inst/apps/ANOVABetweenWithin/app.R
In sfcheung/lstatdemo: Demonstrations, usually shiny apps, for learning statistics
# Illustrate the idea of residual and sum of squares in one-way ANOVA
# Global variables
anova.data <- read.csv("anova.data.csv", header = TRUE, as.is=1)
gp_means <- tapply(anova.data$score, anova.data$group, mean)
g_mean <- mean(anova.data$score)
gp_f <- factor(levels(anova.data$group))
anova.data$score <- anova.data$score -
rep(gp_means, times=table(anova.data$group))
#anova.data.wide <- cast(anova.data, person ~ group, value="score")
person_def <- rep(c("Person 1", "Person 2", "Person 3", "Person 4", "Person 5"), times=4)
person_hi <- person_def[c(1:5, 5+c(1,2,3,5,4), 10+c(1,2,5,4,3), 15+c(1,2,5,3,4))]
person_lo <- person_def[c(1:5, 5+c(4,3,2,5,1), 10+c(1,4,5,2,3), 15+c(2,1,5,4,3))]
persons <- list(person_lo, person_def, person_hi)
# Initial gp_means
gp_means <- c(24,16,6,22)
n_total <- nrow(anova.data)
n_gp <- table(anova.data$group)
score_max <- max(anova.data$score)
score_min <- min(anova.data$score)
sdC_max <- 2
sdC_min <- 0
gp_means_max <- max(gp_means) + 5
gp_means_min <- 5
yAxis_max <- sdC_max*score_max + gp_means_max
yAxis_min <- sdC_max*score_min - gp_means_min
per_corr=2
# UI
ui <- fluidPage(
titlePanel("Illustrate the difference in results between one-way indepdent group ANOVA and repeated measures ANOVA"),
fluidRow(
column(12,
wellPanel(
p("This demonstration shows how repeated measures one-way ",
"ANOVA can be different from independent group one-way",
"ANOVA. The scenario has 20 scores. On the left, the ",
"indepdent group case, there are four groups of people, ",
"each with five persons.",
"Each person was measured once, resulting in four means, each ",
"with five scores.",
"On the right, the repeated measures scenario, we have ",
"exactly the same 20 scores. However, this scenario only has",
"five persons, each measured four times, again resulting in ",
"four measns."),
p("This is analogous to a situation in which we want to study",
"differences in the four years of study on a variable, say, ",
"stress. We can recruit four groups of students, from Year 1 to ",
"Year 4, and measure their stress levels. We can also recruit ",
"one group of students, and measure their stress levels once",
"every year for four years."),
p("You can change the means for each group/time, and see how ",
"the two analyses, based on exactly the same set of 20 scores",
"differ, especially in the F test of effect."),
p("You can also change the degree of correlation of the four",
"scores from a person, and see how the residual sums of squares",
"in repeated measures analysis changes."),
p("Last, you can change the within-measure variance, and see how",
"the within-person sum of squaresin the independent",
"group analysis changes.")
),
fluidRow(
column(4,
wellPanel(
p("Change the following and see how the residuals change:"),
h4("Means:"),
sliderInput('m1', "Group 1",
min=gp_means_min, max=gp_means_max, value=gp_means[1], step=1),
sliderInput('m2', "Group 2",
min=gp_means_min, max=gp_means_max, value=gp_means[2], step=1),
sliderInput('m3', "Group 3",
min=gp_means_min, max=gp_means_max, value=gp_means[3], step=1),
sliderInput('m4', "Group 4",
min=gp_means_min, max=gp_means_max, value=gp_means[4], step=1),
br(),
h4("Within-Person Correlation"),
radioButtons('per_corr',
"Select how correlated a person's scores are",
c("Low"=1, "Default"=2, "High"=3), selected=2),
h4("Within-Measure Variation"),
sliderInput('sdC',
"Increase/decrease variation within a measure by this factor",
min=sdC_min, max=sdC_max, value=1, step=.05)
)
),
column(8,
plotOutput('plot', height="800px")
)
)
)
),
fluidRow(
column(12,
wellPanel(
p("This webpage is included in the package",
a("lstatdemo",
href="https://github.com/sfcheung/lstatdemo/"),
" at GitHub.")
)
)
)
)
# Server
server <- function(input, output, session) {
output$plot <- renderPlot({
gp_means[1] <- input$m1
gp_means[2] <- input$m2
gp_means[3] <- input$m3
gp_means[4] <- input$m4
sdC <- input$sdC
per_corr <- input$per_corr
# Create the data frame
anova.data.i <- anova.data
anova.data.i$score <- sdC*anova.data.i$score +
rep(gp_means, times=n_gp)
g_mean <- mean(anova.data.i$score)
anova.data.i$person <- persons[[as.numeric(per_corr)]]
# Conduct the one-way independent group ANOVA
anova.results <- aov(score ~ group, data=anova.data.i)
anova.F <- summary(anova.results)[[1]]$F[1]
dfs <- summary(anova.results)[[1]]$Df
anova.F.p <- summary(anova.results)[[1]]$Pr[1]
SSb <- summary(anova.results)[[1]]$Sum[1]
SSw <- summary(anova.results)[[1]]$Sum[2]
dfb <- dfs[1]
dfw <- dfs[2]
F.cut <- qf(1-.05, dfb, dfw)
# Conduct the one-way repeated measures ANOVA
anova_r.results <- aov(score ~ group + Error(person/group), data=anova.data.i)
anova_r.F <- summary(anova_r.results)[[2]][[1]]$F[1]
dfs_r <- summary(anova_r.results)[[2]][[1]]$Df
anova_r.F.p <- summary(anova_r.results)[[2]][[1]]$Pr[1]
SSb_r <- summary(anova_r.results)[[2]][[1]]$Sum[1]
SSw_r <- summary(anova_r.results)[[2]][[1]]$Sum[2]
SSr_r <- summary(anova_r.results)[[1]][[1]]$Sum[1]
dfb_r <- dfs_r[1]
dfw_r <- dfs_r[2]
dfr_r <- summary(anova_r.results)[[1]][[1]]$Df
F_r.cut <- qf(1-.05, dfb_r, dfw_r)
# Set graph parameters
yMin <- min(anova.data.i$score)
yMax <- max(anova.data.i$score)
yMin <- yAxis_min
yMax <- yAxis_max
Flo <- 0
Fhi <- max(anova.F*1.25, qf(1-.0005, dfb, dfw))
FRange <- seq(Flo, Fhi, length.out=100)
Fd <- df(FRange, dfb, dfw)
FdMax <- max(Fd)
FpRange <- c(anova.F, seq(anova.F, Fhi, length.out=50), Fhi)
Fpd <- df(FpRange, dfb, dfw)
Flo_r <- 0
Fhi_r <- max(anova_r.F*1.25, qf(1-.0005, dfb_r, dfw_r))
FRange_r <- seq(Flo_r, Fhi_r, length.out=100)
Fd_r <- df(FRange_r, dfb_r, dfw_r)
FdMax_r <- max(Fd_r)
FpRange_r <- c(anova_r.F, seq(anova_r.F, Fhi_r, length.out=50), Fhi_r)
Fpd_r <- df(FpRange_r, dfb_r, dfw_r)
cexAll <- 1
cexPt <- 2
# Don't know why cex cannot control the magnification of all elements
# So used cexAll here
# Generate the plot object
par(mfrow=c(3,2))
par(mar=c(5,2,3,2))
# Plot group means
#plot(gp_f, gp_means, border="white",
# ylim=c(yMin, yMax),
# ylab="Score",
# xlab="Group",
# main=c("Group Means"), cex.axis=1.5, cex.main=1.5, cex.lab=1.5)
#points(gp_f, gp_means, cex=cexPt, pch=16)
#lines(gp_f, gp_means, col="blue", lwd=4)
#abline(h=g_mean, lty="dotted", lwd=2, col="red")
plot(gp_means,
type="o", ylim=c(yMin, yMax), axes=FALSE,
xlab="Group", ylab="Score", main="Independent Group", pch=16,
col="blue", cex=2, lwd=4, cex.axis=1.5, cex.main=1.5, cex.lab=1.5)
axis(2, at=seq(yMin, yMax, 5), cex.axis=1.5)
axis(1, at=1:4, labels=c("Group 1", "Group 2", "Group 3", "Group 4"),
cex.axis=1.5)
abline(h=g_mean, lty="dotted", lwd=2, col="red")
box()
# Plot deviation from grand mean
#plot(anova.data.i$score,
# ylim=c(yMin, yMax),
# ylab="Score",
# xlab="Case",
# pch=16, cex=cexPt,
# main=c("Deviation of Each Case from Grand Mean",
# "(Total Sum of Squares)"), cex.axis=1.5, cex.main=1.5,
# cex.lab=1.5)
#abline(h=g_mean, lty="dotted", lwd=2, col="grey")
#segments(1:n_total, g_mean, 1:n_total, anova.data.i$score, lty="dotted",
# col="red", lwd=2)
# Plot person lines
plot(anova.data.i[anova.data.i$person == "Person 1", "score"],
type="o", ylim=c(yMin, yMax), axes=FALSE,
xlab="Time", ylab="Score", main="Repeated Measures", pch=16,
col="red", cex=2, lwd=2, cex.axis=1.5, cex.main=1.5, cex.lab=1.5)
axis(2, at=seq(yMin, yMax, 5), cex.axis=1.5)
axis(1, at=1:4, labels=c("Time 1", "Time 2", "Time 3", "Time 4"),
cex.axis=1.5)
lines(1:4, anova.data.i[anova.data.i$person == "Person 2", "score"],
type="o", col="blue", cex=2, lwd=2)
lines(1:4, anova.data.i[anova.data.i$person == "Person 3", "score"],
type="o", col="darkgreen", cex=2, lwd=2)
lines(1:4, anova.data.i[anova.data.i$person == "Person 4", "score"],
type="o", col="orange", cex=2, lwd=2)
lines(1:4, anova.data.i[anova.data.i$person == "Person 5", "score"],
type="o", col="black", cex=2, lwd=2)
abline(h=g_mean, lty="dotted", lwd=2, col="red")
box()
# Plot sums of squares
anova.SS <- matrix(c(SSb, SSw), 2, 1)
rownames(anova.SS) <- c("Between", "Within")
colnames(anova.SS) <- c("SS")
barplot(anova.SS,
xlab="", ylab="",
col=c(rgb(1,0.5,0.5,.25),rgb(0.5,0.5,1,.25)),
horiz=FALSE,
main=c("Independent Group: Partition the Total Sum of Squares",
paste("(Between SS:",sprintf("%8.2f",SSb),
" / Within SS:",sprintf("%8.2f",SSw),")",
sep="")), cex.axis=1.5, cex.main=1.5, cex.lab=1.5)
legend("right", legend=rownames(anova.SS), cex=1.75,
fill=c(rgb(1,0.5,0.5,.25),rgb(0.5,0.5,1,.25)))
# Plot sums of squares
anova_r.SS <- matrix(c(SSb_r, SSw_r, SSr_r), 3, 1)
rownames(anova_r.SS) <- c("Measures", "Residual", "Person")
colnames(anova_r.SS) <- c("SS")
barplot(anova_r.SS,
xlab="", ylab="",
col=c(rgb(1,0.5,0.5,.25),rgb(0.5,0.5,1,.25),rgb(0.5,0.5,0.5,.25)),
horiz=FALSE,
main=c("Repeated Measures: Partition the Total Sum of Squares",
paste("(Measures SS:",sprintf("%8.2f",SSb_r),
" / Residual SS:",sprintf("%8.2f",SSw_r),
" / Person SS:",sprintf("%8.2f",SSr_r),")",
sep="")), cex.axis=1.5, cex.main=1.5, cex.lab=1.5)
legend("right", legend=rownames(anova_r.SS), cex=1.75,
fill=c(rgb(1,0.5,0.5,.25),rgb(0.5,0.5,1,.25),rgb(0.5,0.5,0.5,.25)))
# Plot deviation of group mean from grand mean
#plot(anova.data.i$score,
# ylim=c(yMin, yMax),
# ylab="Score",
# xlab="Case",
# pch=16, cex=cexPt,
# main=c("Deviation of Group Mean from Grand Mean",
# "(Between-Group Sum of Squares)"),
# cex.main=1.5, cex.axis=1.5, cex.lab=1.5)
#abline(h=g_mean, lty="dotted", lwd=2, col="red")
#segments(cumsum(n_gp) - n_gp + 1, gp_means, cumsum(n_gp), gp_means,
# col="black", lwd=2)
#segments(1:n_total, g_mean, 1:n_total, rep(gp_means, times=n_gp),
# col="red", lty="solid", lwd=2)
# Plot F distribution
plot(FRange,Fd,type="l",
xlab="F statistic",
ylab="",yaxt="n",
main=c("Independent Group: Theoretical distribution of F statistic",
paste("(df Between =", dfb, ", df Within =", dfw, ")",
sep="")), cex.axis=1.5, cex.lab=1.5, cex.main=1.5)
polygon(FRange,Fd,col=rgb(0,1,0,.5))
abline(v=F.cut, lwd=1, col="black", lty="dotted")
text(F.cut, FdMax,
paste("Critical value\n", sprintf("%3.2f",F.cut), sep=""),
adj=c(0.5,1), cex=1.75)
abline(v=anova.F, lwd=1, col="red")
text(anova.F, FdMax*.5, paste("Sample F\n", sprintf("%3.2f", anova.F),
"\np-value=", sprintf("%5.4f", anova.F.p),
sep=""), cex=1.75)
# Plot F distribution
plot(FRange_r,Fd_r,type="l",
xlab="F statistic",
ylab="",yaxt="n",
main=c("Repeated Measures: Theoretical distribution of F statistic",
paste("(df Measures =", dfb_r, ", df Residual =", dfw_r, ")",
sep="")), cex.axis=1.5, cex.lab=1.5, cex.main=1.5)
polygon(FRange_r,Fd_r,col=rgb(0,1,0,.5))
abline(v=F_r.cut, lwd=1, col="black", lty="dotted")
text(F_r.cut, FdMax_r,
paste("Critical value\n", sprintf("%3.2f",F_r.cut), sep=""),
adj=c(0.5,1), cex=1.75)
abline(v=anova_r.F, lwd=1, col="red")
text(anova_r.F, FdMax_r*.5, paste("Sample F\n", sprintf("%3.2f", anova_r.F),
"\np-value=", sprintf("%5.4f", anova_r.F.p),
sep=""), cex=1.75)
# Plot deviation from group mean
#plot(anova.data.i$score,
# ylim=c(yMin, yMax),
# ylab="Score",
# xlab="Case",
# pch=16, cex=cexPt,
# main=c("Deviation of Each Case from Group Mean",
# "(Within-Group Sum of Squares)"), cex.axis=1.5,
# cex.main=1.5, cex.lab=1.5)
#abline(h=g_mean, lty="dotted", lwd=2, col="red")
#segments(cumsum(n_gp) - n_gp + 1, gp_means, cumsum(n_gp), gp_means,
# col="black", lwd=2)
#segments(1:n_total, rep(gp_means, times=n_gp), 1:n_total, anova.data.i$score,
# col="blue", lty="solid", lwd=2)
})
}
shinyApp(ui=ui, server=server)
sfcheung/lstatdemo documentation built on May 2, 2020, 1:21 p.m.
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# Illustrate the idea of residual and sum of squares in one-way ANOVA
# Global variables
anova.data <- read.csv("anova.data.csv", header = TRUE, as.is=1)
gp_means <- tapply(anova.data$score, anova.data$group, mean)
g_mean <- mean(anova.data$score)
gp_f <- factor(levels(anova.data$group))
anova.data$score <- anova.data$score -
rep(gp_means, times=table(anova.data$group))
#anova.data.wide <- cast(anova.data, person ~ group, value="score")
person_def <- rep(c("Person 1", "Person 2", "Person 3", "Person 4", "Person 5"), times=4)
person_hi <- person_def[c(1:5, 5+c(1,2,3,5,4), 10+c(1,2,5,4,3), 15+c(1,2,5,3,4))]
person_lo <- person_def[c(1:5, 5+c(4,3,2,5,1), 10+c(1,4,5,2,3), 15+c(2,1,5,4,3))]
persons <- list(person_lo, person_def, person_hi)
# Initial gp_means
gp_means <- c(24,16,6,22)
n_total <- nrow(anova.data)
n_gp <- table(anova.data$group)
score_max <- max(anova.data$score)
score_min <- min(anova.data$score)
sdC_max <- 2
sdC_min <- 0
gp_means_max <- max(gp_means) + 5
gp_means_min <- 5
yAxis_max <- sdC_max*score_max + gp_means_max
yAxis_min <- sdC_max*score_min - gp_means_min
per_corr=2
# UI
ui <- fluidPage(
titlePanel("Illustrate the difference in results between one-way indepdent group ANOVA and repeated measures ANOVA"),
fluidRow(
column(12,
wellPanel(
p("This demonstration shows how repeated measures one-way ",
"ANOVA can be different from independent group one-way",
"ANOVA. The scenario has 20 scores. On the left, the ",
"indepdent group case, there are four groups of people, ",
"each with five persons.",
"Each person was measured once, resulting in four means, each ",
"with five scores.",
"On the right, the repeated measures scenario, we have ",
"exactly the same 20 scores. However, this scenario only has",
"five persons, each measured four times, again resulting in ",
"four measns."),
p("This is analogous to a situation in which we want to study",
"differences in the four years of study on a variable, say, ",
"stress. We can recruit four groups of students, from Year 1 to ",
"Year 4, and measure their stress levels. We can also recruit ",
"one group of students, and measure their stress levels once",
"every year for four years."),
p("You can change the means for each group/time, and see how ",
"the two analyses, based on exactly the same set of 20 scores",
"differ, especially in the F test of effect."),
p("You can also change the degree of correlation of the four",
"scores from a person, and see how the residual sums of squares",
"in repeated measures analysis changes."),
p("Last, you can change the within-measure variance, and see how",
"the within-person sum of squaresin the independent",
"group analysis changes.")
),
fluidRow(
column(4,
wellPanel(
p("Change the following and see how the residuals change:"),
h4("Means:"),
sliderInput('m1', "Group 1",
min=gp_means_min, max=gp_means_max, value=gp_means[1], step=1),
sliderInput('m2', "Group 2",
min=gp_means_min, max=gp_means_max, value=gp_means[2], step=1),
sliderInput('m3', "Group 3",
min=gp_means_min, max=gp_means_max, value=gp_means[3], step=1),
sliderInput('m4', "Group 4",
min=gp_means_min, max=gp_means_max, value=gp_means[4], step=1),
br(),
h4("Within-Person Correlation"),
radioButtons('per_corr',
"Select how correlated a person's scores are",
c("Low"=1, "Default"=2, "High"=3), selected=2),
h4("Within-Measure Variation"),
sliderInput('sdC',
"Increase/decrease variation within a measure by this factor",
min=sdC_min, max=sdC_max, value=1, step=.05)
)
),
column(8,
plotOutput('plot', height="800px")
)
)
)
),
fluidRow(
column(12,
wellPanel(
p("This webpage is included in the package",
a("lstatdemo",
href="https://github.com/sfcheung/lstatdemo/"),
" at GitHub.")
)
)
)
)
# Server
server <- function(input, output, session) {
output$plot <- renderPlot({
gp_means[1] <- input$m1
gp_means[2] <- input$m2
gp_means[3] <- input$m3
gp_means[4] <- input$m4
sdC <- input$sdC
per_corr <- input$per_corr
# Create the data frame
anova.data.i <- anova.data
anova.data.i$score <- sdC*anova.data.i$score +
rep(gp_means, times=n_gp)
g_mean <- mean(anova.data.i$score)
anova.data.i$person <- persons[[as.numeric(per_corr)]]
# Conduct the one-way independent group ANOVA
anova.results <- aov(score ~ group, data=anova.data.i)
anova.F <- summary(anova.results)[[1]]$F[1]
dfs <- summary(anova.results)[[1]]$Df
anova.F.p <- summary(anova.results)[[1]]$Pr[1]
SSb <- summary(anova.results)[[1]]$Sum[1]
SSw <- summary(anova.results)[[1]]$Sum[2]
dfb <- dfs[1]
dfw <- dfs[2]
F.cut <- qf(1-.05, dfb, dfw)
# Conduct the one-way repeated measures ANOVA
anova_r.results <- aov(score ~ group + Error(person/group), data=anova.data.i)
anova_r.F <- summary(anova_r.results)[[2]][[1]]$F[1]
dfs_r <- summary(anova_r.results)[[2]][[1]]$Df
anova_r.F.p <- summary(anova_r.results)[[2]][[1]]$Pr[1]
SSb_r <- summary(anova_r.results)[[2]][[1]]$Sum[1]
SSw_r <- summary(anova_r.results)[[2]][[1]]$Sum[2]
SSr_r <- summary(anova_r.results)[[1]][[1]]$Sum[1]
dfb_r <- dfs_r[1]
dfw_r <- dfs_r[2]
dfr_r <- summary(anova_r.results)[[1]][[1]]$Df
F_r.cut <- qf(1-.05, dfb_r, dfw_r)
# Set graph parameters
yMin <- min(anova.data.i$score)
yMax <- max(anova.data.i$score)
yMin <- yAxis_min
yMax <- yAxis_max
Flo <- 0
Fhi <- max(anova.F*1.25, qf(1-.0005, dfb, dfw))
FRange <- seq(Flo, Fhi, length.out=100)
Fd <- df(FRange, dfb, dfw)
FdMax <- max(Fd)
FpRange <- c(anova.F, seq(anova.F, Fhi, length.out=50), Fhi)
Fpd <- df(FpRange, dfb, dfw)
Flo_r <- 0
Fhi_r <- max(anova_r.F*1.25, qf(1-.0005, dfb_r, dfw_r))
FRange_r <- seq(Flo_r, Fhi_r, length.out=100)
Fd_r <- df(FRange_r, dfb_r, dfw_r)
FdMax_r <- max(Fd_r)
FpRange_r <- c(anova_r.F, seq(anova_r.F, Fhi_r, length.out=50), Fhi_r)
Fpd_r <- df(FpRange_r, dfb_r, dfw_r)
cexAll <- 1
cexPt <- 2
# Don't know why cex cannot control the magnification of all elements
# So used cexAll here
# Generate the plot object
par(mfrow=c(3,2))
par(mar=c(5,2,3,2))
# Plot group means
#plot(gp_f, gp_means, border="white",
# ylim=c(yMin, yMax),
# ylab="Score",
# xlab="Group",
# main=c("Group Means"), cex.axis=1.5, cex.main=1.5, cex.lab=1.5)
#points(gp_f, gp_means, cex=cexPt, pch=16)
#lines(gp_f, gp_means, col="blue", lwd=4)
#abline(h=g_mean, lty="dotted", lwd=2, col="red")
plot(gp_means,
type="o", ylim=c(yMin, yMax), axes=FALSE,
xlab="Group", ylab="Score", main="Independent Group", pch=16,
col="blue", cex=2, lwd=4, cex.axis=1.5, cex.main=1.5, cex.lab=1.5)
axis(2, at=seq(yMin, yMax, 5), cex.axis=1.5)
axis(1, at=1:4, labels=c("Group 1", "Group 2", "Group 3", "Group 4"),
cex.axis=1.5)
abline(h=g_mean, lty="dotted", lwd=2, col="red")
box()
# Plot deviation from grand mean
#plot(anova.data.i$score,
# ylim=c(yMin, yMax),
# ylab="Score",
# xlab="Case",
# pch=16, cex=cexPt,
# main=c("Deviation of Each Case from Grand Mean",
# "(Total Sum of Squares)"), cex.axis=1.5, cex.main=1.5,
# cex.lab=1.5)
#abline(h=g_mean, lty="dotted", lwd=2, col="grey")
#segments(1:n_total, g_mean, 1:n_total, anova.data.i$score, lty="dotted",
# col="red", lwd=2)
# Plot person lines
plot(anova.data.i[anova.data.i$person == "Person 1", "score"],
type="o", ylim=c(yMin, yMax), axes=FALSE,
xlab="Time", ylab="Score", main="Repeated Measures", pch=16,
col="red", cex=2, lwd=2, cex.axis=1.5, cex.main=1.5, cex.lab=1.5)
axis(2, at=seq(yMin, yMax, 5), cex.axis=1.5)
axis(1, at=1:4, labels=c("Time 1", "Time 2", "Time 3", "Time 4"),
cex.axis=1.5)
lines(1:4, anova.data.i[anova.data.i$person == "Person 2", "score"],
type="o", col="blue", cex=2, lwd=2)
lines(1:4, anova.data.i[anova.data.i$person == "Person 3", "score"],
type="o", col="darkgreen", cex=2, lwd=2)
lines(1:4, anova.data.i[anova.data.i$person == "Person 4", "score"],
type="o", col="orange", cex=2, lwd=2)
lines(1:4, anova.data.i[anova.data.i$person == "Person 5", "score"],
type="o", col="black", cex=2, lwd=2)
abline(h=g_mean, lty="dotted", lwd=2, col="red")
box()
# Plot sums of squares
anova.SS <- matrix(c(SSb, SSw), 2, 1)
rownames(anova.SS) <- c("Between", "Within")
colnames(anova.SS) <- c("SS")
barplot(anova.SS,
xlab="", ylab="",
col=c(rgb(1,0.5,0.5,.25),rgb(0.5,0.5,1,.25)),
horiz=FALSE,
main=c("Independent Group: Partition the Total Sum of Squares",
paste("(Between SS:",sprintf("%8.2f",SSb),
" / Within SS:",sprintf("%8.2f",SSw),")",
sep="")), cex.axis=1.5, cex.main=1.5, cex.lab=1.5)
legend("right", legend=rownames(anova.SS), cex=1.75,
fill=c(rgb(1,0.5,0.5,.25),rgb(0.5,0.5,1,.25)))
# Plot sums of squares
anova_r.SS <- matrix(c(SSb_r, SSw_r, SSr_r), 3, 1)
rownames(anova_r.SS) <- c("Measures", "Residual", "Person")
colnames(anova_r.SS) <- c("SS")
barplot(anova_r.SS,
xlab="", ylab="",
col=c(rgb(1,0.5,0.5,.25),rgb(0.5,0.5,1,.25),rgb(0.5,0.5,0.5,.25)),
horiz=FALSE,
main=c("Repeated Measures: Partition the Total Sum of Squares",
paste("(Measures SS:",sprintf("%8.2f",SSb_r),
" / Residual SS:",sprintf("%8.2f",SSw_r),
" / Person SS:",sprintf("%8.2f",SSr_r),")",
sep="")), cex.axis=1.5, cex.main=1.5, cex.lab=1.5)
legend("right", legend=rownames(anova_r.SS), cex=1.75,
fill=c(rgb(1,0.5,0.5,.25),rgb(0.5,0.5,1,.25),rgb(0.5,0.5,0.5,.25)))
# Plot deviation of group mean from grand mean
#plot(anova.data.i$score,
# ylim=c(yMin, yMax),
# ylab="Score",
# xlab="Case",
# pch=16, cex=cexPt,
# main=c("Deviation of Group Mean from Grand Mean",
# "(Between-Group Sum of Squares)"),
# cex.main=1.5, cex.axis=1.5, cex.lab=1.5)
#abline(h=g_mean, lty="dotted", lwd=2, col="red")
#segments(cumsum(n_gp) - n_gp + 1, gp_means, cumsum(n_gp), gp_means,
# col="black", lwd=2)
#segments(1:n_total, g_mean, 1:n_total, rep(gp_means, times=n_gp),
# col="red", lty="solid", lwd=2)
# Plot F distribution
plot(FRange,Fd,type="l",
xlab="F statistic",
ylab="",yaxt="n",
main=c("Independent Group: Theoretical distribution of F statistic",
paste("(df Between =", dfb, ", df Within =", dfw, ")",
sep="")), cex.axis=1.5, cex.lab=1.5, cex.main=1.5)
polygon(FRange,Fd,col=rgb(0,1,0,.5))
abline(v=F.cut, lwd=1, col="black", lty="dotted")
text(F.cut, FdMax,
paste("Critical value\n", sprintf("%3.2f",F.cut), sep=""),
adj=c(0.5,1), cex=1.75)
abline(v=anova.F, lwd=1, col="red")
text(anova.F, FdMax*.5, paste("Sample F\n", sprintf("%3.2f", anova.F),
"\np-value=", sprintf("%5.4f", anova.F.p),
sep=""), cex=1.75)
# Plot F distribution
plot(FRange_r,Fd_r,type="l",
xlab="F statistic",
ylab="",yaxt="n",
main=c("Repeated Measures: Theoretical distribution of F statistic",
paste("(df Measures =", dfb_r, ", df Residual =", dfw_r, ")",
sep="")), cex.axis=1.5, cex.lab=1.5, cex.main=1.5)
polygon(FRange_r,Fd_r,col=rgb(0,1,0,.5))
abline(v=F_r.cut, lwd=1, col="black", lty="dotted")
text(F_r.cut, FdMax_r,
paste("Critical value\n", sprintf("%3.2f",F_r.cut), sep=""),
adj=c(0.5,1), cex=1.75)
abline(v=anova_r.F, lwd=1, col="red")
text(anova_r.F, FdMax_r*.5, paste("Sample F\n", sprintf("%3.2f", anova_r.F),
"\np-value=", sprintf("%5.4f", anova_r.F.p),
sep=""), cex=1.75)
# Plot deviation from group mean
#plot(anova.data.i$score,
# ylim=c(yMin, yMax),
# ylab="Score",
# xlab="Case",
# pch=16, cex=cexPt,
# main=c("Deviation of Each Case from Group Mean",
# "(Within-Group Sum of Squares)"), cex.axis=1.5,
# cex.main=1.5, cex.lab=1.5)
#abline(h=g_mean, lty="dotted", lwd=2, col="red")
#segments(cumsum(n_gp) - n_gp + 1, gp_means, cumsum(n_gp), gp_means,
# col="black", lwd=2)
#segments(1:n_total, rep(gp_means, times=n_gp), 1:n_total, anova.data.i$score,
# col="blue", lty="solid", lwd=2)
})
}
shinyApp(ui=ui, server=server)
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