Comparing Groups

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Comparing Groups Part 2
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Wilcoxon Signed Rank (again)
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H0 ? 0 HA ? ? 0
? represents the population mean or median
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or in colors add up the rank_AbsDiff for the
green negative scores
or in colors add up the rank_AbsDiff for the
blue positive scores
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or in colors add up the rank_AbsDiff for the
green negative scores
R- 1.5 3 4.5 4.5 7.5 7.57.514.518.5
64.5
or in colors add up the rank_AbsDiff for the
blue positive scores
R 1.5 7.5 11 11 11 14.5 14.5
14.518.518.518.52122 188.5
188.5-64.5/262
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One-way ANOVA in R

• In the last lecture I gave you a demonstration of
  using SAS to conduct a one-way ANOVA. Many
  people think that R is a superior tool for doing
  analyses like ANOVA. While R is not critical for
  simple models like you have seen, it is
  invaluable for graphics to describe more
  complicated models.

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R and Anxiety Disorders

• Start R and then type library(Rcmdr)
• Load the dataset using the Import Data option on
  the Data menu.
• Load the Generalized Anxiety Disorder (GAD) data.
  It has Hamilton Rating Scale for Anxiety data
  for people taking placebo, high or low dose drug.

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Summarize the Data
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Show me the means.

• You want to see if there is a difference in means
  in the 3rd variable for the levels of the 2nd
  variable. You can request the mean plot

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The Plot of the Design
I really like boxplots to see the variability
around these means.
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Set Factor Order
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Side-by-side Boxplot
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Boxplot Reordered
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I want means.
Gad lt- na.omit(Gad) plot.design(Gad,
c(2,3)) attach(Gad) thePlot (boxplot(HAMADOSEG
RP, ylab"HAMA", xlab"DOSEGRP")) where
seq(thePlotn) theMeans tapply(HAMA, DOSEGRP,
mean) points(where, theMeans, col "red", pch
18)
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Testing for Differences

• Once the data is set with the placebo group as
  the baseline, it is easy to ask for tests for the
  differences vs. the baseline level.

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General Linear Models

• It is important for you to know that ANOVAs are
  more than stand-alone analyses that are not
  related to modeling. ANOVA fits into a class of
  statistics called General Linear Models. They are
  well implemented in R and Rcmdr.

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Checking the Model

• With the working model you can get lots of
  summary information, including diagnostic plots.

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More Advanced Contrasts

• There is a plethora of methods for dealing with
  multiple comparisons. You can search CRAN for
  specific methods you see in textbooks. For
  example, Walker uses Dunnetts T test for
  contrasting the placebo vs. the other levels.
• I start search CRAN with RSiteSearch(blah)

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Nasty code.

• I eventually found the method implemented in a
  package called multcomp
• library(multcomp)
• gad.aov aov(HAMA DOSEGRP, data Gad)
• summary(glht(gad.aov, linfct mcp(DOSEGRP"Dunnet
  t")))
• confint(glht(gad.aov, linfct mcp(DOSEGRP"Dunnet
  t")))

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Two-Way ANOVA

• When you have two or more predictors, you want to
  know if the variables impact the outcome means by
  themselves and also if they interact. If
  variables interact, it means that together they
  do things to the outcome variable beyond what you
  would expect from looking at each variable alone.
  For example, smoking and eating too much both
  hurt longevity but the combination of the two
  factors may not be as bad as expected or the
  combination may be especially lethal.

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Anemia

• People with Cervical (C), Prostate(P) or
  Colorectal (R) cancers with chemotherapy-induced
  anemia were treated either with a drug or placebo
  and the changes in their hemoglobin levels were
  assessed. The question of interest is, does the
  drug reduce anemia?

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Box Plots of Course

• With code or R commander get boxplots for the
  levels of the predictors

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Design Plots

• You have analysis variables in columns 1, 2 and
  4. So specify the design plot like this

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Interaction Plots

• In addition to the main effects for the
  predictors, you want to see if the drug behaves
  differently in the people with the three
  different cancer groups. Perhaps it helps
  increase hemoglobin in one group and decreases it
  another.

Type your outcome variable last.
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• It looks like there are differences between the
  cancer types and the drug seems to increase the
  hemoglobin relative to the placebo.

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Modeling
Anova with a capital A is part of the car package
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Results
To turn off the stuff, type this code before
you model options(show.signif.starsFALSE)
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ANOVA as a Model

• You can build this ANOVA as a linear model.

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used for nesting y A/B y A AB y A B
in A
interaction only
main effect and interaction
Set interaction limits (ABC) 2 is equal
to ABC - ABC
Main effect
Remove an explanatory effect.
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SAS EG example

• See the parallel information in the SAS EG
  project.