Correlation

Up Until Now T Tests, Anova: Categories Predicting a Continuous Dependent Variable Correlation: Very different way of thinking about variables How closely are two (usually continuous) variables related?

Covariance

Correlation

So What is the Correlation Telling Us? How much of one variable can be predicted by the other What the correlation between a bunch of measurements in feet and in meters? What is a probable correlation of height and weight?

Even Better

Final Question So what does this have to do with inferential statistics? Well…it turns out that there is some true variance of the population, but when we sample we are only estimating it Whenever we sample there is some error based on the n-size With a correlation we are generally asking “Is this correlation significantly different from zero?”

The F-Test Again The correlation coefficient can be tested with an F-Test or a T test (this will make more sense when we talk about multiple regression) The simple idea is that it is a F-Test because you are testing whether the variance explained (r-squared) is different from zero. The only thing you need to know is the size of the correlation and the sample size, and you can look the significance up in a table (degrees of freedom will be N-2…this will make sense when we talk about regression)