Comparable Data: Correlational studies yield a standardized coefficient, such as Pearson’s r, ranging from -1 to +1. This makes relationships easy to interpret and compare across studies.
• Foundation for Future Research: A strong correlation can generate new hypotheses, which researchers then test using more controlled experimental methods.
• Ecological Validity: Correlational studies often observe behavior as it naturally occurs, capturing real-world attitudes more authentically than lab experiments can.

Limitations of Correlational Research

Despite its usefulness, correlational research carries significant methodological limitations that restrict how the data can be interpreted.

• Inability to Establish Causation: Correlational research cannot prove cause and effect, only that variables change together. We cannot know whether violent television causes aggression, or aggressive children simply watch more of it.
• The Third-Variable Problem: As explained above, an apparent correlation can vanish once a hidden third variable, like city size, is accounted for.
• Failure to Capture Curvilinear Relationships: Correlation coefficients measure only linear relationships. A true U-shaped pattern, such as the Yerkes–Dodson law relating arousal to performance, can return a coefficient near zero.
• Spurious Correlations: Testing many variables raises the chance some correlations appear significant purely by chance. Reporting only these “significant” findings promotes false patterns.
• Lack of Explanatory Depth: A correlation shows that a relationship exists but not why. Self-report data is also vulnerable to social desirability bias and limited self-insight.

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