psych 100a - lecture 15-16

Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E.

Heinzen

Correlation

Chapter 13

Revised by Jeffrey B. Henriques, Ph.D.

University of Wisconsin-Madison

Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E.

Heinzen

• 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

Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E.

Heinzen

Defining Correlation

• Co-relation between two variables

• These variables change together

• Usually scale (interval or ratio) variables

• Correlation does NOT mean causation

Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E.

Heinzen

Misleading Correlations• Ice-cream sales in U.S. are associated with murders

• What else might be happening here?

• Are there any other misleading correlations we might find?

Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E.

Heinzen

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.

Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E.

Heinzen

Misleading Correlations

Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E.

Heinzen

Correlation Coefficient

• A statistic that quantifies a relation between two variables

• Can be either positive or negative

• Falls between -1.00 and 1.00

• The value of the number (not the sign) indicates the strength of the relation

Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E.

Heinzen

Positive Correlation

• Association between variables such that high scores on one variable tend to have high scores on the other variable• A direct relation between the variables

Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E.

Heinzen

A Positive Correlation

Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E.

Heinzen

Negative Correlation

• Association between variables such that high scores on one variable tend to have low scores on the other variable• An inverse relation between the variables

Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E.

Heinzen

A Negative Correlation

Final Exam Score Diff

Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E.

Heinzen

Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E.

Heinzen

Three Possible Causal Explanations for a Correlation

Correlation is NOT Causation

Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E.

Heinzen

The Pearson Correlation Coefficient

• Sample correlation symbolized by r

• Population correlation symbolized by ρ• Intended for scale data on both variables

• Both a descriptive and inferential statistic

Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E.

HeinzenCalculating the Pearson Correlation Coefficient

• Always start with a scatterplot• Confirm linear relationship• Check for outliers

Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E.

Heinzen

Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E.

Heinzen

Always Start with a Scatterplot

Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E.

Heinzen

Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E.

Heinzen

Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E.

Heinzen

Calculating the Pearson r

Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E.

HeinzenHypothesis Testing with the

Pearson Correlation Coefficient• Step 1: Identify the populations,

distribution, and assumptions

• Step 2: State the null and research hypotheses

• Step 3: Determine the characteristics of the comparison distribution

• Step 4: Determine the critical values

• Step 5: Calculate the test statistic

• Step 6: Make a decision

Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E.

Heinzen

Applying Correlation in Psychometrics

• Psychometrics is the branch of statistics used in the development of tests and measures

• Psychometricians use correlation to examine two important aspects of the development of measures—reliability and validity

Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E.

Heinzen

• A reliable measure is one that is consistent

• One particular type of reliability is test–retest reliability• Whether the tool provides consistent information every

time the test is taken

• Coefficient alpha is a measure of a test’s internal reliability• The average of all possible split-half correlations

Reliability

Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E.

Heinzen

Validity

• A valid measure is one that measures what it was designed or intended to measure

• Correlation is used to calculate validity, often by correlating a new measure with existing measures known to assess the variable of interest

• Establishing validity is usually much more difficult than establishing reliability, and so is not always done