6.1. Covariance and Correlation Flashcards
Correlation and regression…
Shows the strength of the linear relationship between ratio scale variables.
Can also test the significance of the linear strength.
Covariance…
A descriptive measure of the linear association between two variables (i.e. the number of TV adverts and sales recorded).
Can be positive, negative or nonlinear.
As covariance measures the linear relationship, just because covariance equals zero, doesn’t mean there is no relationship. It just implies there is no linear relationship.
Can calculate for both a sample and a population (examples on Google Docs).
Relationships with covariance…
If the covariance is negative, we would expect a negative linear relationship.
If the covariance is positive, we would expect a positive linear relationship.
Correlation coefficient…
The Pearson product moment correlation coefficient.
A measure of linear association between variables, which is unit free.
Between -1 and 1, with a negative value indicating a negative linear relationship and vice versa. (Interpreting the value of r, ranging from a perfect positive to perfect negative linear relationship).
A larger absolute value indicates a stronger relationship.
If r=0, this doesn’t mean there isn’t a correlation, just means there isn’t a linear correlation.
Equation and examples on Google Docs.
Testing the significance of the correlation coefficient…
To make inference about the population based on samples, we test the significance.
If the test value > critical value, we reject the null hypothesis.
For the correlation coefficient, we use the t-distribution table.
Spearman’s Rank…
If original data is unavailable but ranked data is.
Or, if the original data is highly skewed.
If the test statistic > critical value, we reject the null hypothesis.
A correlation shows a linear relationship between variables, but does not imply causality.
