Lecture 5

Correlation

Analysis of linear relationship between two variables, without drawing causal conclusions. Not applicable for curvilinear relationships.

Covariance

Simplest measure of relationship between two variables, indicating the direction but not the strength. Reflects how deviations from the mean of one variable change with deviations of another variable.

Positive covariance

Indicates that two variables tend to increase or decrease together.

Negative covariance

Indicates that one variable tends to increase when the other decreases.

Pearson correlation

Provides information about the direction and strength of the relationship between variables. Absolute value is considered, ignoring the minus sign. Values between 0 and -0.3 are weak, 0.31 and -0.5 are moderate, 0.51 and -0.7 are strong, and 0.71 and -1 are very strong.

Positive correlation

As variable X increases, variable Y also increases (e.g., the more I read, the more I know).

Negative correlation

As variable X increases, variable Y decreases (e.g., the more I run, the less I weigh).

The fact that two variable are correlated:

does not mean that one variable causes or influences another.

Assumptions of Pearson's r

Linear relationships, quantitative scales of the variables, and normal distribution of both correlated variables.

Non-directional hypothesis

Suggests that there is no relationship between something.

Directional hypothesis

Suggests that there is no positive relationship between something.