Chapter 7: Correlational Research

Ch 7: Correlational Research

Correlational research examines the relationship between two or more naturally occurring variables without manipulation.
Examples of research questions include: Is socioeconomic status related to SAT scores? Is age related to shyness?
Correlation Coefficient: A statistic that quantifies the degree of linear relationship between two variables, ranging from -1.00 to +1.00.
Positive correlation indicates that as one variable increases, the other also increases, while negative correlation indicates an inverse relationship.

The coefficient of determination (r-squared) indicates the proportion of variance in one variable that can be explained by another variable.
For example, if the correlation between children's and parents' IQ scores is .40, then r-squared is .16, meaning 16% of the variance in children's IQ can be explained by their parents' IQ.
This measure helps in understanding the strength of the relationship and the predictive power of one variable over another.

A correlation coefficient is considered statistically significant if the probability of it being zero in the population is very low (commonly set at an alpha level of .05).
Factors affecting statistical significance include sample size, effect size, and the chosen alpha level.
Larger sample sizes increase power, while larger effect sizes also enhance the likelihood of finding significant results.

It is crucial to remember that correlation does not imply causation. A correlation between two variables does not mean one causes the other.
Criteria for inferring causality include covariation, directionality, and controlling for extraneous variables.
Correlational research can satisfy the first two criteria but often fails to control for all extraneous variables.

Partial correlation measures the relationship between two variables while controlling for the influence of one or more additional variables.
This technique helps clarify the relationship between two variables by removing the effects of confounding variables.
For example, if studying the correlation between motivation and test performance, controlling for study time may reveal a clearer relationship

Spearman Rank-Order Correlation: Used for ordinal data, reflecting the rank ordering of participants.
Phi Coefficient: Used for two dichotomous variables, such as gender and dropout rates.

Point-Biserial Correlation: Used when one variable is dichotomous and the other is continuous, such as gender and IQ scores.