## ----setup, include=FALSE, cache=FALSE----------------------------------------
require(knitr)
opts_chunk$set(
  dev="pdf",
  fig.path="figures/",
        fig.height=3,
        fig.width=4,
        out.width=".47\\textwidth",
        fig.keep="high",
        fig.show="hold",
        fig.align="center",
        prompt=TRUE,  # show the prompts; but perhaps we should not do this
        comment=NA    # turn off commenting of ouput (but perhaps we should not do this either
  )

## ----pvalues, echo=FALSE, message=FALSE---------------------------------------
print.pval = function(pval) {
  threshold = 0.0001
    return(ifelse(pval < threshold, paste("p<", sprintf("%.4f", threshold), sep=""),
                ifelse(pval > 0.1, paste("p=",round(pval, 2), sep=""),
                       paste("p=", round(pval, 3), sep=""))))
}

## ----setup2,echo=FALSE,message=FALSE------------------------------------------
require(Sleuth3)
require(mosaic)
trellis.par.set(theme=col.mosaic())  # get a better color scheme
set.seed(123)
# this allows for code formatting inline.  Use \Sexpr{'function(x,y)'}, for exmaple.
knit_hooks$set(inline = function(x) {
if (is.numeric(x)) return(knitr:::format_sci(x, 'latex'))
x = as.character(x)
h = knitr:::hilight_source(x, 'latex', list(prompt=FALSE, size='normalsize'))
h = gsub("([_#$%&])", "\\\\\\1", h)
h = gsub('(["\'])', '\\1{}', h)
gsub('^\\\\begin\\{alltt\\}\\s*|\\\\end\\{alltt\\}\\s*$', '', h)
})
showOriginal=FALSE
showNew=TRUE

## ----install_mosaic,eval=FALSE------------------------------------------------
#  install.packages('mosaic')               # note the quotation marks

## ----load_mosaic,eval=FALSE---------------------------------------------------
#  require(mosaic)

## ----install_Sleuth3,eval=FALSE-----------------------------------------------
#  install.packages('Sleuth3')               # note the quotation marks

## ----load_Sleuth3,eval=FALSE--------------------------------------------------
#  require(Sleuth3)

## ----eval=TRUE----------------------------------------------------------------
trellis.par.set(theme=col.mosaic())  # get a better color scheme for lattice
options(digits=3, show.signif.stars=FALSE)

## -----------------------------------------------------------------------------
summary(case0201)
fav = favstats(Depth ~ Year, data=case0201); fav

## -----------------------------------------------------------------------------
bwplot(Year ~ Depth, data=case0201)

## -----------------------------------------------------------------------------
densityplot(~ Depth, groups=Year, auto.key=TRUE, data=case0201)

## -----------------------------------------------------------------------------
# Calculate Pooled SD
n1 = fav["1976", "n"]; n1
n2 = fav["1978", "n"]; n2
s1 = fav["1976", "sd"]; s1
s2 = fav["1978", "sd"]; s2
Sp = sqrt(((n1-1)*(s1)^2+(n2-1)*(s2)^2)/(n1+n2-2)); Sp
# Calculate standard error
SE = Sp*sqrt(1/n1+1/n2); SE

## -----------------------------------------------------------------------------
Y1 = fav["1976", "mean"]; Y1
Y2 = fav["1978", "mean"]; Y2
Yd = Y2-Y1; Yd
df = n1+n2-2; df
qt = qt(0.975, df); qt
hw = qt*SE; hw
lower = Yd-hw; lower
upper = Yd+hw; upper

## -----------------------------------------------------------------------------
tstats = (Yd-0)/SE; tstats      # The hypothesis difference=0
onepval = 1-pt(tstats, df); onepval
twopval = 2*onepval; twopval

## -----------------------------------------------------------------------------
t.test(Depth ~ Year, var.equal=TRUE, data=case0201)
confint(lm(Depth ~ Year, data=case0201))

## -----------------------------------------------------------------------------
summary(case0202)

## ----transform----------------------------------------------------------------
case0202 = transform(case0202, DIFF = Unaffected - Affected)
favstats(~ DIFF, data=case0202)

## -----------------------------------------------------------------------------
densityplot(~ DIFF, data=case0202)

## -----------------------------------------------------------------------------
# Calculate t-statistics
difmean = mean(~ DIFF, data=case0202); difmean
difsd = sd(~ DIFF, data=case0202); difsd
difn = nrow(case0202); difn
difSE = difsd/sqrt(difn); difSE
tscore = (difmean-0)/difSE; tscore         # hypothesis difference=0
twopvalue = 2*(1-pt(tscore, difn-1)); twopvalue
# Construct confidence interval
tstar = qt(0.975, difn-1); tstar
schizolower = difmean - tstar*difSE; schizolower
schizoupper = difmean + tstar*difSE; schizoupper

## -----------------------------------------------------------------------------
with(case0202, t.test(Unaffected, Affected, paired=TRUE))