Module 3: Correlations, scatterplots, Pearson correlation coefficient, Spearman's Rank correlation

Scatterplot

A plot has points that show the relationship between two sets of data. (The data is plotted on the graph as "Cartesian (x,y) Coordinates")

Correlations (The word Correlation is made of Co- (meaning "together"), and Relation)

Evaluates the relationship between variables and evaluates the direction of the relationship

What does a coefficient of zero indicate?

That there is no discernable relationship between fluctuations of the variables.

Negative correlation (Negatively related)

When one value decreases as the other increases (When they move in opposite direction of each other, one goes up as the other goes down), A coefficient of -1 indicates a perfect negative correlation:

Positive correlation (Positively related)

When the values increase together (when both move in the same direction, as one increases, so does the other), A coefficient of +1 indicates a perfect positive correlation

What is a correlation coefficient?

a number between −1 and +1 calculated so as to represent the linear dependence of two variables or sets of data.

Pearson Correlation

is a Parametric (assumptions) test that measures the strength and direction of association that exists between two continuous variables. The Pearson correlation generates a coefficient called the Pearson correlation coefficient, denoted as r.

Spearman's Correlation

is a nonparametric (does not have really have assumptions) test which measures the strength and direction of association between two variables that are measured on an ordinal or continuous scale. The Spearman correlation coefficient is often denoted by the symbol rs (or the Greek letter ρ, pronounced rho). It is a useful test when Pearson's correlation cannot be run due to violations of normality, a non-linear relationship or when ordinal variables are being used.

Assumptions of Spearman's Correlation

1. Your two variables should be measured on an ordinal or continuous scale. 2. There needs to be a monotonic relationship between the two variables. A monotonic relationship exists when either the variables increase in value together, or as one variable value increases, the other variable value decreases.

Assumptions of Pearson's Correlation

1. Your two variables should be measured at the continuous level. (If either of your two variables was measured on an ordinal scale, you need to use Spearman's correlation instead) 2. There needs to be a linear relationship between your two variables (Whilst there are a number of ways to check whether a Pearson's correlation exists, we suggest creating a scatterplot) 3. There should be no significant outliers 4. Your variables should be approximately normally distributed (you need to have bivariate normality)

What does "Correlation Is Not Causation" mean?

that a correlation does not mean that one thing causes the other (there could be other reasons the data has a good correlation).