#
#
############### T-test and Analysis of Variance ###############
#
# This script assumes you have worked through all the previous notes from 
# the web page and you have downloaded, installed, and updated all available
# R packages.  

# Load the following libraries if you have not already; if an additional 
# library is needed, it will be listed in the script and loaded.

library(foreign)
library(Rcmdr)

# Start by importing the data from the web, assigning the name 'example1'. 

example1 <- read.spss("http://www.unt.edu/rss/class/Jon/R_SC/Module3/ExampleData1.sav", 
  use.value.labels=TRUE, max.value.labels=Inf, to.data.frame=TRUE)

attach(example1)

summary(example1)
names(example1)

##############################################################################
############ T-tests ###############

### Single sample t-tests with Recall1; specifying one- and two-tailed tests against
# various values of the population mean.

t.test(Recall1, alternative='two.sided', mu=0.0, conf.level=.95)
t.test(Recall1, alternative='less', mu=15.0, conf.level=.95)
t.test(Recall1, alternative='greater', mu=11.5, conf.level=.95)

### Dependent or paired samples t-tests.
# Is the difference between Recall1 and Recall2 less than zero? 

t.test(Recall1, Recall2, alternative='less', conf.level=.95, paired=TRUE)

# Is the difference between Recall1 and Recall2 greater than zero? 

t.test(Recall1, Recall2, alternative='greater', conf.level=.95, paired=TRUE)

### Independent samples t-tests.
# Two-tailed test of Skittles vs. No candy on Recall1 WITHOUT assuming 
# homogeneity of variances (Welch t-test).

t.test(Recall1~Candy, alternative='two.sided', conf.level=.95, 
  var.equal=FALSE, data=example1)

# Boxplot of Recall1 by groups of Candy.

boxplot(Recall1~Candy, ylab="Recall1", xlab="Candy", data=example1)

# One-tailed test of males vs. females on Recall1 ASSUMING equal variances. 

t.test(Recall1~Sex, alternative='less', conf.level=.95, var.equal=TRUE, 
  data=example1)

### Robust t-test.
# First create an object (called 'x1' here) to show each group of Candy 
# on Recall1.

x1 <- split(Recall1, Candy)
x1

# Load required library(WRS).
# If not installed, it can be found only on R-Forge. 
# To install this package directly within R type: install.packages("WRS", repos="http://R-Forge.R-project.org") 

library(WRS)

# Robust t-test (Yuen bootstrapped t-test); 600 bootstrapped resamples; one 
# tailed test (side=T).

yuenbt(x1$Skittles, x1$None, tr=.0, alpha=.05, nboot=600, side=T)

# With 20% trimmed means.

yuenbt(x1$Skittles,x1$None,tr=.2,alpha=.05,nboot=600,side=T)

### Cohen's d effect size (and confidence interval for Cohen's d) for the 
### difference between two means. 
# Load required library(MBESS)

library(MBESS)

# Calculate the Cohen's d (also known as Standardized Measure of Difference).

smd(x1$Skittles, x1$None)

# To get the confidence interval for Cohen's d; we need the Noncentrality 
# Parameter (generally the observed t-statistic from the t-test). Here we are 
# using the NCP from the Yuen bootstrapped and trimmed t-test just above.

ci.smd(ncp = -6.3, n.1 = 27, n.2 = 27, conf.level = .95)

# To test the assumption of homogeneity of variances; the first line simply 
# reports the variances of each group, the second runs the 'Levene's test'.

tapply(example1$Recall1, example1$Candy,  var, na.rm=TRUE)

var.test(Recall1 ~ Candy, alternative='two.sided', conf.level=.95, data=example1)


##############################################################################
############### ANOVA ###############

### Oneway ANOVA comparing three types of distraction on ability to Recall.

library(multcomp, pos=4)
library(abind, pos=4)

# Conduct the Analysis of Variance (aov).

AnovaModel.1 <- aov(Recall1 ~ Distraction, data=example1)
summary(AnovaModel.1)

# Summary for types of distraction.

numSummary(Recall1 , groups=Distraction,statistics=c("mean", "sd"))

# Pairwise comparisons: Tukey.

.Pairs <- glht(AnovaModel.1, linfct = mcp(Distraction = "Tukey"))
summary(.Pairs)
confint(.Pairs) # confidence intervals
cld(.Pairs) # compact letter display

# Plotting the means with tail displays.

old.oma <- par(oma=c(0,5,0,0))
plot(confint(.Pairs))
par(old.oma)
remove(.Pairs)

### Factorial ANOVA comparing 3 types of Distraction and 2 types of Candy on 
### ability to Recall.
# Conduct the ANOVA. This can be 'read' as: Linear Model of Recall predicted 
# by Candy and Distraction. 

AnovaModel.2 <- (lm(Recall1 ~ Candy*Distraction, data=example1))

# Summary of the ANOVA Model 2.

Anova(AnovaModel.2)

# Individual cell/condition summaries (mean, sd, n).

tapply(Recall1, list(Candy=Candy,Distraction=Distraction), mean, na.rm=TRUE)
tapply(Recall1, list(Candy=Candy,Distraction=Distraction), sd, na.rm=TRUE)
tapply(Recall1, list(Candy=Candy,Distraction=Distraction), function(x) 
  sum(!is.na(x)))

# Plot of means from ANOVA Model 2.

plotMeans(Recall1, Distraction, Candy, error.bars="se")


#### SEE ALSO ### 
# (1): http://www.unt.edu/benchmarks/archives/2003/august03/rss.htm
# (2): http://www.unt.edu/benchmarks/archives/2002/april02/rss.htm




# END: December 2010.