Section #1 Quiz 1 Stem and Leaf Plot (N=29)

X|8 2|2255667899999 3|0011222456668 4|00

Mean=29.9; M=30; Mode= 29; s=6.38;

Section #2 Quiz 1 Stem and Leaf Plot (N=36)

X| 7 1|147889 2|244689 3|11122223333444567799 4|002

Mean=29.36; M=32; Mode= 32, 33; s=8.68;

Part IIigma Freud & Descriptive Statistics

Chapter 5 Ice Cream and Crime: Computing Correlation Coefficients

What you will learn in Chapter 5

What correlations are and how they work

All about correlations... How to compute them How to interpret them

Other types of correlations that exist

Chapter 6 5

What they are not

Correlations only tell us about the relationship and the strength of the relationship.

Correlations do NOT tell us about cause and effect.

Chapter 6 6

What they are not

Correlations do not imply causation Examples

Marijuana use and heroin Milk use and cancer Church attendance and drug use Lead levels and behavior Cigarette smoking and Alzheimer’s Education and sexual activity Sex life and longevity Coffee and suicide risk

What Correlations are about…

Examines the relationship between variables

How the value of one variable changes in relation to changes in another variable Range between -1 and 1 Bivariate correlation (2 variables) Pearson product-moment correlation

Karl Pearson

Types of Correlation Coefficients

Positive Correlation Direction Correlation

When variables change in the same direction

Negative Correlation Indirect Correlation

When variables change in opposite directions

rXY = correlation between X and Y

Relationships Between Variables

Things to Remember

Correlations… Range in value from -1 to +1 Absolute value indicates strength Reflect situation where there are at least

two data points May want to use “indirect” and “direct”

instead of “positive” and “negative” to keep from assigning value to the relationship

Computing Simple Correlations

Pearson product-moment…

What do these symbols represent?

Steps in Computation

List the two values for each participant Compute the sum of X values, and

compute the sum of Y values Find square of sum for x and y Find sum of squares for x and y Find the sum of the XY products Now “plug” these values into the formula

Chapter 6 13

Pearson’s product-momentSteps in the process

Step 1: Calculate

Σx Σx2

(Σx)2

Σy Σy2

(Σy)2

Chapter 6 14

Pearson’s product-momentSteps in the process

Step 2: Calculate Σxy Sometimes referred to as the sum of the

cross-products Step 3:

Substitute the values derived above into the formula Note that N = number of pairs of scores

The Visual Picture

Scatterplot

Strong Positive Relationship

Strong Negative Relationship

Correlation Matrix

Income Education Attitude Vote

Income 1.00 0.574 -0.08 -0.291

Education 1.00 -0.149 -0.199

Attitude 1.00 -0.169

Vote 1.00

Interpreting Correlation Coefficients

Is Rate My Professor Valid?

The Rate My Professor system relies on students who are willing to rate their professors anonymously. While this could encourage more candid feedback, the anonymous system has also at times provided what could be inaccurate ratings.

Is Rate My Professor Valid?

One study showed the easier a class was and the more attractive the teacher, the more likely they would get a good rating on Rate My Professor. Others have expressed worry that Rate My Professor listings often give good ratings to teachers that may not provide the most comprehensive, educational, or quality courses available.

Chapter 6 22

Now You Try!!

Participant Hours/Week Video Games College GPA

1 3 3.8

2 15 2.1

3 22 2.5

4 30 0.6

5 11 3.1

6 25 1.9

7 6 3.9

8 12 3.8

9 17 1.7

Computing Simple Correlations

Pearson product-moment…

What do these symbols represent?

Variance Explained

Coefficient of Determination rxy = .70 .702 = .49 or 49%

Coefficient of Alienation rxy = .70 .702 = .49 1.00 - .49 = .51 or 51%

How Variables Share Variance

Remember: Association NOT Causation

Different Types of Correlations

Using the Computer

Computing Correlation Coefficients using SPSS

SPSS Output

SPSS Scatterplot

Selecting Variables

SPSS Scatterplot

Entering variables

SPSS Scatterplot

Simple Scatterplot

Glossary Terms to Know

Pearson-product moment correlation Direct correlation

Positive correlation Indirect correlation

Negative correlation Scatterplot