19 ANOVA #2 - Statistical Information Statistical Analysis...

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Statistical Information Statistical Information Analysis of Variance II Analysis of Variance II Checking ANOVA Checking ANOVA Assumptions Assumptions
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Methods for Communicating Methods for Communicating Statistical Information Statistical Information • Confidence Intervals –How confident are we in the estimates we have? • Hypothesis Tests –Can we reject the null hypothesis? • Significance Levels (p-values) –How strong is the evidence against the null hypothesis?
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Bethic Bethic Study after Exxon Valdez Study after Exxon Valdez • Following the March 24, 1989 grounding of the tanker Exxon Valdez in Alaska, approximately 35,500 tons of crude oil were released into Prince William Sound. The paper “The deep benthos of Prince William Sound, Alaska, 16 months after the Exxon Valdez oil spill” [Marine Pollution Bulletin (1998), 36:118-130 reports on an evaluation of deep benthic infauna after the spill.
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The observational setup The observational setup • Thirteen sites were selected for study. Seven of the sites were within the oil trajectory and six were outside the oil trajectory. Collection of environmental and biological data at two depths, 40 m and 100 m, occurred in the period July 1-23, 1990. One of the variables measured was population abundance (individuals per square meter).
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Original Exxon Data Original Exxon Data Site 40m 100m Trajectory 1 5124 3228 1 2 2904 2032 1 3 3600 3256 1 4 2880 3816 1 5 2578 2438 1 6 4146 4897 1 7 1048 1346 1 1 1336 1676 2 2 394 2008 2 3 7370 2224 2 4 6762 1234 2 5 744 1598 2 6 1874 2182 2
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exxon.ssc exxon.ssc ExxonOil = read.table("ExxonOil.csv",header=T,sep=",") exxon = data.frame( rbind( as.matrix(ExxonOil[,c(1,2,4)]), as.matrix(ExxonOil[,c(1,3,4)]))) names(exxon) = c("Site","Abundance","Trajectory") attach(exxon) boxplot(Abundance[Trajectory==1],Abundance[Trajectory==2], ylab="Abundance", names=c("Inside Oil","Outside Oil"), main= "Prince William Sound Benthos After Exxon Valdez Oil Spill")
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Exxon Data Exxon Data Site Abundance Trajectory 1 1 5124 1 2 2 2904 1 3 3 3600 1 4 4 2880 1 5 5 2578 1 6 6 4146 1 7 7 1048 1 8 1 1336 2 9 2 394 2 10 3 7370 2 11 4 6762 2 12 5 744 2 13 6 1874 2 14 1 3228 1 15 2 2032 1 …etc…
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2000 4000 6000 Inside Oil Outside Oil Prince William Sound Benthos After Exxon Valdez Oil Spill Abundance
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Mean Abundance Estimates Trajectory Mean Abundance 1000 1500 2000 2500 3000 3500 Inside Oil Outside Oil
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Making Confidence Intervals Making Confidence Intervals make.CI = function(x,y,names=NA) { my.means = tapply(y,x,mean) my.sterr = tapply(y,x,sterr) my.n = tapply(y,x,length) my.t.crit = qt(0.025,my.n-1)
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This note was uploaded on 11/12/2009 for the course BTRY 3010 at Cornell University (Engineering School).

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19 ANOVA #2 - Statistical Information Statistical Analysis...

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