Psych 100A - Lecture 15-16
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Transcript of Psych 100A - Lecture 15-16
![Page 1: Psych 100A - Lecture 15-16](https://reader036.fdocuments.net/reader036/viewer/2022062314/55cf9164550346f57b8d312c/html5/thumbnails/1.jpg)
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
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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
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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
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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?
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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.
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Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E.
Heinzen
Misleading Correlations
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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
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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
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Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E.
Heinzen
A Positive Correlation
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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
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Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E.
Heinzen
A Negative Correlation
Final Exam Score Diff
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Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E.
Heinzen
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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
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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
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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
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Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E.
Heinzen
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Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E.
Heinzen
Always Start with a Scatterplot
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Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E.
Heinzen
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Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E.
Heinzen
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Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E.
Heinzen
Calculating the Pearson r
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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
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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
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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
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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