12_Ch15_Correlation

12_Ch15_Correlation - You should be able to . . ....

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Describing Relationships Correlation You should be able to . . . • Describe relationships using correlation • Define and identify: – Positive correlations – Negative correlations – Zero correlations • Construct and interpret scatterplots • Compute and interpret the Pearson Product- Moment Correlation Coefficient Correlation • The degree of relationship between two or more variables • The co-relationship between variables Example • Is there a relationship between height and salary? • Do taller people tend to make more money? • Do taller people tend to make less money? • Is there any relationship at all?
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Height and Salary Height (in.) Salary (thousands) --------------- ------------------------- 77 47.1 73 46.2 70 42.8 69 45.4 67 42.1 66 34.1 63 33.1 Height and Salary Height (in.) Salary (thousands) --------------- ------------------------- 77 47.1 73 46.2 70 42.8 69 45.4 67 42.1 66 34.1 63 33.1 Height and Salary Height (in.) Salary (thousands) --------------- ------------------------- 77 47.1 73 46.2 70 42.8 69 45.4 67 42.1 66 34.1 63 33.1 Three types of relationships • Positive • Negative • None
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Positive correlation • A high score on one variable is associated with a high score on the other variable • Likewise, a low score is associated with a low score • There is a direct relationship between the variables Negative correlation • A high score on one variable is associated with a low score on the other variable and vice versa Zero correlation • There is no relationship • It is equally likely that a high score will be associated with a high or low score Displaying correlations: Scatterplot • A graph that plots pairs of scores • Values for one variable are plotted on the x axis • Values for the other variable are plotted on the y axis • You choose which variable to plot on which axis
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Height and Salary 60 65 70 75 80 30 35 40 45 50 Salary (thous) Height (inches) Salary (thousands) Height and Salary 60 65 70 75 80 30 35 40 45 50 Salary (thousands) Height and Salary 60 65 70 75 80 30 35 40 45 50 Salary (thousands) Height and Salary 60 65 70 75 80 30 35 40 45 50 63 inch person; $33,100 salary Salary (thousands)
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Height and Salary 60 65 70 75 80 30 35 40 45 50 Height (inches) 77 inch person; $47,100 salary Salary (thousands) Example: Positive Correlation • Among people that have smoked sometime in their lives, what is the relationship between number of years since stopped smoking and age at death? • Variable A: Number of years since last cigarette • Variable B: Age at which individual died Example: Positive Correlation Individual Years Since Age at Stopped Smoking Death A 28 95 B 25 95 C 3 58 D 10 75 E 0 44 F 15 83 G 20 91 H 24 87 I 7 65 J 8 70 No. of Years Since Stopped Smoking and Age at Death 40 50 60 70 80 90 100 0 10 20 30 No. of Years Since Stopped Smoking Age at Death Number of Years Since Stopped Smoking
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Example: Negative Correlation • If an animal suffers brain damage, what is the relationship between percentage of brain damage and percentage of savings in relearning a maze?
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12_Ch15_Correlation - You should be able to . . ....

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