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Correlation

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1. Correlation

2. In this lesson you will cover: • How to measure and interpret correlation • About the effects of scaling data on correlation

3. 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?

4. 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 - = +

5. 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.

6. 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)

7. Pearson Moment Correlation Coefficient • 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 Karl Pearson 1857 - 1936

8. Pearson Moment Correlation Coefficient can be simplified to: This is the covariance This is the standard deviation of y This is the standard deviation of x

9. Task • Exercise A • Page 140

10. 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.

11. 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

12. Task • Exercise C • Page 144 • Test yourself • Page 145 • HOMEWORK!!!!!!!!!!!! • Past papers • Past papers • Past papers • Go through each of the chapters: • PowerPoint's • revision notes • Unanswered questions