Chapter 8 (3-4), 9Chapter 8 (3-4), 9

More about CorrelationMore about Correlation

Today’s LectureToday’s Lecture

SD LineSD Line

Calculating rCalculating r

correlation vs causationcorrelation vs causation

The SD LineThe SD Line the line the points cluster aroundthe line the points cluster around

passes through the point of averages: passes through the point of averages: (AVGx (AVGx , , AVGAVGYY))

Has slope : Has slope :

if 0Y

X

SDr

SD

if 0Y

X

SDr

SD

Calculating rCalculating r(call variables “X” and “Y”)(call variables “X” and “Y”)

Step 1: Calculate Step 1: Calculate AVGxAVGx and and AVGyAVGy Step 2: Calculate Step 2: Calculate SDxSDx and and SDySDy Step 3: Standardize each variableStep 3: Standardize each variable

Step 4: Find average of products of z-Step 4: Find average of products of z-scores (standard scores)scores (standard scores)

value AVGz

SD

{ }X Yr AVG Z Z

NOTE: The Correlation Coefficient is unaffected if the units of measurement are changed

Example:

Correlation between height and weight remains the same whether height is measured in inches, cm., feet, etc.

Important Note: Important Note: Correlation Correlation DOES NOT DOES NOT

Imply CausationImply Causation strong association between 2 strong association between 2

variables is not enough to justify variables is not enough to justify conclusions about cause and effectconclusions about cause and effect

ExamplesExamplesStrong association between:Strong association between: number of firefighters and amount of number of firefighters and amount of

damagedamage– Does sending more firefighters Does sending more firefighters causecause more more

damage?damage?

shoe size and score on a reading shoe size and score on a reading comprehension exam for elementary school comprehension exam for elementary school children children – What’s the explanation?What’s the explanation?

SAT and GPA scores SAT and GPA scores – What’s the explanation?What’s the explanation?

Important Note: Important Note: Correlation Correlation DOES NOT DOES NOT

Imply CausationImply Causation

strong association between 2 strong association between 2 variables is not enough to justify variables is not enough to justify conclusions about cause and effectconclusions about cause and effect

best way to get evidence that X best way to get evidence that X causes Y is through a causes Y is through a controlled controlled experimentexperiment