CHAPTER 5

# CHAPTER 5 - CHAPTER 5: CORRELATION 5.1 Introduction to...

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CHAPTER 5: CORRELATION 5.1 Introduction to Correlation Correlation and regression are procedures for examining the relationship between two variables; interested in predicting a score for one variable from a score for the other variable or knowing the strength of the relationship between two variables Correlation and Regression Distinguished Regression - one dependent variable and one or more independent variables Independent variable- variable controlled or manipulated by the researcher so its effect on the dependent variable can be determined In regression- clearly defined independent variable, random assignment to preselected dosage levels, value of the dependent variable is free to vary, researcher wants to predict Y from a knowledge of X In correlation- have paired X and Y scores and want to see if the variables are related and if so how strong is the association, researcher might want to predict either variable from a knowledge of the other, no obvious independent variable, no preselected values of X or Y so both are free to vary Same- both assess relationship between two variables where scores for one variable are paired with the scores for the other variable Different- nature of the variables (independent variable present or absent), use of random assignment of participants to the experimental conditions, to some extent the kinds of conclusions that can be drawn A Bit of History Correlation and regression concepts developed by Sir Francis Galton Bivariate frequency distribution or scatterplot, scatter diagram, scattergram- representation of the joint frequency of 2 variables Galton developed procedure for finding the straight line of best fit

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Regression or reversion toward the mean - tendency for tall parents to have slightly shorter offspring and for short parents to have slightly taller offspring Regression line or reversion line - the best fitting line in a scatterplot 5.2 A Numerical Index of Correlation Correlation coefficient- number representing the degree of association or strength of relationship between two variables; Pearson product moment correlation coefficient measures the linear relationship between two variables X and Y, denoted by r xy or just r, population correlation coefficient is denoted by (rho) ρ Value of r ranges from -1 to +1; +1 denotes perfect positive relationship- high scores on one variable paired with high scores on other variable and low scores for one variable paired with low scores for the other variable, data points fall on a straight line sloping upward; coefficient of -1 denotes a perfect negative or inverse relationship - high scores on one variable are paired with low scores on the other variable and low scores on one paired with high scores on the other, data points fall on a straight line sloping downward If r=0 there is no linear association between the variables; data points fall in a circle Intermediate degrees of association are represented by coefficients less than 0 (-1 < r < 0) or greater than 0 (0 < r < 1); data points tend to form an ellipse, the
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## This note was uploaded on 04/30/2008 for the course STATS 2402-04 taught by Professor Kirk during the Spring '08 term at Baylor.

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CHAPTER 5 - CHAPTER 5: CORRELATION 5.1 Introduction to...

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