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inst/app_twosampt/global.R
In ABACUS: Apps Based Activities for Communicating and Understanding Statistics
# Hypothesis Testing of Means: Two Samples, Unknown Equal Variance
# Global code for Two-sample t-test
library(shiny)
library(ggplot2)
#_________________________________________________________________________________________
# Function to fit Model
fn_InputData <- function(pmean1, pmean2,
psd, n1, n2, p, p_tail){
xrs1 <- round(rnorm(n = n1, mean = pmean1, sd = psd), digits = 1)
smean1 <- round(mean(xrs1, na.rm = TRUE), 2)
ssd1 <- round(sd(xrs1, na.rm = TRUE), 2)
sse1 <- round(ssd1 / sqrt(n1), 2)
xrs2 <- round(rnorm(n = n2, mean = pmean2, sd = psd), digits = 1)
smean2 <- round(mean(xrs2, na.rm = TRUE), 2)
ssd2 <- round(sd(xrs2, na.rm = TRUE), 2)
sse2 <- round(ssd2 / sqrt(n2), 2)
gr <- c(rep(x = 'Group 1', length = n1), rep(x = 'Group 2', length = n2))
sDF <- data.frame(Group = gr, xrs = c(xrs1, xrs2)) # density not required
sstat <- data.frame(Group = c('Group 1', 'Group 2'),
n = c(n1, n2),
pmean = c(pmean1, pmean2),
psd = c(psd, psd),
smean = c(smean1, smean2),
ssd = c(ssd1, ssd2),
sse = c(sse1, sse2))
sstat$lower <- sstat$smean - 1.96*sstat$sse
sstat$upper <- sstat$smean + 1.96*sstat$sse
alt <- switch(p_tail,
'lower' = 'less',
'upper' = 'greater',
'both' = 'two.sided')
fm <- t.test(xrs ~ Group, data = sDF,
alternative = alt,
mu = 0, paired = FALSE,
var.equal = TRUE,
conf.level = 0.95)
tcal <- unname(round(fm$statistic, digits = 4))
df1 <- unname(fm$parameter)
pcal <- round(fm$p.value, digits = 4)
sed <- round(fm$stderr, digits = 4)
mean_diff <- round((smean1 - smean2), digits = 2)
ci_mean_diff <- round(fm$conf.int, digits = 2)
xmin <- min(pmean1 - 3.5*psd, pmean2 - 3.5*psd)
xmax <- max(pmean1 + 3.5*psd, pmean2 + 3.5*psd)
norm_xlim <- c(xmin, xmax)
tr <- rt(n = 10000, df = df1)
t_xlim <- c(min(tr), max(tr))
rm(tr)
q_out <- switch(EXPR = p_tail,
lower = qt(p = p, df = df1, lower.tail = TRUE),
upper = qt(p = p, df = df1, lower.tail = FALSE),
both = c(qt(p = p/2, df = df1, lower.tail = TRUE),
qt(p = p/2, df = df1, lower.tail = FALSE)))
tstat <- c(tcal = round(tcal, 4),
df1 = round(df1, 4),
pcal = round(pcal, 4),
p = round(p, 4),
q_out = round(q_out, 4))
tail <- c(p_tail = p_tail)
if(p_tail == 'lower' | p_tail == 'upper'){
q_out_txt <- paste0('p = ', tstat['p'], '; q = ', tstat['q_out'] )
xpos1 <- tstat['q_out']
} else {
q_out_txt <- paste0('p = ', tstat['p'], '; q = ', round(q_out[1], 2), ', ', round(q_out[2], 2) )
xpos1 <- tstat['q_out2']
}
qText = q_out_txt
annotateText <- c('pText')
annotateDF <- data.frame(
xpos = c(xpos1),
ypos = c(Inf),
annotateText = c(qText),
hjustvar = c(0) ,
vjustvar = c(2)) #<- adjust
hTitle <- paste0('H0: mu1 = mu2, ; H1: mu1 <> mu2')
dTitle <- paste0( 'Population: Mean1 = ', round(pmean1,2),
', Mean2 = ', round(pmean2,2),
', SD = ', round(psd,2) )
rTitle <- paste0( 'Sample: Mean1 = ', round(smean1,2),
', SD1 = ', round(ssd1,2),
'; Mean2 = ', round(smean2,2),
', SD2 = ', round(ssd2,2) )
tTitle1 <- paste0( 'Calculated t-statistic: ',
round(tcal, 4),
', df = ', df1,
', p-value = ', round(pcal, 4) )
tTitle2 <- paste0('Mean difference = ', round(mean_diff,2),
'; 95% CI = ', ci_mean_diff[1], ', ', ci_mean_diff[2])
txtTitle <- c(hTitle = hTitle, dTitle = dTitle, rTitle = rTitle,
tTitle1 = tTitle1, tTitle2 = tTitle2)
out <- list(sDF = sDF,
sstat = sstat, tstat = tstat, tail = tail,
mean_diff = mean_diff, ci_mean_diff = ci_mean_diff,
norm_xlim = norm_xlim, t_xlim = t_xlim,
annotateDF = annotateDF,
txtTitle = txtTitle)
return(out)
}
#_________________________________________________________________________________________
# Population density: Density plot
fn_dnorm <- function(inputData){
list2env(inputData, envir = environment())
rm(inputData)
pmean1 <- sstat$pmean[1]
pmean2 <- sstat$pmean[2]
psd <- sstat$psd[1]
dTitle1 <- bquote( 'Population Mean & SD: ' ~
mu[1] == .(pmean1) ~ ', ' ~
sigma[1] == .(psd) ~ '; ' ~
mu[2] == .(pmean2) ~ ', ' ~
sigma[2] == .(psd) )
dTitle2 <- 'Rugplots represent the random samples drawn from two populations'
g <- ggplot(data = NULL, mapping = aes(norm_xlim))
g <- g + geom_area(stat = 'function', fun = dnorm,
args = list(mean = pmean1, sd = psd),
xlim = norm_xlim, fill = '#F8766D', alpha = 0.3)
g <- g + geom_area(stat = 'function', fun = dnorm,
args = list(mean = pmean2, sd = psd),
xlim = norm_xlim, fill = '#00BFC4', alpha = 0.3)
g <- g + geom_rug(data = sDF[(sDF$Group == 'Group 1'),],
mapping = aes(x = xrs),
colour = '#F8766D', sides = 'b')
g <- g + geom_rug(data = sDF[(sDF$Group == 'Group 2'),],
mapping = aes(x = xrs),
colour = '#00BFC4', sides = 'b')
g <- g + geom_vline(xintercept = pmean1, size = 1, linetype = 2, colour = 'darkred')
g <- g + geom_vline(xintercept = pmean2, size = 1, linetype = 2, colour = 'blue')
g <- g + labs(title = dTitle1, subtitle = dTitle2,
x = 'Populations: X (unit)', y = 'Density')
xscale <- seq(from = norm_xlim[1], to = norm_xlim[2], length.out = 21)
xscale <- round(xscale, digits = 1)
g <- g + scale_x_continuous(breaks = xscale, limits = norm_xlim)
g <- g + theme_bw()
g <- g + theme(axis.text.x = element_text(face = 'plain', color = 'blue',
size = 14, angle = 0),
axis.text.y = element_text(face = 'plain', color = 'blue',
size = 14, angle = 90, vjust = 0.5),
axis.title.x = element_text(size = 16, colour = 'purple'),
axis.title.y = element_text(size = 16, colour = 'purple'),
title = element_text(face = 'plain', color = 'blue',
size = 16, angle = 0))
print(g)
}
#_________________________________________________________________________________________
# Sample distribution: dotplot
fn_dotplot <- function(inputData){
list2env(inputData, envir = environment())
rm(inputData)
type <- 'density'
xmean1 <- sstat$smean[1]
xmean2 <- sstat$smean[2]
xsd1 <- sstat$ssd[1]
xsd2 <- sstat$ssd[2]
rTitle <- bquote( 'Sample Mean & SD: ' ~
bar(x[1]) == .(round(xmean1,2)) ~ ', ' ~
s[1] == .(round(xsd1,2)) ~ '; ' ~
bar(x[2]) == .(round(xmean2,2)) ~ ', ' ~
s[2] == .(round(xsd2,2)) )
xmean <- mean(sDF$xrs, na.rm = TRUE)
scale_factor <- (norm_xlim[2] - norm_xlim[1])/100
g <- ggplot(data = sDF, aes(x = xrs, fill = Group))
g <- g + labs(title = rTitle, x = 'Variable (unit)')
g <- g + geom_dotplot(method = 'dotdensity',
binwidth = scale_factor, # dotsize = 0.3,
stackdir = 'center', stackratio = 0.9, alpha = 0.7)
g <- g + scale_y_continuous(NULL, breaks = NULL)
g <- g + geom_rug(mapping = aes(colour = Group))
g <- g + geom_vline(xintercept = xmean, size = 1, linetype = 1, colour = 'purple')
g <- g + geom_vline(xintercept = xmean1, size = 1, linetype = 2, colour = 'darkred')
g <- g + geom_vline(xintercept = xmean2, size = 1, linetype = 2, colour = 'blue')
g <- g + theme_bw()
g <- g + theme(axis.text.x = element_text(face = 'plain', color = 'blue',
size = 14, angle = 0),
axis.text.y = element_text(face = 'plain', color = 'blue',
size = 14, angle = 90, vjust = 0.5),
axis.title.x = element_text(size = 16, colour = 'purple'),
axis.title.y = element_text(size = 16, colour = 'purple'),
title = element_text(face = 'plain', color = 'blue',
size = 16, angle = 0))
g <- g + theme(legend.position = 'bottom')
print(g)
}
#_________________________________________________________________________________________
# Sample distribution: boxplot
fn_boxplot <- function(inputData){
list2env(inputData, envir = environment())
rm(inputData)
xmean1 <- sstat$smean[1]
xmean2 <- sstat$smean[2]
xsd1 <- sstat$ssd[1]
xsd2 <- sstat$ssd[2]
rTitle <- bquote( 'Sample Mean & SD: ' ~
bar(x[1]) == .(round(xmean1,2)) ~ ', ' ~
s[1] == .(round(xsd1,2)) ~ '; ' ~
bar(x[2]) == .(round(xmean2,2)) ~ ', ' ~
s[2] == .(round(xsd2,2)) )
xmean <- mean(sDF$xrs, na.rm = TRUE)
g <- ggplot(data = sDF, aes(x = Group, y = xrs, fill = Group))
g <- g + geom_boxplot(mapping = aes(colour = factor(Group), fill = factor(Group)),
alpha = 0.4, size = 1.0)
g <- g + geom_jitter(mapping=aes(fill = factor(Group)),
width = 0.25, height = 0.001,
shape = 21, size=10, alpha = 0.7)
g <- g + geom_rug(mapping = aes(colour = factor(Group)), sides = 'b')
g <- g + geom_hline(yintercept = xmean, size = 1, linetype = 1, colour = 'purple')
g <- g + geom_hline(yintercept = xmean1, size = 1, linetype = 2, colour = 'darkred')
g <- g + geom_hline(yintercept = xmean2, size = 1, linetype = 2, colour = 'blue')
g <- g + labs(title = rTitle, x = 'Group', y = 'Variable (unit)')
yscale <- seq(from = norm_xlim[1], to = norm_xlim[2], length.out = 21)
yscale <- round(yscale, digits = 1)
g <- g + scale_y_continuous(breaks = yscale, limits = norm_xlim)
g <- g + coord_flip()
g <- g + theme_bw()
g <- g + theme(axis.text.x = element_text(face = 'plain', color = 'blue',
size = 14, angle = 0),
axis.text.y = element_text(face = 'plain', color = 'blue',
size = 14, angle = 90, vjust = 0.5),
axis.title.x = element_text(size = 16, colour = 'purple'),
axis.title.y = element_text(size = 16, colour = 'purple'),
title = element_text(face = 'plain', color = 'blue',
size = 16, angle = 0))
g <- g + theme(legend.position = 'none')
print(g)
}
#_________________________________________________________________________________________
# Standard t Density: Plot1 with Type 1 error
fn_dt_plot1 <- function(inputData){
list2env(inputData, envir = environment())
rm(inputData)
p_tail <- unname(tail['p_tail'])
q_tail <- unname(tail['q_tail'])
p <- unname(tstat['p'])
if(p_tail == 'both'){
q_out <- unname(c(tstat['q_out1'], tstat['q_out2']))
} else {
q_out <- unname(tstat['q_out'])
}
tcal <- unname(tstat['tcal'])
df1 <- unname(tstat['df1'])
hTitle <- bquote(H[0] ~ ':' ~ mu[1] == mu[2] ~ '; ' ~ H[A] ~ ':' ~ mu[1] != mu[2])
tTitle1 <- unname(txtTitle['tTitle1'])
g <- ggplot(data = NULL, mapping = aes(t_xlim))
# p-value
if(p_tail == 'lower'){
t_xlim1 <- c(t_xlim[1], q_out)
t_xlim2 <- c(q_out, t_xlim[2])
g <- g + geom_area(stat = 'function', fun = dt,
args = list(df = df1), colour = 'darkred',
xlim = t_xlim1, fill = '#ff0000', alpha = 0.5)
g <- g + geom_area(stat = 'function', fun = dt,
args = list(df = df1), colour = 'darkred',
xlim = t_xlim2, fill = '#ffff00', alpha = 0.7)
g <- g + geom_vline(xintercept = q_out, size = 1, linetype = 2, colour = 'orange')
}
if(p_tail == 'upper'){
t_xlim1 <- c(t_xlim[1], q_out)
t_xlim2 <- c(q_out, t_xlim[2])
g <- g + geom_area(stat = 'function', fun = dt,
args = list(df = df1), colour = 'darkred',
xlim = t_xlim1, fill = '#ffff00', alpha = 0.7)
g <- g + geom_area(stat = 'function', fun = dt,
args = list(df = df1), colour = 'darkred',
xlim = t_xlim2, fill = '#ff0000', alpha = 0.5)
g <- g + geom_vline(xintercept = q_out, size = 1, linetype = 2, colour = 'orange')
}
if(p_tail == 'both'){
t_xlim1 <- c(t_xlim[1], q_out[1])
t_xlim2 <- c(q_out[1], q_out[2])
t_xlim3 <- c(q_out[2], t_xlim[2])
g <- g + geom_area(stat = 'function', fun = dt,
args = list(df = df1), colour = 'darkred',
xlim = t_xlim1, fill = '#ff0000', alpha = 0.5)
g <- g + geom_area(stat = 'function', fun = dt,
args = list(df = df1), colour = 'darkred',
xlim = t_xlim2, fill = '#ffff00', alpha = 0.7)
g <- g + geom_area(stat = 'function', fun = dt,
args = list(df = df1), colour = 'darkred',
xlim = t_xlim3, fill = '#ff0000', alpha = 0.5)
g <- g + geom_vline(xintercept = q_out[1], size = 1, linetype = 2, colour = 'orange')
g <- g + geom_vline(xintercept = q_out[2], size = 1, linetype = 2, colour = 'orange')
}
g <- g + geom_vline(xintercept = tcal, size = 2, linetype = 1, colour = 'red')
g <- g + labs(title = hTitle, subtitle = tTitle1, x = 'Test Statistic: t', y = 'Density')
g <- g + geom_text(data = annotateDF[1,],
aes(x = xpos, y = ypos,
hjust = hjustvar, vjust = vjustvar,
label = annotateText),
colour = c('blue'), size = 4)
g <- g + geom_text(data = annotateDF[1,],
aes(x = xpos, y = ypos,
hjust = hjustvar, vjust = vjustvar,
label = annotateText),
colour = c('blue'), size = 4)
g <- g + theme_bw()
g <- g + theme(axis.text.x = element_text(face = 'plain', color = 'blue',
size = 14, angle = 0),
axis.text.y = element_text(face = 'plain', color = 'blue',
size = 14, angle = 90, vjust = 0.5),
axis.title.x = element_text(size = 16, colour = 'purple'),
axis.title.y = element_text(size = 16, colour = 'purple'),
title = element_text(face = 'plain', color = 'blue',
size = 16, angle = 0))
print(g)
}
#_________________________________________________________________________________________
# Mean & CI
fn_mean_diff <- function(inputData){
list2env(inputData, envir = environment())
rm(inputData)
tTitle2 <- unname(txtTitle['tTitle2'])
mDF <- data.frame(mean_diff = mean_diff, lower = ci_mean_diff[1], upper = ci_mean_diff[2], y = 0)
g <- ggplot(data = mDF, mapping=aes(x = mean_diff, y = y))
g <- g + geom_errorbarh(aes(xmin = lower, xmax = upper), size = 1.5, colour = '#0000cc')
g <- g + geom_point(size = 20, shape = 15, colour = '#ff9966')
g <- g + labs(title = '', subtitle = tTitle2,
x = 'Mean difference & 95% CI: Mean1 - Mean2 (unit)', y = NULL)
g <- g + scale_y_continuous(expand = c(0,0))
g <- g + geom_vline(xintercept = 0, size = 1.5, linetype = 1, colour = 'orange')
g <- g + theme_bw()
g <- g + theme(axis.text.x = element_text(face = 'plain', color = 'blue',
size = 14, angle = 0),
axis.title.x = element_text(size = 16, colour = 'purple'),
title = element_text(face = 'plain', color = 'blue',
size = 16, angle = 0),
axis.title.y = element_blank(),
axis.text.y = element_blank(),
axis.ticks.y = element_blank(),
axis.ticks.length = unit(0, "pt"),
axis.line = element_blank(),
panel.grid.major = element_blank(), panel.grid.minor = element_blank())
print(g)
}
#_________________________________________________________________________________________
# Report preparation
fn_Report <- function(inputData){
list2env(inputData, envir = environment())
rm(inputData)
p_tail <- unname(tail['p_tail'])
txtH <- switch(EXPR = p_tail,
lower = paste0("Hypothesis:
H<sub>0</sub>: μ <sub>1</sub> = μ <sub>2</sub>
H<sub>1</sub>: μ <sub>1</sub> - μ <sub>2</sub> < 0"),
upper = paste0("Hypothesis:
H<sub>0</sub>: μ <sub>1</sub> = μ <sub>2</sub>
H<sub>1</sub>: μ <sub>1</sub> - μ <sub>2</sub> > 0"),
both = ("Hypothesis:
H<sub>0</sub>: μ <sub>1</sub> = μ <sub>2</sub>
H<sub>1</sub>: μ <sub>1</sub> ≠ μ <sub>2</sub>") )
H <- tags$h3(HTML(txtH), style="color:blue")
pval <- paste0('Probability = ', tstat['p'], '; Tail: ', unname(tail))
names(sDF) <- c('Group', 'X')
sDF$SampleID <- 1:nrow(sDF)
sDF <- sDF[, c('SampleID', 'Group', 'X')]
sstat <- sstat[, 1:7]
names(sstat) <- c('Group', 'N', 'Population Mean', 'Population SD', 'Sample Mean', 'Sample SD', 'SE')
tstat <- as.data.frame(t(tstat))
tstat <- tstat[,1:5]
tstat[,5] <- abs(tstat[,5]) # only take absolute Tabulated t
tstat$tcal = sprintf('%.4f', tstat$tcal)
tstat$pcal= sprintf('%1.4f', tstat$pcal)
names(tstat) <- c('Cal t', 'DF', 'Pr(>|t|)', 'Type 1 Error', 'Tabulated |t|')
txtCI <- paste0('Mean difference & 95% CI: ', mean_diff,
' (', ci_mean_diff[1], ', ', ci_mean_diff[2], ')')
txtCI <- h4(HTML(txtCI), style="color:blue")
rpt <- list(H = H, sDF = sDF, sstat = sstat, tstat = tstat, txtCI = txtCI)
}
#_________________________________________________________________________________________
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# Hypothesis Testing of Means: Two Samples, Unknown Equal Variance
# Global code for Two-sample t-test
library(shiny)
library(ggplot2)
#_________________________________________________________________________________________
# Function to fit Model
fn_InputData <- function(pmean1, pmean2,
psd, n1, n2, p, p_tail){
xrs1 <- round(rnorm(n = n1, mean = pmean1, sd = psd), digits = 1)
smean1 <- round(mean(xrs1, na.rm = TRUE), 2)
ssd1 <- round(sd(xrs1, na.rm = TRUE), 2)
sse1 <- round(ssd1 / sqrt(n1), 2)
xrs2 <- round(rnorm(n = n2, mean = pmean2, sd = psd), digits = 1)
smean2 <- round(mean(xrs2, na.rm = TRUE), 2)
ssd2 <- round(sd(xrs2, na.rm = TRUE), 2)
sse2 <- round(ssd2 / sqrt(n2), 2)
gr <- c(rep(x = 'Group 1', length = n1), rep(x = 'Group 2', length = n2))
sDF <- data.frame(Group = gr, xrs = c(xrs1, xrs2)) # density not required
sstat <- data.frame(Group = c('Group 1', 'Group 2'),
n = c(n1, n2),
pmean = c(pmean1, pmean2),
psd = c(psd, psd),
smean = c(smean1, smean2),
ssd = c(ssd1, ssd2),
sse = c(sse1, sse2))
sstat$lower <- sstat$smean - 1.96*sstat$sse
sstat$upper <- sstat$smean + 1.96*sstat$sse
alt <- switch(p_tail,
'lower' = 'less',
'upper' = 'greater',
'both' = 'two.sided')
fm <- t.test(xrs ~ Group, data = sDF,
alternative = alt,
mu = 0, paired = FALSE,
var.equal = TRUE,
conf.level = 0.95)
tcal <- unname(round(fm$statistic, digits = 4))
df1 <- unname(fm$parameter)
pcal <- round(fm$p.value, digits = 4)
sed <- round(fm$stderr, digits = 4)
mean_diff <- round((smean1 - smean2), digits = 2)
ci_mean_diff <- round(fm$conf.int, digits = 2)
xmin <- min(pmean1 - 3.5*psd, pmean2 - 3.5*psd)
xmax <- max(pmean1 + 3.5*psd, pmean2 + 3.5*psd)
norm_xlim <- c(xmin, xmax)
tr <- rt(n = 10000, df = df1)
t_xlim <- c(min(tr), max(tr))
rm(tr)
q_out <- switch(EXPR = p_tail,
lower = qt(p = p, df = df1, lower.tail = TRUE),
upper = qt(p = p, df = df1, lower.tail = FALSE),
both = c(qt(p = p/2, df = df1, lower.tail = TRUE),
qt(p = p/2, df = df1, lower.tail = FALSE)))
tstat <- c(tcal = round(tcal, 4),
df1 = round(df1, 4),
pcal = round(pcal, 4),
p = round(p, 4),
q_out = round(q_out, 4))
tail <- c(p_tail = p_tail)
if(p_tail == 'lower' | p_tail == 'upper'){
q_out_txt <- paste0('p = ', tstat['p'], '; q = ', tstat['q_out'] )
xpos1 <- tstat['q_out']
} else {
q_out_txt <- paste0('p = ', tstat['p'], '; q = ', round(q_out[1], 2), ', ', round(q_out[2], 2) )
xpos1 <- tstat['q_out2']
}
qText = q_out_txt
annotateText <- c('pText')
annotateDF <- data.frame(
xpos = c(xpos1),
ypos = c(Inf),
annotateText = c(qText),
hjustvar = c(0) ,
vjustvar = c(2)) #<- adjust
hTitle <- paste0('H0: mu1 = mu2, ; H1: mu1 <> mu2')
dTitle <- paste0( 'Population: Mean1 = ', round(pmean1,2),
', Mean2 = ', round(pmean2,2),
', SD = ', round(psd,2) )
rTitle <- paste0( 'Sample: Mean1 = ', round(smean1,2),
', SD1 = ', round(ssd1,2),
'; Mean2 = ', round(smean2,2),
', SD2 = ', round(ssd2,2) )
tTitle1 <- paste0( 'Calculated t-statistic: ',
round(tcal, 4),
', df = ', df1,
', p-value = ', round(pcal, 4) )
tTitle2 <- paste0('Mean difference = ', round(mean_diff,2),
'; 95% CI = ', ci_mean_diff[1], ', ', ci_mean_diff[2])
txtTitle <- c(hTitle = hTitle, dTitle = dTitle, rTitle = rTitle,
tTitle1 = tTitle1, tTitle2 = tTitle2)
out <- list(sDF = sDF,
sstat = sstat, tstat = tstat, tail = tail,
mean_diff = mean_diff, ci_mean_diff = ci_mean_diff,
norm_xlim = norm_xlim, t_xlim = t_xlim,
annotateDF = annotateDF,
txtTitle = txtTitle)
return(out)
}
#_________________________________________________________________________________________
# Population density: Density plot
fn_dnorm <- function(inputData){
list2env(inputData, envir = environment())
rm(inputData)
pmean1 <- sstat$pmean[1]
pmean2 <- sstat$pmean[2]
psd <- sstat$psd[1]
dTitle1 <- bquote( 'Population Mean & SD: ' ~
mu[1] == .(pmean1) ~ ', ' ~
sigma[1] == .(psd) ~ '; ' ~
mu[2] == .(pmean2) ~ ', ' ~
sigma[2] == .(psd) )
dTitle2 <- 'Rugplots represent the random samples drawn from two populations'
g <- ggplot(data = NULL, mapping = aes(norm_xlim))
g <- g + geom_area(stat = 'function', fun = dnorm,
args = list(mean = pmean1, sd = psd),
xlim = norm_xlim, fill = '#F8766D', alpha = 0.3)
g <- g + geom_area(stat = 'function', fun = dnorm,
args = list(mean = pmean2, sd = psd),
xlim = norm_xlim, fill = '#00BFC4', alpha = 0.3)
g <- g + geom_rug(data = sDF[(sDF$Group == 'Group 1'),],
mapping = aes(x = xrs),
colour = '#F8766D', sides = 'b')
g <- g + geom_rug(data = sDF[(sDF$Group == 'Group 2'),],
mapping = aes(x = xrs),
colour = '#00BFC4', sides = 'b')
g <- g + geom_vline(xintercept = pmean1, size = 1, linetype = 2, colour = 'darkred')
g <- g + geom_vline(xintercept = pmean2, size = 1, linetype = 2, colour = 'blue')
g <- g + labs(title = dTitle1, subtitle = dTitle2,
x = 'Populations: X (unit)', y = 'Density')
xscale <- seq(from = norm_xlim[1], to = norm_xlim[2], length.out = 21)
xscale <- round(xscale, digits = 1)
g <- g + scale_x_continuous(breaks = xscale, limits = norm_xlim)
g <- g + theme_bw()
g <- g + theme(axis.text.x = element_text(face = 'plain', color = 'blue',
size = 14, angle = 0),
axis.text.y = element_text(face = 'plain', color = 'blue',
size = 14, angle = 90, vjust = 0.5),
axis.title.x = element_text(size = 16, colour = 'purple'),
axis.title.y = element_text(size = 16, colour = 'purple'),
title = element_text(face = 'plain', color = 'blue',
size = 16, angle = 0))
print(g)
}
#_________________________________________________________________________________________
# Sample distribution: dotplot
fn_dotplot <- function(inputData){
list2env(inputData, envir = environment())
rm(inputData)
type <- 'density'
xmean1 <- sstat$smean[1]
xmean2 <- sstat$smean[2]
xsd1 <- sstat$ssd[1]
xsd2 <- sstat$ssd[2]
rTitle <- bquote( 'Sample Mean & SD: ' ~
bar(x[1]) == .(round(xmean1,2)) ~ ', ' ~
s[1] == .(round(xsd1,2)) ~ '; ' ~
bar(x[2]) == .(round(xmean2,2)) ~ ', ' ~
s[2] == .(round(xsd2,2)) )
xmean <- mean(sDF$xrs, na.rm = TRUE)
scale_factor <- (norm_xlim[2] - norm_xlim[1])/100
g <- ggplot(data = sDF, aes(x = xrs, fill = Group))
g <- g + labs(title = rTitle, x = 'Variable (unit)')
g <- g + geom_dotplot(method = 'dotdensity',
binwidth = scale_factor, # dotsize = 0.3,
stackdir = 'center', stackratio = 0.9, alpha = 0.7)
g <- g + scale_y_continuous(NULL, breaks = NULL)
g <- g + geom_rug(mapping = aes(colour = Group))
g <- g + geom_vline(xintercept = xmean, size = 1, linetype = 1, colour = 'purple')
g <- g + geom_vline(xintercept = xmean1, size = 1, linetype = 2, colour = 'darkred')
g <- g + geom_vline(xintercept = xmean2, size = 1, linetype = 2, colour = 'blue')
g <- g + theme_bw()
g <- g + theme(axis.text.x = element_text(face = 'plain', color = 'blue',
size = 14, angle = 0),
axis.text.y = element_text(face = 'plain', color = 'blue',
size = 14, angle = 90, vjust = 0.5),
axis.title.x = element_text(size = 16, colour = 'purple'),
axis.title.y = element_text(size = 16, colour = 'purple'),
title = element_text(face = 'plain', color = 'blue',
size = 16, angle = 0))
g <- g + theme(legend.position = 'bottom')
print(g)
}
#_________________________________________________________________________________________
# Sample distribution: boxplot
fn_boxplot <- function(inputData){
list2env(inputData, envir = environment())
rm(inputData)
xmean1 <- sstat$smean[1]
xmean2 <- sstat$smean[2]
xsd1 <- sstat$ssd[1]
xsd2 <- sstat$ssd[2]
rTitle <- bquote( 'Sample Mean & SD: ' ~
bar(x[1]) == .(round(xmean1,2)) ~ ', ' ~
s[1] == .(round(xsd1,2)) ~ '; ' ~
bar(x[2]) == .(round(xmean2,2)) ~ ', ' ~
s[2] == .(round(xsd2,2)) )
xmean <- mean(sDF$xrs, na.rm = TRUE)
g <- ggplot(data = sDF, aes(x = Group, y = xrs, fill = Group))
g <- g + geom_boxplot(mapping = aes(colour = factor(Group), fill = factor(Group)),
alpha = 0.4, size = 1.0)
g <- g + geom_jitter(mapping=aes(fill = factor(Group)),
width = 0.25, height = 0.001,
shape = 21, size=10, alpha = 0.7)
g <- g + geom_rug(mapping = aes(colour = factor(Group)), sides = 'b')
g <- g + geom_hline(yintercept = xmean, size = 1, linetype = 1, colour = 'purple')
g <- g + geom_hline(yintercept = xmean1, size = 1, linetype = 2, colour = 'darkred')
g <- g + geom_hline(yintercept = xmean2, size = 1, linetype = 2, colour = 'blue')
g <- g + labs(title = rTitle, x = 'Group', y = 'Variable (unit)')
yscale <- seq(from = norm_xlim[1], to = norm_xlim[2], length.out = 21)
yscale <- round(yscale, digits = 1)
g <- g + scale_y_continuous(breaks = yscale, limits = norm_xlim)
g <- g + coord_flip()
g <- g + theme_bw()
g <- g + theme(axis.text.x = element_text(face = 'plain', color = 'blue',
size = 14, angle = 0),
axis.text.y = element_text(face = 'plain', color = 'blue',
size = 14, angle = 90, vjust = 0.5),
axis.title.x = element_text(size = 16, colour = 'purple'),
axis.title.y = element_text(size = 16, colour = 'purple'),
title = element_text(face = 'plain', color = 'blue',
size = 16, angle = 0))
g <- g + theme(legend.position = 'none')
print(g)
}
#_________________________________________________________________________________________
# Standard t Density: Plot1 with Type 1 error
fn_dt_plot1 <- function(inputData){
list2env(inputData, envir = environment())
rm(inputData)
p_tail <- unname(tail['p_tail'])
q_tail <- unname(tail['q_tail'])
p <- unname(tstat['p'])
if(p_tail == 'both'){
q_out <- unname(c(tstat['q_out1'], tstat['q_out2']))
} else {
q_out <- unname(tstat['q_out'])
}
tcal <- unname(tstat['tcal'])
df1 <- unname(tstat['df1'])
hTitle <- bquote(H[0] ~ ':' ~ mu[1] == mu[2] ~ '; ' ~ H[A] ~ ':' ~ mu[1] != mu[2])
tTitle1 <- unname(txtTitle['tTitle1'])
g <- ggplot(data = NULL, mapping = aes(t_xlim))
# p-value
if(p_tail == 'lower'){
t_xlim1 <- c(t_xlim[1], q_out)
t_xlim2 <- c(q_out, t_xlim[2])
g <- g + geom_area(stat = 'function', fun = dt,
args = list(df = df1), colour = 'darkred',
xlim = t_xlim1, fill = '#ff0000', alpha = 0.5)
g <- g + geom_area(stat = 'function', fun = dt,
args = list(df = df1), colour = 'darkred',
xlim = t_xlim2, fill = '#ffff00', alpha = 0.7)
g <- g + geom_vline(xintercept = q_out, size = 1, linetype = 2, colour = 'orange')
}
if(p_tail == 'upper'){
t_xlim1 <- c(t_xlim[1], q_out)
t_xlim2 <- c(q_out, t_xlim[2])
g <- g + geom_area(stat = 'function', fun = dt,
args = list(df = df1), colour = 'darkred',
xlim = t_xlim1, fill = '#ffff00', alpha = 0.7)
g <- g + geom_area(stat = 'function', fun = dt,
args = list(df = df1), colour = 'darkred',
xlim = t_xlim2, fill = '#ff0000', alpha = 0.5)
g <- g + geom_vline(xintercept = q_out, size = 1, linetype = 2, colour = 'orange')
}
if(p_tail == 'both'){
t_xlim1 <- c(t_xlim[1], q_out[1])
t_xlim2 <- c(q_out[1], q_out[2])
t_xlim3 <- c(q_out[2], t_xlim[2])
g <- g + geom_area(stat = 'function', fun = dt,
args = list(df = df1), colour = 'darkred',
xlim = t_xlim1, fill = '#ff0000', alpha = 0.5)
g <- g + geom_area(stat = 'function', fun = dt,
args = list(df = df1), colour = 'darkred',
xlim = t_xlim2, fill = '#ffff00', alpha = 0.7)
g <- g + geom_area(stat = 'function', fun = dt,
args = list(df = df1), colour = 'darkred',
xlim = t_xlim3, fill = '#ff0000', alpha = 0.5)
g <- g + geom_vline(xintercept = q_out[1], size = 1, linetype = 2, colour = 'orange')
g <- g + geom_vline(xintercept = q_out[2], size = 1, linetype = 2, colour = 'orange')
}
g <- g + geom_vline(xintercept = tcal, size = 2, linetype = 1, colour = 'red')
g <- g + labs(title = hTitle, subtitle = tTitle1, x = 'Test Statistic: t', y = 'Density')
g <- g + geom_text(data = annotateDF[1,],
aes(x = xpos, y = ypos,
hjust = hjustvar, vjust = vjustvar,
label = annotateText),
colour = c('blue'), size = 4)
g <- g + geom_text(data = annotateDF[1,],
aes(x = xpos, y = ypos,
hjust = hjustvar, vjust = vjustvar,
label = annotateText),
colour = c('blue'), size = 4)
g <- g + theme_bw()
g <- g + theme(axis.text.x = element_text(face = 'plain', color = 'blue',
size = 14, angle = 0),
axis.text.y = element_text(face = 'plain', color = 'blue',
size = 14, angle = 90, vjust = 0.5),
axis.title.x = element_text(size = 16, colour = 'purple'),
axis.title.y = element_text(size = 16, colour = 'purple'),
title = element_text(face = 'plain', color = 'blue',
size = 16, angle = 0))
print(g)
}
#_________________________________________________________________________________________
# Mean & CI
fn_mean_diff <- function(inputData){
list2env(inputData, envir = environment())
rm(inputData)
tTitle2 <- unname(txtTitle['tTitle2'])
mDF <- data.frame(mean_diff = mean_diff, lower = ci_mean_diff[1], upper = ci_mean_diff[2], y = 0)
g <- ggplot(data = mDF, mapping=aes(x = mean_diff, y = y))
g <- g + geom_errorbarh(aes(xmin = lower, xmax = upper), size = 1.5, colour = '#0000cc')
g <- g + geom_point(size = 20, shape = 15, colour = '#ff9966')
g <- g + labs(title = '', subtitle = tTitle2,
x = 'Mean difference & 95% CI: Mean1 - Mean2 (unit)', y = NULL)
g <- g + scale_y_continuous(expand = c(0,0))
g <- g + geom_vline(xintercept = 0, size = 1.5, linetype = 1, colour = 'orange')
g <- g + theme_bw()
g <- g + theme(axis.text.x = element_text(face = 'plain', color = 'blue',
size = 14, angle = 0),
axis.title.x = element_text(size = 16, colour = 'purple'),
title = element_text(face = 'plain', color = 'blue',
size = 16, angle = 0),
axis.title.y = element_blank(),
axis.text.y = element_blank(),
axis.ticks.y = element_blank(),
axis.ticks.length = unit(0, "pt"),
axis.line = element_blank(),
panel.grid.major = element_blank(), panel.grid.minor = element_blank())
print(g)
}
#_________________________________________________________________________________________
# Report preparation
fn_Report <- function(inputData){
list2env(inputData, envir = environment())
rm(inputData)
p_tail <- unname(tail['p_tail'])
txtH <- switch(EXPR = p_tail,
lower = paste0("Hypothesis:
H<sub>0</sub>: μ <sub>1</sub> = μ <sub>2</sub>
H<sub>1</sub>: μ <sub>1</sub> - μ <sub>2</sub> < 0"),
upper = paste0("Hypothesis:
H<sub>0</sub>: μ <sub>1</sub> = μ <sub>2</sub>
H<sub>1</sub>: μ <sub>1</sub> - μ <sub>2</sub> > 0"),
both = ("Hypothesis:
H<sub>0</sub>: μ <sub>1</sub> = μ <sub>2</sub>
H<sub>1</sub>: μ <sub>1</sub> ≠ μ <sub>2</sub>") )
H <- tags$h3(HTML(txtH), style="color:blue")
pval <- paste0('Probability = ', tstat['p'], '; Tail: ', unname(tail))
names(sDF) <- c('Group', 'X')
sDF$SampleID <- 1:nrow(sDF)
sDF <- sDF[, c('SampleID', 'Group', 'X')]
sstat <- sstat[, 1:7]
names(sstat) <- c('Group', 'N', 'Population Mean', 'Population SD', 'Sample Mean', 'Sample SD', 'SE')
tstat <- as.data.frame(t(tstat))
tstat <- tstat[,1:5]
tstat[,5] <- abs(tstat[,5]) # only take absolute Tabulated t
tstat$tcal = sprintf('%.4f', tstat$tcal)
tstat$pcal= sprintf('%1.4f', tstat$pcal)
names(tstat) <- c('Cal t', 'DF', 'Pr(>|t|)', 'Type 1 Error', 'Tabulated |t|')
txtCI <- paste0('Mean difference & 95% CI: ', mean_diff,
' (', ci_mean_diff[1], ', ', ci_mean_diff[2], ')')
txtCI <- h4(HTML(txtCI), style="color:blue")
rpt <- list(H = H, sDF = sDF, sstat = sstat, tstat = tstat, txtCI = txtCI)
}
#_________________________________________________________________________________________
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