Chapter 12: The correlational research strategy

Correlational research

A type of research aiming to establish relationships between variables without manipulating them.

Correlational Data

Data points for each individual representing two variables, often displayed in a table or scatter plot.

strong correlation

0.70 – 1.00

moderate correlation

0.30 – 0.69

weak correlation

0.00 – 0.29

Relation

Looking for patterns in data that suggest a consistent and predictable relationship. Linear relationship vs. non-linear relationship

Use Pearson r when…

The two variables are either ratio or interval

Use the Spearman rho when…

If one variable is ordinal

Direction of the relation

Describes how changes in one variable correspond to changes in another, either positively (+) or negatively (-) correlated.

Positive correlation

Increases in 𝑥are paired with increases in 𝑦

Negative correlation

Increases in 𝑥 are paired with decreases in 𝑦

Strength of the relation

The degree of association between variables, measured by the correlation coefficient (r) ranging from -1 to 1.

What does 𝑟 near 0 indicate

Weak relations

Correlation Matrix

A table showing correlation coefficients between sets of variables

What does 𝑟 close to -1 or 1 indicate

That points lie close to a straight line

What does 𝑟 equal to -1 or 1 indicate

That points lie exactly along a straight line

Regression line

Indicates a linear relationship between the dependent variables on the y-axis and the independent variables on the x-axis.

What does it mean when data points are closer to the line?

The greater the association (relation) between the variables

Significance of the Correlation

Determined by statistical tables considering sample size and alpha level, with r needing to meet criteria for significance.

Statistical Significance

r must be equal to or larger than the value corresponding to the appropriate df and p level. 

Degree of freedom

Sample size - 2

Correlation results will be misleading under what circumstances?

Non-linear relationships and restricted ranges

Restricted range

When the range of values measured for one of the variables is restricted for some reason. Leads to misleading results

Strengths of Correlational research

Record what exists naturally, Helps identify where to look for causes, Can investigate what is otherwise unethical to examine experimentally, High external validity

Weaknesses of correlational research

Cannot assess causality , Low internal validity 

Third Variable Problem

Unidentified variable may be responsible for producing the observed relation

Shared variance

The common ground between variables, calculated as the coefficient of determination (r^2) indicating the percentage of changes in one variable explained by another.

Correlation

Describes the relationship between variables, useful for predictions and establishing validity and reliability.

Epidemiological Studies

Attempt to determine what factors are associated with diseases (risk factors), and what factors may protect people or animals against disease (protective factors).

Spurious correlation

When variables appear correlated but are not truly related, cautioning against assuming direct relationships.

Directionality problem

Uncertainty about which variable causes the effect in a relationship.

Potential Problems

Issues like nonlinear relationships and restricted ranges can mislead correlation results, affecting internal validity.

Regression analysis 

Way of using associations between variables as a method of prediction.

Non-linearity

The relationship must be linear – a curvilinear relationship may give a misleading value.