Lecture17 - Lecture 17: Correlation Analysis Simultaneous...

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Lecture 17: Correlation Analysis Æ Simultaneous analysis of 2 variables Sources of Information Motulsky: Chapter 17 Triola et al.: Chapter 9 Sokal & Rohlf: Chapter 15 Dytham: p. 154-171
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Correlation versus Regression Correlation tells us whether there is a relationship between 2 variables and how strong the relationship is between them. Î tells us how well the response variable (Y) is predicted from the predictor variable (X)
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Correlation versus Regression Regression tells us how to predict Y from X Î provides the equation to predict Y from X
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Introducing Correlation Analysis In correlation analysis, we generally want to determine whether two variables are interdependent, or covary – that is, do they vary together? Definition : A correlation exists between two variables when one of them is related to the other in some way. In common usage, the word ‘correlation’ describes any type of relationship between objects and events. In statistical usage, correlation refers to a quantitative relationship between two variables measured on ordinal or continuous scales. When we wish to establish the degree of association between pairs of variables in a sample from a population, correlation analysis is the proper approach.
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(Triola Fig. 9-1) y x no correlation +ve -ve
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The Linear Correlation Coefficient • Correlation coefficients measure the strength of the linear association between two variables. • Both parametric (Pearson) and non-parametric (Spearman or Kendall) correlation coefficients are common. • The parametric correlation ( Pearson Product-Moment correlation coefficient, r ) quantifies the relationship between the variables in the raw or transformed metric. • The non-parametric correlation ( Spearman rank correlation coefficient (r s ) or Kendall’s tau ) measures the strength of the relationship of the ranks of the data. • The correlation coefficient (r) is a sample statistic that is calculated from sample data, and is used to estimate the corresponding population parameter ( ρ = Greek symbol rho).
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No correlation r = 0 r = 0
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An Example: A medical researcher wanted to know if heart rate and blood pressure are correlated in healthy adults. He collected a random sample of 30 healthy adults and measured both variables (heart rate and blood pressure) in each subject.
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Look for : 1. Form linear or not 2. Direction positive or negative 3. Strength strong or weak subject heartrate bloodpres 1 67 179 2 75 197 3 63 175 4 89 209 5 53 164 6 76 180 7 98 212 8 75 187 9 71 189 10 65 176 11 69 167 12 74 186 13 80 198 14 58 170 15 76 187 16 68 175 17 64 169 18 76 190 19 79 176 20 72 168 21 60 158 22 67 160 23 63 167 24 90 221 25 50 149 26 73 180 27 64 168 28 68 162 29 65 168 30 70 157 r = +0.86
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Relating Sample Correlation Coefficients to Populations • As with statistics, we would like to make inferences about the correlation coefficient for the entire statistical population.
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This note was uploaded on 07/10/2010 for the course BIOL 361 taught by Professor Hall during the Winter '08 term at Waterloo.

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Lecture17 - Lecture 17: Correlation Analysis Simultaneous...

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