1. Correlation Correlation measures the strength of the linear association between two quantitative variables Get the correlation coefficient (r) from your calculator or computer r value graph.xls r has a value between -1 and +1: Correlation has no units

2. What can go wrong? Use correlation only if you have two quantitative variables (variables that can be measured) There is an association between gender and weight but there isn’t a correlation between gender and weight! Gender is not quantitative Use correlation only if the relationship is linear Beware of outliers!

3. Always plot the data before looking at the correlation! r = 0 No linear relationship, but there is a relationship! r = 0.9 No linear relationship, but there is a relationship!

4. Tick the plots where it would be OK to use a correlation coefficient to describe the strength of the relationship: 9876543210 400 0 300 0 200 0 100 0 0 Position Number Distance (million miles) Distances of Planets from the Sun Reaction Times (seconds) for 30 Year 10 Students 0 0. 2 0. 4 0. 6 0. 8 00.20.40. 6 0. 8 1 Non-dominant Hand Dominant Hand 4540 35 20 19 18 17 16 15 14 Latitude (°S) Mean January Air Temperatures for 30 New Zealand Locations Temperature (°C) Female ($) Average Weekly Income for Employed New Zealanders in 2001 Male ($) 0 200 400 600 800 1000 1200 0200400 600 80 0

5. Tick the plots where it would be OK to use a correlation coefficient to describe the strength of the relationship: 9876543210 400 0 300 0 200 0 100 0 0 Position Number Distance (million miles) Distances of Planets from the Sun Reaction Times (seconds) for 30 Year 10 Students 0 0. 2 0. 4 0. 6 0. 8 00.20.40. 6 0. 8 1 Non-dominant Hand Dominant Hand 4540 35 20 19 18 17 16 15 14 Latitude (°S) Mean January Air Temperatures for 30 New Zealand Locations Temperature (°C) Female ($) Average Weekly Income for Employed New Zealanders in 2001 Male ($) 0 200 400 600 800 1000 1200 0200400 600 80 0   Not linear Remove two outliers, nothing happening

6. What do I see in this scatter plot? Appears to be a linear trend, with a possible outlier (tall person with a small foot size.) Appears to be constant scatter. Positive association. 2223242526272829 150 160 170 180 190 200 Foot size (cm) Height (cm) Height and Foot Size for 30 Year 10 Students

7. What will happen to the correlation coefficient if the tallest Year 10 student is removed? It will get smaller It won’t change It will get bigger 2223242526272829 150 160 170 180 190 200 Foot size (cm) Height (cm) Height and Foot Size for 30 Year 10 Students

8. What will happen to the correlation coefficient if the tallest Year 10 student is removed? It will get bigger 2223242526272829 150 160 170 180 190 200 Foot size (cm) Height (cm) Height and Foot Size for 30 Year 10 Students

9. What do I see in this scatter plot? Appears to be a strong linear trend. Outlier in X (the elephant). Appears to be constant scatter. Positive association. 6005004003002001000 40 30 20 10 Gestation (Days) Life Expectancy (Years) Life Expectancies and Gestation Period for a sample of non-human Mammals Elephant

10. What will happen to the correlation coefficient if the elephant is removed? It will get smaller It won’t change It will get bigger 6005004003002001000 40 30 20 10 Gestation (Days) Life Expectancy (Years) Life Expectancies and Gestation Period for a sample of non-human Mammals Elephant

11. What will happen to the correlation coefficient if the elephant is removed? It will get smaller 6005004003002001000 40 30 20 10 Gestation (Days) Life Expectancy (Years) Life Expectancies and Gestation Period for a sample of non-human Mammals Elephant