You can calculate: Central tendency Variability You could graph the data

You can calculate: Central tendency Variability You could graph the data

Bivariate Distribution

Positive Correlation

Regression Line

Correlation r = 1.00

Regression Line..... r =.64

Regression Line.... r =.64.

Negative Correlation

r =

Negative Correlation..... r = -.85

Zero Correlation

..... r =.00

Correlation Coefficient The sign of a correlation (+ or -) only tells you the direction of the relationship The value of the correlation only tells you about the size of the relationship (i.e., how close the scores are to the regression line)

Which is a bigger effect? r =.40 or r = -.40 How are they different?

Interpreting an r value What is a “big r” Rule of thumb: Smallr =.10 Mediumr =.30 Larger =.50

Practice Do you think the following variables are positively, negatively or uncorrelated to each other? Alcohol consumption & Driving skills Miles of running a day & speed in a foot race Height & GPA Forearm length & foot length Test #1 score and Test#2 score

Practice –#6.8 –#6.5 1) Draw a scatter plot 2) Estimate the correlation

6.8 A) -.60 B) -.95 C).50 D).25

6.5 r =.51

.....

Statistics Needed Need to find the best place to draw the regression line on a scatter plot Need to quantify the cluster of scores around this regression line (i.e., the correlation coefficient)

Correlation Coefficient A correlation coefficient provides a quantitative way to express the degree of relationship between two variables There are 3 different formulas presented in the book Z-score formula is a good way to see “what's going on”

Blanched Formula XY = product of each X value multiplied by its paired Y value X = mean of variable X Y = mean of variable Y S x = standard deviation of variable X S y = standard deviation of variable Y N = number of pairs of observations r =

Mean Y = 4.6; S Y = 2.41 Mean X = 3.0; S X = 1.41

Blanched Formula  XY = 84 X = 3.0 Y = 4.6 S x = 1.41 S y = 2.41 N = 5 r =

Blanched Formula r = 84  XY = 84 X = 3.0 Y = 4.6 S x = 1.41 S y = 2.41 N = 5

Blanched Formula r =  XY = 84 X = 3.0 Y = 4.6 S x = 1.41 S y = 2.41 N = 5

Blanched Formula r =  XY = 84 X = 3.0 Y = 4.6 S x = 1.41 S y = 2.41 N =

Blanched Formula r =  XY = 84 X = 3.0 Y = 4.6 S x = 1.41 S y = 2.41 N = 5

Blanched Formula r =  XY = 84 X = 3.0 Y = 4.6 S x = 1.41 S y = 2.41 N = 5

Practice What is the relationship between aggression and happiness?

Mean aggression = 14.50; S aggression = 4.43 Mean happiness = 6.00; S happiness = 2.16

Blanched Formula  XY = 326 X = 6.0 Y = S x = 2.16 S y = 4.43 N = 4 r =

Blanched Formula -.57 =  XY = 326 X = 6.0 Y = S x = 2.16 S y = 4.43 N = 4