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# Lecture15 - 26 June 2003 Biostatistics 6650-L15 1 Todays...

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26 June 2003 Biostatistics 6650--L15 1

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26 June 2003 Biostatistics 6650--L15 2 Today’s Schedule Association of continuous X with continuous Y brief introduction Scatter plots Correlation Pearson/Spearman Regression simple linear regression least squares Wrap-up
26 June 2003 Biostatistics 6650--L15 3 Scatter Plots Before doing any calculations---PLOT the DATA Assume Y and X are two continuous variables of interest both are measured on each subject one is not calculated from the other data arrangement N subjects 2 columns Y and X JMP: analyze Fit Y*X or analyze multivariate specify two continuous variables default output is a scatter plot

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26 June 2003 Biostatistics 6650--L15 4 Scatter Plots Lab 3 IgA Nephropathy baseline data, N=106 X=age, Y=systolic blood pressure 80 90 100 110 120 130 140 150 160 170 180 SBP_0 10 20 30 40 50 60 70 80 AGE_RAN Bivariate Fit of SBP_0 By AGE_RAN
26 June 2003 Biostatistics 6650--L15 5 Correlation Covariance= E{(X-6 x )(Y-6 y )} measures how X and Y vary together or co-vary if X and Y are independent, then Covariance= E(X-6 x )*E(Y-6 y )=0*0=0 if X and Y are positively related, then when X is high relative to its mean, Y will also be high. This leads to large positive covariance. Population Correlation coefficient(6 6 = standardized covariance = E{(X-6 x )(Y-6 y )} / (6 x 6 y ), independent of units of X&Y measures strength of linear association between Y and X ranges from -1 (perfect negative association) to 0 (no association) to 1 (perfect positive association) Caution: combining groups with different 6’s may produce spurious results

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26 June 2003 Biostatistics 6650--L15 6 Correlations Fig 5.16 Rosner -2.5 0 2.5 5 7.5 10 y 0 2 4 6 8 x Bivariate Fit of y By x i =0, but perfect non-linear relationship between Y and X---plot the data!
26 June 2003 Biostatistics 6650--L15 7 Correlation Sample estimate of 6, is r(Pearson’s r) defined as: Spearman’s rank correlation(r s ) Calculate Pearson’s r using the ranks of X and Y.

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