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Chapter 11

PSYC 3525 Chapter Notes - Chapter 11: Phi Coefficient, Contingency Table


Department
Psychology
Course Code
PSYC 3525
Professor
Josee Rivest
Chapter
11

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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)
Pearson's ris a standard index of linear relationship, with the possible values running from -1.0 to +1.0
Linearity-- correlations that reflect the degree to which mutual relations between X and Y resemble a straight line
Continuous-- a value can fall between any two adjacent scores (e.g., age)
Dichotomous-- the variable is divided into two distinct or separate parts (e.g., gender)
Pearson r-- two continuous variables, such as the correlation of scores on the SAT with GPA after 4 years of
college
Point-biserial r ()-- one continuous and one discreet variable, such as the correlation of subjects' gender
with their performance on the SAT
Phi coefficient (Φ)-- two discreet variables, such as the correlation of subjects' gender with their "yes" or
"no" responses to a specific question
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)
Forms of correlations:
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.
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

First calculate the mean and SD of the data, then transform all raw scores into z scores using the formula  

Calculation formula for Pearson r--










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
Used in calculations of correlations
How is dummy coding used in correlation?
Two dichotomous variables
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
Computation based on a contingency table
   
        
When is the phi coefficient used?
Ch. 11 - Correlating Variables
Sunday, March 3, 2013
4:10 PM
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