Lecture 5_measures of relationship

# Lecture 5_measures - Measures of Relationship Covariation Covariance Correlation 1 Working with Pairs of Variables Until now we have focused on

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9/1/2010 1 Measures of Relationship: Covariation, Covariance, & Correlation 1 Working with Pairs of Variables • Until now we have focused on analyzing one variable at a time – Frequency distributions displayed scores on a single variable – Bar graphs and histograms illustrated the frequency of a variable – Measures of central tendency and variability were computed on a single variable • We can also study two variables at a time to consider the relationship between variables 2 Working with Pairs of Variables • When you study the relationship between two variables you analyze pairs of variables for each subject – e.g., To see if a student’s grades across his/her classes are related, you could record their grades in English and Math class… giving each subject a pair of scores in the data (their grade in each of the courses) • Pairs of scores are kept together through the analysis and analyzed simultaneously 3

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9/1/2010 2 Working with Pairs of Variables • When one variable was being studied the notation used to refer to the variable was simply X • When two variables are being studied, the X notation is retained to identify one of the variables and another notation, Y , is added to refer to the second variable in analysis 4 Possible Types of Relationships Between Pairs of Variables POSITIVE RELATIONSHIP : as one variable increases, the other variable also increases OR equivalently as one variable decreases, the other variable also decreases – e.g., the more food you consume, the more weight you will gain; or the less food you consume, the less weight you will gain 5 Possible Types of Relationships Between Pairs of Variables POSITIVE RELATIONSHIP : If a relationship is positive then it means if a person is above the mean on one variable (X) they will likely be above the mean on the other variable (Y); if a person is below the mean on one variable (X) they will likely be below the mean on the other variable (Y) 6
9/1/2010 3 Possible Types of Relationships Between Pairs of Variables POSITIVE RELATIONSHIP : Pairs a (+) deviation score with a (+) deviation score or pairs a (-) deviation score with a (-) deviation score So the product of deviations for a positive relationship will always be positive 7 1 -1 2 -3 3 1 8 3 X M X X Y Y M Y 2 X M 5 Y M 0 ) ( X M X 0 ) ( Y M Y = 3 = 3 Examples of Positive Relationship Between Variables • SAT scores and college GPA • Age and reading ability • Years of education and salary • Height and weight • Death rate and speed limit • Insurance rates and speeding tickets • HW scores and tests scores in a class 8 Possible Types of Relationships Between Pairs of Variables NEGATIVE RELATIONSHIP : as one variable increases, the other variable decreases OR equivalently as one variable decreases, the other variable increases – e.g., the more you exercise per week the less weight you will gain; or the less you exercise a week the more weight you will gain 9

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9/1/2010 4 Possible Types of Relationships
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## This note was uploaded on 02/17/2011 for the course PYSC 227 taught by Professor Fairchild during the Spring '10 term at South Carolina.

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Lecture 5_measures - Measures of Relationship Covariation Covariance Correlation 1 Working with Pairs of Variables Until now we have focused on

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