4. Correlational analysis

Statistical relationship

Describes and quantifies how the change in one variable is related to the change in another variable

Positive relationship/correlation

The two variables change in the same direction. Value close to 1

Negative relationship/correlation

The two variables change in the opposite direction. Value close to -1

Variance

A measure reflecting how far each observation is from its mean in squared units

Calculate the variance

Covariance

A measure reflecting the relationship between the deviations of two variables from their corresponding means

Calculate the covariance

Pearson’s correlation coefficient r

A standardized measure of covariance, reflecting the linear relationship between two variables (similarly to Z-scores, it is not affected by the scale of the measurement)

Pearson’s r ranges

-1 from 1, with 0 indicating no correlation, whereas1 and -1 reflect perfect positive and negative correlations

Calculate Pearsons r -

General assumptions/criteria for Pearson’s correlation analysis

Linear relationship, related pairs, numeric values (interval or ratio), normal distribution, homogeneity, and no outliers

How do we interpert results from a correlation

By looking at size (weak to strong), sign (positive or negative), and significance (p < .05)

Confounder

A third variable in a research study that influences both the supposed cause (independent variable) and the supposed effect (dependent variable), creating a false or distorted association between them

Correlation vs causation

Correlation is the measure of how two variables relate or associate with each other. Causation is a cause-and-effect link where changes in one variable force a change in the other.

Partial correlation

Measures the strength and direction of a linear relationship between two variables while removing the influence of one or more control variables (covariates)

Confounder

An outside or third variable in a research study that influences both the supposed cause (independent variable) and the supposed effect (dependent variable), creating a false or distorted association between them

APA for repporting correlations

r(df) = value, p = value (two-tailed)

• df = degrees of freedom (n-2)

• value (Pearsons r = .00)

• p = < .001

• Example = r(18) = .89, p < .001 (to-halet)