• What should we do when variables are continuous?• Drinking and fighting; social support and

depression; IQ at age 5 and 25• What are our options?

ANOVAs don’t always work

Misleading Correlations

• Ice-cream sales in California and drowning deaths

• What else might be happening here?

• Are there any other misleading correlations we might find?

Misleading Correlations

• In investigating the relationship between age and some physical characteristics of women, begin by measuring the angle of the feet in walking.

• the angle tends to be greater among older women.

• You might first consider whether this indicates that women grow older because they toe out… NO!

• So it appears that age increases the angle between the feet, and-most women must come to toe out more as they grow older.

Misleading Correlations

• Children with longer arms reason better than those with shorter arms

• Bottled water linked to healthier babies

• Families that own cappuccino makers are more likely to have healthy babies.

• Breast fed babies have IQs that are 6 points higher than babies who are not breast fed

Misleading Correlations

                                                               Discussion. If fat in the diet causes cancer, then the points in the diagram should slope up, other things being equal. So the diagram is some evidence for the theory

X independent variable

Y dependent variable

SX STANDARD DEVIATION OF X

SY STANDARD DEVIATION OF Y

ZX A SUBJECT’S Z-SCORE ON X

ZY A SUBJECT’S Z-SCORE ON Y

Describing a relationship between 2 variables

- SO WHAT IS THE LINEAR RELATION BETWEEN X AND Y? •DIRECTION•DEGREE

- ANSWER IS • r = Pearson PRODUCT-MOMENT CORRELATION

A PLOT OF SCORES ON X AND Y

GIVES THE DIRECTION OF RELATIONSHIP

CORRELATIONS ‘R’ RANGE FROM –1 TO +1

r = 0 NO CORRELATION, INDEPENDENT

r = + POSITIVE CORRELATION

r = - NEGATIVE CORRELATION

• THE CLOSER r IS TO 1 OR –1, THE STRONGER THE LINEAR RELATIONSHIP BETWEEN TWO VARIABLES

THE SCATTER DIAGRAM

R=.08

R2=.007

R=.37

R2=.137

R=.689

R2=.474

R=.943

R2=.891

R=-.817,

R2=.668

R=?

R=?

R=?

Extreme scores can have huge influence on correlation

R=.75 R=.-75

R=-.05

R2=.002

Correlation only handles linear relationship

Cannot handle more complicated curvilinear relatiomships

1x y

xy

z zr

n

WHY DOES THIS WORK? IF ZX+ AND ZY+ THEN ZXZY POSITIVE IF ZX- AND ZY- THEN ZXZY POSITIVE IF ZX+ AND ZY- THEN ZXZY NEGATIVE IF ZX- AND ZY+ THEN ZXZY NEGATIVE

R

- ABSOLUTE VALUE OF r INDICATES STRENGTH - BUT DIFFICULT TO INTERPRET - r2 PERCENT OF VARIANCE ACCOUNTED FOR - IT TELLS YOU HOW MUCH OF THE VARIANCE IN ONE VARIABLE IS “ACCOUNTED” FOR BY THE OTHER VARIABLE

R

R