Section 1 Quiz 1 Stem and Leaf Plot

Section #1 Quiz 1 Stem and Leaf Plot (N=29) n n n 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) n n n X| 7 1|147889 2|244689 3|11122223333444567799 4|002 Mean=29. 36; M=32; Mode= 32, 33; s=8. 68;

Part II Sigma Freud & Descriptive Statistics Chapter 5 Ice Cream and Crime: Computing Correlation Coefficients

What you will learn in Chapter 5 n n What correlations are and how they work All about correlations. . . ¡ ¡ n How to compute them How to interpret them Other types of correlations that exist

What they are not n Correlations only tell us about the relationship and the strength of the relationship. n Correlations do NOT tell us about cause and effect. Chapter 6 5

What they are not n n Correlations do not imply causation Examples ¡ ¡ ¡ ¡ Chapter 6 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 6

What Correlations are about… n n 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 n Karl Pearson

Types of Correlation Coefficients n Positive Correlation ¡ Direction Correlation n n When variables change in the same direction Negative Correlation ¡ Indirect Correlation n When variables change in opposite directions r. XY = correlation between X and Y

Relationships Between Variables

Things to Remember n Correlations… ¡ ¡ Range in value from -1 to +1 Absolute value indicates strength Reflect situation where there 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 n Pearson product-moment… n What do these symbols represent?

Steps in Computation n n n 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

Pearson’s product-moment Steps in the process n Step 1: ¡ Calculate n n n Chapter 6 Σx Σx 2 (Σx)2 Σy Σy 2 (Σy)2 13

Pearson’s product-moment Steps in the process n Step 2: ¡ ¡ n Calculate Σxy Sometimes referred to as the sum of the cross-products Step 3: ¡ Substitute the values derived above into the formula n Chapter 6 Note that N = number of pairs of scores 14

The Visual Picture n Scatterplot

Strong Positive Relationship

Strong Negative Relationship

Correlation Matrix Income Education Attitude Vote 1. 00 0. 574 -0. 08 -0. 291 1. 00 -0. 149 -0. 199 1. 00 -0. 169 1. 00

Interpreting Correlation Coefficients

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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 Chapter 6 22

Computing Simple Correlations n Pearson product-moment… n What do these symbols represent?

Variance Explained n Coefficient of Determination ¡ ¡ n rxy =. 702 =. 49 or 49% Coefficient of Alienation ¡ ¡ ¡ rxy =. 702 =. 49 1. 00 -. 49 =. 51 or 51%

How Variables Share Variance n Remember: Association NOT Causation

Different Types of Correlations

Using the Computer n Computing Correlation Coefficients using SPSS

SPSS Output

SPSS Scatterplot n Selecting Variables

SPSS Scatterplot n Entering variables

SPSS Scatterplot n Simple Scatterplot

Glossary Terms to Know n n Pearson-product moment correlation Direct correlation ¡ n Indirect correlation ¡ n Positive correlation Negative correlation Scatterplot