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Chapter 11

This

**preview**shows half of the first page. to view the full**2 pages of the document.**PSYC 2520: Introduction to Experimental Psychology

Beginning Behavioral Research: A Conceptual Primer (7th ed. 2012) Rosnow & Rosenthal

Chapter 11: Correlating Variables (pp. 204-214)

Correlation coefficient-- a single number indicating the strength of association between two variables (X and Y)

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Pearson's ris a standard index of linear relationship, with the possible values running from -1.0 to +1.0

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Linearity-- correlations that reflect the degree to which mutual relations between X and Y resemble a straight line

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Continuous-- a value can fall between any two adjacent scores (e.g., age)

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Dichotomous-- the variable is divided into two distinct or separate parts (e.g., gender)

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Continuous vs. discreet (dichotomous) variables

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Pearson r-- two continuous variables, such as the correlation of scores on the SAT with GPA after 4 years of

college

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Point-biserial r ()-- one continuous and one discreet variable, such as the correlation of subjects' gender

with their performance on the SAT

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Phi coefficient (Φ)-- two discreet variables, such as the correlation of subjects' gender with their "yes" or

"no" responses to a specific question

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Spearman rho (

)-- Two ranked variables, such as the correlation of the ranking of the top 25 college

basketball teams by sports writers (Associated Press ranking) with the ranking of the same teams by college

coaches (USA Today ranking)

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Forms of correlations:

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What are different forms of correlations?

Scatter plots let us visualize the clustering and slope of dots that represent the relationship between X and Y. The

cloud of dots slopes up for positive correlations and slopes down for negative correlations.

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How are correlations visualized in scatter plots?

The linear correlation between X and Y is equal to the sum of the products of the z scores of X and Y divided

by the number (N) of pairs of X and Y scores

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First calculate the mean and SD of the data, then transform all raw scores into z scores using the formula

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Calculation formula for Pearson r--

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How is a product-moment correlation calculated?

Dummy coding-- when numerical values such as 0 and 1 are used to indicate the two parts of a discreet variable

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Used in calculations of correlations

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How is dummy coding used in correlation?

Two dichotomous variables

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To calculate the correlation between two dichotomous variables, we can (a) dummy code both variables and then

use the corresponding z scores to compute the Pearson r or (b) compute directly from a 2 x 2 contingency table

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Computation based on a contingency table

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When is the phi coefficient used?

Ch. 11 - Correlating Variables

Sunday, March 3, 2013

4:10 PM

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