Note that ANOVA and post-hoc tests can be performed in Prism too.

== One-way ANOVA ==

See the [http://www.graphpad.com/support/faqid/1745/ Prism help page] for some general considerations.

==== Reading in data ====


  * Use read.* or create appropriate dataframe

{{{
# Input data from a tab-delimited text file of the format
# weight group
# 56   a
# 29   b
# ...
strains = read.delim("brain_weights.txt",header=TRUE)

# Input data for 4 different groups by creating a dataframe by hand
a = c(56,60,44,53)
b = c(29,38,18,35)
c = c(11,25,7,18)
d = c(26,44,20,32)
strains.frame = data.frame(a, b, c, d)
strains = stack(strains.frame)
colnames(strains) = c("weight", "group")
}}}
  
==== Creating an ANOVA table ====
  * Use the command //anova// or //aov// with summary.  The first argument is the dependent variable, followed by ~, and then by independent variable(s).
  * So if we want to set up a model where weight is a function of the group (e.g., the weight potentially depends on the group)

{{{
# Syntax 1
anova( lm(weight ~ group, data=strains) )

# Syntax 2
summary( aov(weight ~ group, data=strains) )
}}}

== Post-test: Comparing all pairs of means ==

==== Tukey ====
    * "Tukey's method is more conservative but may miss real differences too often" - Intuitive Biostatistics (p.259)


{{{
TukeyHSD( aov(weight ~ group, data=strains) )
}}}

==== Dunnett ====
  * Useful if you want to compare a reference group to all other groups (instead of doing an all vs. all comparison) 
  * The first group ("a" in this example) is used as the reference group.  If this is not the case, use the relevel() command to set the reference, like ''strains$group = relevel(strains$group, "b")''

{{{
library(multcomp)
summary(glht(aov(weight ~ group, data=strains), linfct=mcp(group="Dunnett")))
}}}

== Repeated-measures ANOVA ==

Repeated-measures ANOVA is typically needed if multiple measurements are made on the same sample (such as assaying a mouse's weight during a time course).

== Two-way ANOVA ==

Two-way ANOVA should be used for experiments where two different factors are being studied (such as comparing different treatments of different genotypes of mice).

==== Reading in data, plotting, and summarizing ====


  * Use read.* or create appropriate dataframe

{{{
# Input data from a tab-delimited text file of the format
# weight treatment genotype
# 56   a   ko
# 29   b   wt
# 60   a   wt
# ...
strains = read.delim("brain_weights.txt",header=TRUE)

# Plot the data by group
boxplot(weight ~ paste(genotype, treatment), data=strains)
stripchart(weight ~ paste(genotype, treatment), data=strains, vert=T, method="jitter", jitter = 0.4, pch=19, cex=2, add=T)

# Summarize the data by group
tapply(strains$weight, paste(strains$genotype, strains$treatment), mean)
}}}

==== Creating an ANOVA Table ====
  * Use the command //anova// or //aov// with summary.  The first argument is the dependent variable, followed by ~, and then by independent variable(s).
  * So if we want to set up a model where weight is a function of the group and/or the genotype, with a potential interaction (e.g., the difference between groups depends on the genotype), the typical analysis would look like

{{{
# Syntax 1
anova( lm(weight ~ group * genotype, data=strains) )
anova( lm(weight ~ genotype * group, data=strains) )

# Syntax 2
summary( aov(weight ~ group * genotype, data=strains) )
summary( aov(weight ~ genotype * group, data=strains) )
}}}

Note that the p-value for each factor depends on the order of the factors in the above formulas.

== Post-test: Comparing all pairs of means ==

As before, with 1-way ANOVA,
{{{
TukeyHSD( aov (weight ~ group * genotype, data=strains) )
}}}

If the experimental design is unbalanced (e.g., some groups are more replicated than others), we need a more complex model.