Reversal Paradox Fire Damage, Severity, and Number of Fire Fighters PDF

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Reversal Paradox Fire Damage, Severity, and Number of Fire Fighters...

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Reversal Paradox: Fire Damage, Severity, and Number of Fire Fighters The data employed here are entirely fictional, created just to illustrate one of my favorite examples of a reversal paradox. In a reversal paradox, the association between two variables in aggregated data (ignoring a third variable) is opposite in direction what it is at each level of the third variable The data are in an Excel file that can be downloaded. Open it with Excel and look at the data. You will see that there are five different levels of severity of the fire and that the data are already sorted by severity. There are ten cases for each level of severity. For each block of ten cases, look at the covariance between damage and severity. You should be able to see that when more firefighters are sent, the less the damage, hold severity constant. Now, bring the data into SAS and run this code: Proc Corr nosimple; run; Proc Reg; Model Damage = Severity FFighters / stb; run; Proc Corr nosimple; Var Damage; With FFighters; By Severity; run; Symbol1 interpol=r value=dot cv=red ci=black width=2; Proc Gplot; Plot Damage * FFighters; run; quit; Proc Gplot; Plot Damage * FFighters; By Severity; run; quit;

Here is the annotated output. The SAS System The CORR Procedure

3 Variables: Damage Severity FFighters Pearson Correlation Coefficients, N = 50 Prob > |r| under H0: Rho=0 Damage Severity FFighters Damage

1.00000 0.72056

0.41348

Damage...