Correlation – PMCC Monday 18 th March 2013 Learning objective: To be confident finding the Product Moment Correlation Coefficient and using it to interpret data. Accuracy Interpretation Starter: Can you find my mistakes?

Product moment correlation coefficient Weight, xCalories, yx2x2 y2y2 xy A B C D E th (∑x) 2 (∑y) 2 ∑x∑y 7 th ∑x = ∑y 2 = ∑x 2 = ∑y = ∑xy =

When two sets of random variables (bivariate data) are displayed on a scatter graph; we are used to describing the correlation but how do you measure it?

Two sets of random variables (bivariate data) we can describe correlation but how do you measure it? x - = - y - = + - x + = - x - = + y - = + + x + = + x - = - y - = - - x - = + x - = + y - = - + x - = -

Covariance – how do you interpret it? When the covariance is positive it suggests positive correlation When covariance is negative it suggests negative correlation When the covariance is close to zero it suggests no correlation.

Covariance – can you see any potential problems with this method alone? –When the covariance is positive it suggest positive correlation –When covariance is negative it suggest negative correlation –When the covariance is close to zero it suggests no correlation. You guessed it: –(you don’t know the range)

Pearson Moment Correlation Coefficient Karl Pearson Is to standardise the covariance so that it can interpreted easily. It converts the covariance to a number between -1 to 1, where: -1 is a perfect negative correlation 1 is a perfect positive correlation 0 is no correlation

The effect of scaling If you work out the correlation coefficient for sales of ice-cream & temperature (t) in Fahrenheit. Would you expect the correlation to change if you worked on the same data but in Celsius? No – scaling has no effect on correlation.

Be aware of correlation claims Some things may look like they are connected but they are not: –General knowledge and height: Children in a school from year 7 to year 13 are asked general knowledge questions. The correlation is worked out using height and their score. In your opinion does height have any effect on their score? If not can you suggest what is the explanatory factor that is connected to both? Outliners –As all data items are used outliners will effect the correlation coefficient. When outliners are obvious it is worth ignoring them altogether. Non-linear relationships. –Pearson's p.m.c.c. is only suitable for linear relationships