Correlations (College Board AP® Psychology): Study Guide

What is correlational research?

• Correlational research is a non-experimental methodology — there is no manipulation of variables and no IV

• Instead, two co-variables are measured and compared to identify whether a relationship exists between them

  • Because there is no manipulation of an IV, correlational research cannot establish cause and effect

Co-variables

• In correlational research, the variables being studied are called co-variables

• One or both co-variables may be pre-existing data, e.g.

  • average number of hours of sleep per night and GPA scores

  • daily temperature and number of violent crimes reported in a city

• One or both co-variables may be measured as part of the research itself, e.g.

  • number of hours spent on social media per day and self-reported levels of anxiety

  • number of hours of exercise per week and self-reported stress levels

• Each participant produces two scores (one for each co-variable) which are then used to calculate whether a relationship exists

Types of correlation

• Correlational data is typically displayed on a scatterplot, where each point represents one participant's two scores

• There are three possible outcomes:

  • Positive correlation:

    • One co-variable increases as the other co-variable increases (but not necessarily at the same rate)

    • E.g., as the number of hours spent studying increases, GPA scores also increase

    • On a scatterplot, the data points trend upward from left to right

  • Negative correlation:

    • One co-variable increases as the other co-variable decreases (but not necessarily at the same rate)

    • E.g. as the number of hours spent on social media increases, self-reported sleep quality decreases

    • On a scatterplot, the data points trend downward from left to right

  • Zero correlation:

    • There is no relationship between the two co-variables

    • E.g. shoe size and IQ score

    • On a scatterplot, the data points are scattered with no clear pattern

The correlation coefficient

• The strength and direction of a correlation can be calculated as a correlation coefficient — a numerical value expressed between -1 and +1:

  • A perfect positive correlation = +1

  • A perfect negative correlation = -1

  • No relationship = 0

• The closer the value is to +1 or -1, the stronger the relationship between the co-variables

• Both positive and negative correlations can be described as weak, moderate, or strong:

  • A coefficient of +0.8 indicates a strong positive correlation

  • A coefficient of -0.4 indicates a moderate negative correlation

  • A coefficient of +0.1 indicates a weak positive correlation

Evaluation of types of correlation

• The data may be readily available for researchers to quickly analyze large amounts of information that would otherwise be impossible to collect from scratch

  • This increases the reliability of the findings

• Correlational research allows researchers to identify relationships between variables and make predictions, which can inform real-world interventions

  • E.g., identifying a relationship between sleep deprivation and academic performance could be used to develop interventions supporting at-risk students

• Correlational research can be used to establish whether a relationship exists before designing a more controlled experiment to test causation

Limitations

• Correlational research cannot establish cause and effect

  • The directionality problem and the third variable problem mean that alternative explanations for any relationship can always be proposed

• Extraneous factors connected to one or both co-variables may affect the results and lead to invalid conclusions

  • E.g. a correlation between school absence and low GPA may reflect underlying illness rather than a direct relationship between attendance and achievement

• Correlational research is most effective for linear relationships e.g. height and shoe size

  • It is less useful when the relationship between co-variables is non-linear, which limits the types of conclusions that can be drawn

Correlation vs experiment

• It is important to distinguish correlational research from experimental research:

• Even when a strong correlation is found between two co-variables, causation cannot be assumed. There are two key reasons for this:

  • The directionality problem

  • The third variable problem

The directionality problem

• When a correlation is found, it is not possible to determine which co-variable influenced the other

• Either co-variable could be influencing the other, or the relationship could be bidirectional

  • E.g. a positive correlation between social media use and anxiety could mean:

    • social media use causes anxiety, or

    • anxiety causes increased social media use, or

    • both variables are influencing each other simultaneously

The third variable problem

• A correlation between two co-variables may be caused by a third, unmeasured variable that influences both

  • E.g. a positive correlation between ice cream sales and violent crime rates is not because ice cream causes violence — a third variable (hot weather) increases both independently

    • The third variable is a confounding variable — it offers an alternative explanation for the relationship and means a causal conclusion cannot be drawn