psych 100a - lecture 15-16

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

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Correlation

Chapter 13

Revised by Jeffrey B. Henriques, Ph.D.

University of Wisconsin-Madison


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• 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


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Defining Correlation

• Co-relation between two variables

• These variables change together

• Usually scale (interval or ratio) variables

• Correlation does NOT mean causation


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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?


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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.


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Misleading Correlations


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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


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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


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A Positive Correlation


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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


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A Negative Correlation

Final Exam Score Diff


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Three Possible Causal Explanations for a Correlation

Correlation is NOT Causation


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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


HeinzenCalculating the Pearson Correlation Coefficient

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


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Always Start with a Scatterplot


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Calculating the Pearson r


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


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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


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• 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


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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

psych 100a - lecture 15-16

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