inst/shiny-apps/visualizess/app.R
In bcdudek/bcdstats: A collection of functions to support B. Dudek's APSY510/511 classes
library(shiny)
library(shinyBS)
library(ggplot2)
# Define UI for application
ui <- fluidPage(
# Application title
titlePanel("Visualize Sum of Squares and Variance"),
# Sidebar with a slider input for number of bins
sidebarLayout(
sidebarPanel(
checkboxInput("high", "Show Variable with Higher Dispersion", TRUE),
bsTooltip("null", "placeholder so that addPopover wil work",
"right", options = list(container = "body")),
# this conditional panel controls figure components for the high disperson graph
conditionalPanel(
condition= "input.high",
wellPanel(
radioButtons("highfig", "Choose plot components:",
c("Show Only the Data" = "data",
"Show the mean as a dashed line" = "mean",
"Show the deviation from the mean for the largest value" = "xdev",
"Show the same X deviation in a vertical orientation" = "xdevvert",
"Show the Square implied by X deviation 'Squared'" ="square",
"Show the Squares for all Data Points" = "squares",
"Add a square for the average, the Sample Variance" = 'variance')
) # end radiobuttons
) # end wellpanel
),
checkboxInput("low", "Show Variable with Lower Dispersion", FALSE),
# this conditional panel controls figure components for the low disperson graph
conditionalPanel(
condition= "input.low",
wellPanel(
radioButtons("lowfig", "Choose plot components:",
c("Show Only the Data" = "data",
"Show the mean as a dashed line" = "mean",
"Show the deviation from the mean for the largest value" = "xdev",
"Show the same X deviation in a vertical orientation" = "xdevvert",
"show the Square implied by X deviation 'Squared'" ="square",
"show the Squares for all Data Points" = "squares",
"Add a square for the average, the Sample Variance" = 'variance')
) # end radiobuttons
) # end wellpanel
) # end conditional panel
),
mainPanel(
tabsetPanel(
tabPanel("Plots",
fluidRow(
column(6,
#HTML("
# Hover your mouse over the plots for more information."),
h5(" Click your mouse on the plots for more information."),
plotOutput("highfigplot")
)),
fluidRow(
column(6,
br(),
plotOutput("lowfigplot")))
),#finish plottab
tabPanel("Show the Data",
HTML("High Dispersion Variable"),
tableOutput("dtable"),
tableOutput("stattable"),
br(),
HTML("Low Dispersion Variable"),
tableOutput("dtable2"),
tableOutput("stattable2")
),
tabPanel("Two Kinds of Variances",
withMathJax(),
p(h5("Visualizing the Variance.")),br(),
p("This app provides a way of visualizing the variance of a variable as a geometric entity. We define
the variance this way, as the average of areas of N squares, because the 'formula' for variance
involves a squared value. Textbook definitions of Sample Variance label it in various ways, including:
\\(S^2\\) (an upper case S), \\(SD^2\\). amd \\(VAR_X\\) "),
br(),
p("This sample variance is usally defined with this expression:
\\(\\frac{{\\sum\\limits_{i = 1}^n {({X_i} - \\bar X)^2} }}{{N}}\\)
"),
p("Expansion of the numerator permits a rewrite:
\\(\\frac{{\\sum\\limits_{i = 1}^n {({X_i} - \\bar X)({X_i} - \\bar X)} }}{{N}}\\)
"),
p("Either of these expressions make it clear that the deviation of each X value from its mean is
multiplied by itself, yielding the 'area of a geometric square'
perspective that the plots in this app emphasize. When this is done for each X value and the N quantities are summed,
that gives us the numerator of the expression. This numerator is usally give a shorthand notation of SS. This is because it is the
'sum of squared deviations from the mean'. So we can write the variance expression a third way:
\\(\\frac{{SS}}{{N}}\\)"
),
br(),
p("Students are encouraged to obtain the data values from the 'show the data' tab of this app and perform the calculations for these
expressions in Excel, or a with a calculator."),
br(),
p("Some users of this app may have been taught to compute the Variance a different way. This expression is similar to the ones above,
differing only in the denominator: \\(\\frac{{\\sum\\limits_{i = 1}^n {({X_i} - \\bar X)^2} }}{{N-1}}\\)."),
br(),
p("The numerator is still called Sum of Squares (SS), but the expression is no longer the arithmetic average of the squared deviations.
It is close, but will be slightly larger.
"),
p("This modified version of the expression is usually denoted as \\(s^2\\), with a lower case s. It is the more commonly used
variance expression. This preference is because it is an unbiased estimate of the variance in the population from which the N X scores
were randomly sampled. Although it is no longer exactly the arithmetic average of areas of squares it is close, especially for larger
sample sizes (N).
"),
p("Introductory Statistics coursework will expand on the difference in these two variance compuations.
In this app we used the first of the two versions which is typicalled the sample variance.
Since the 'area of a square' concept is related to the numerator, the distinction in the two
expressions doesn't alter they way we understand Sum of Squares.
")
),
tabPanel("About the App",
includeMarkdown('about.md')
)
)#finish tabsetpanel
)#finish mainpanel
))
# Define server logic required to draw a histogram
server <- function(input, output, session) {
#################################################################
# first for an n of five, with relatively large variance
set.seed(25)
x <-runif(5,min=82, max=118)+.9025
y <- rep(0,5)
y
xbar <- mean(x)
xdev <- x-xbar
maxxdev <- abs(max(xdev))
rangex <- max(x)-min(x)
xdevsq <- xdev^2
base <- as.data.frame(cbind(y,x,xdev))
basehigh <- as.data.frame(cbind(x,xdev,xdevsq))
colnames(basehigh) <- c("X","X Dev from Mean", "X Dev Squared")
#str(base)
#sd(x)**2
#(var(x)*4/5)**.5
SD1 <- 10.89265
SS <- (SD1**2)*5
halfsd1 <- SD1/2
sampsize <- 5
highstats <- as.data.frame(cbind(xbar, SS, SD1**2))
colnames(highstats) <- c("Mean of X","Sum of Squares", "Sample Variance")
#################################################################
# now repeat the whole thing with a smaller variance
set.seed(3)
x2 <-runif(5,min=92,max=108)
y2 <- rep(0,5)
y2
xbar2 <- mean(x2)
xdev2 <- x2-xbar2
xdevsq2 <- xdev2^2
maxxdev2 <- abs(max(xdev2))
rangex2 <- max(x2)-min(x2)
base2 <- as.data.frame(cbind(y2,x2,xdev2))
baselow <- as.data.frame(cbind(x2,xdev2,xdevsq2))
colnames(baselow) <- c("X","X Dev from Mean", "X Dev Squared")
# str(base2)
#sd(x2)**2
#(var(x2)*4/5)**.5
SD2 <- 3.572762
SS2 <- (SD2**2)*5
halfsd2 <- SD2/2
lowstats <- as.data.frame(cbind(xbar2, SS2, SD2**2))
colnames(lowstats) <- c("Mean of X","Sum of Squares", "Sample Variance")
################################################################
# plots for high dispersion data
# Basic stripchart
p <- ggplot(base, aes(x = x, y=y)) +
geom_dotplot(binwidth=.7) +
xlim(min(x), max(x)) +
ylim(0,rangex) +
labs(y=NULL) + labs(x="X") +
theme(axis.text.y = element_blank())+
theme(aspect.ratio=1)+
theme(axis.title.x=element_text(size=rel(1.3)))+
theme(axis.text.x=element_text(size=rel(1.5)))
p2 <- p + geom_vline(aes(xintercept=xbar),linetype=2)
# depict the x deviation from the mean for the largest data point
p3 <- p2 +
geom_segment(x=max(x), xend=xbar,y=0,yend=0,colour="blue")
# do the same xdeviation in the vertical orientation
p4 <- p3 +
geom_segment(x=max(x), xend=max(x),y=0,yend=maxxdev,colour="blue")
#view it as a square
p5 <- p4 +
geom_segment(x=max(x), xend=xbar, y=maxxdev, yend=maxxdev,colour="blue")+
geom_rect(xmin=mean(x),xmax=max(x), ymin=0,ymax=maxxdev,
fill="skyblue",alpha=.05)
# show all the squares
p6 <- p2 +
geom_segment(x=x, xend=xbar, y=0, yend=0,colour="blue")+ # bottom
geom_segment(x=x, xend=x,y=0,yend=abs(xdev),colour="blue")+ #side
geom_segment(x=x, xend=xbar, y=abs(xdev), yend=abs(xdev),colour="blue") + #top
geom_segment(x=xbar, xend=xbar, y=0, yend=abs(xdev),colour="blue") + #mean
geom_rect(xmin=x,xmax=xbar, ymin=0,ymax=abs(xdev),
fill="skyblue",alpha=.05)
# add a square for the average, the sample variance (SD squared)
p7 <- p6 +
geom_segment(x=xbar-halfsd1, xend=xbar+halfsd1, y=18, yend=18,colour="orange")+ # bottom
geom_segment(x=xbar-halfsd1, xend=xbar+halfsd1, y=18+SD1,yend=18+SD1,colour="orange")+ #top
geom_segment(x=xbar-halfsd1, xend=xbar-halfsd1, y=18, yend=18+SD1, colour="orange") + #left
geom_segment(x=xbar+halfsd1, xend=xbar+halfsd1, y=18, yend=18+SD1, colour="orange") + #right
geom_rect(xmin=xbar-halfsd1, xmax=xbar+halfsd1, ymin=18,ymax=18+SD1,
fill="orange",alpha=.02)
###############################################################
# low dispersion plotting
# Basic stripchart
ps <- ggplot(base2, aes(x = x2, y=y2)) +
geom_dotplot(binwidth=.7)+
xlim(min(x),max(x)) +
ylim(0,rangex) +
labs(y=NULL, x="X") +
theme(axis.text.y = element_blank())+
theme(aspect.ratio=1)+
theme(axis.title.x=element_text(size=rel(1.3)))+
theme(axis.text.x=element_text(size=rel(1.5)))
ps2 <- ps + geom_vline(aes(xintercept=xbar2),linetype=2)
# depict the x deviation from the mean for the largest data point
ps3 <- ps2 +
geom_segment(x=max(x2), xend=xbar2,y=0,yend=0,colour="blue")
# do the same xdeviation in the vertical orientation
ps4 <- ps3 +
geom_segment(x=max(x2), xend=max(x2),y=0,yend=maxxdev2,colour="blue")
#view it as a square
ps5 <- ps4 +
geom_segment(x=max(x2), xend=xbar2, y=maxxdev2, yend=maxxdev2,colour="blue")+
geom_rect(xmin=mean(x2),xmax=max(x2), ymin=0,ymax=maxxdev2,
fill="skyblue",alpha=.05)
# show all the rectangles
ps6 <- ps2 +
geom_segment(x=x2, xend=xbar2, y=0, yend=0,colour="blue")+ # bottom
geom_segment(x=x2, xend=x2,y=0,yend=abs(xdev2),colour="blue")+ #side
geom_segment(x=x2, xend=xbar2, y=abs(xdev2), yend=abs(xdev2),colour="blue") + #top
geom_segment(x=xbar2, xend=xbar2, y=0, yend=abs(xdev2),colour="blue") + #mean
geom_rect(xmin=x2,xmax=xbar2, ymin=0,ymax=abs(xdev2),
fill="skyblue",alpha=.05)
ps7 <- ps6 +
geom_segment(x=xbar2-halfsd2, xend=xbar2+halfsd2, y=18, yend=18,colour="orange")+ # bottom
geom_segment(x=xbar2-halfsd2, xend=xbar2+halfsd2, y=18+SD2,yend=18+SD2,colour="orange")+ #top
geom_segment(x=xbar2-halfsd2, xend=xbar2-halfsd2, y=18, yend=18+SD2, colour="orange") + #left
geom_segment(x=xbar2+halfsd2, xend=xbar2+halfsd2, y=18, yend=18+SD2, colour="orange") + #right
geom_rect(xmin=xbar2-halfsd2, xmax=xbar2+halfsd2, ymin=18,ymax=18+SD2,
fill="orange",alpha=.02)
##############################################################
output$highfigplot <- renderPlot(
if(input$high & input$highfig == 'data'){
p
}
else if(input$high & input$highfig == 'mean'){
p2
}
else if(input$high & input$highfig == 'xdev'){
p3
}
else if(input$high & input$highfig == 'xdevvert'){
p4
}
else if(input$high & input$highfig == 'square'){
p5
}
else if(input$high & input$highfig == 'squares'){
p6
}
else if(input$high & input$highfig == 'variance'){
p7
}
) # end renderplot
###############################################################
output$lowfigplot <- renderPlot(
if(input$low & input$lowfig == 'data'){
ps
}
else if(input$low & input$lowfig == 'mean'){
ps2
}
else if(input$low & input$lowfig == 'xdev'){
ps3
}
else if(input$low & input$lowfig == 'xdevvert'){
ps4
}
else if(input$low & input$lowfig == 'square'){
ps5
}
else if(input$low & input$lowfig == 'squares'){
ps6
}
else if(input$low & input$lowfig == 'variance'){
ps7
}
) # end renderplot
observeEvent(input$high,{
removePopover(session, 'highfigplot')
if (input$high){
addPopover(
session,
"highfigplot",
"What Does the Plot Show?",
content = "Squaring an X value deviation from its mean can be thought of as computing a
the area of a square. This figure shows those squares for all the X values.
When those areas are summed, we call it the Sum of Squares. The average of these square areas
is shown with the orange square and this average defines the Sample Variance, often denoted as S-squared or SD-squared. <BR><BR>
The user should compare the size of these squares for this 'high dispersion' variable with the 'low dispersion' variable shown
in the figure below.",
trigger = 'click',placement="left"
)
}#end if for high fig
})#end observeEvent
observeEvent(input$low,{
removePopover(session, 'lowfigplot')
if (input$low){
addPopover(
session,
"lowfigplot",
"What Does the Plot Show?",
content = "Notice in this figure, where the data points are less dispersed (closer to the mean), that
the squares are smaller and their average (orange - the variance) is considerable smaller.
<br><br>
The user should compare the size of these squares for this 'low dispersion' variable with the 'high dispersion' variable shown
in the figure above.",
trigger = 'click',placement="left"
)
}#end if for low fig
})#end observeEvent
output$dtable <- renderTable({
basehigh
})
output$dtable2 <- renderTable({
baselow
})
output$stattable <- renderTable({
highstats
})
output$stattable2 <- renderTable({
lowstats
})
}# end server
# Run the application
shinyApp(ui = ui, server = server)
bcdudek/bcdstats documentation built on Jan. 3, 2024, 10:09 p.m.
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library(shiny)
library(shinyBS)
library(ggplot2)
# Define UI for application
ui <- fluidPage(
# Application title
titlePanel("Visualize Sum of Squares and Variance"),
# Sidebar with a slider input for number of bins
sidebarLayout(
sidebarPanel(
checkboxInput("high", "Show Variable with Higher Dispersion", TRUE),
bsTooltip("null", "placeholder so that addPopover wil work",
"right", options = list(container = "body")),
# this conditional panel controls figure components for the high disperson graph
conditionalPanel(
condition= "input.high",
wellPanel(
radioButtons("highfig", "Choose plot components:",
c("Show Only the Data" = "data",
"Show the mean as a dashed line" = "mean",
"Show the deviation from the mean for the largest value" = "xdev",
"Show the same X deviation in a vertical orientation" = "xdevvert",
"Show the Square implied by X deviation 'Squared'" ="square",
"Show the Squares for all Data Points" = "squares",
"Add a square for the average, the Sample Variance" = 'variance')
) # end radiobuttons
) # end wellpanel
),
checkboxInput("low", "Show Variable with Lower Dispersion", FALSE),
# this conditional panel controls figure components for the low disperson graph
conditionalPanel(
condition= "input.low",
wellPanel(
radioButtons("lowfig", "Choose plot components:",
c("Show Only the Data" = "data",
"Show the mean as a dashed line" = "mean",
"Show the deviation from the mean for the largest value" = "xdev",
"Show the same X deviation in a vertical orientation" = "xdevvert",
"show the Square implied by X deviation 'Squared'" ="square",
"show the Squares for all Data Points" = "squares",
"Add a square for the average, the Sample Variance" = 'variance')
) # end radiobuttons
) # end wellpanel
) # end conditional panel
),
mainPanel(
tabsetPanel(
tabPanel("Plots",
fluidRow(
column(6,
#HTML("
# Hover your mouse over the plots for more information."),
h5(" Click your mouse on the plots for more information."),
plotOutput("highfigplot")
)),
fluidRow(
column(6,
br(),
plotOutput("lowfigplot")))
),#finish plottab
tabPanel("Show the Data",
HTML("High Dispersion Variable"),
tableOutput("dtable"),
tableOutput("stattable"),
br(),
HTML("Low Dispersion Variable"),
tableOutput("dtable2"),
tableOutput("stattable2")
),
tabPanel("Two Kinds of Variances",
withMathJax(),
p(h5("Visualizing the Variance.")),br(),
p("This app provides a way of visualizing the variance of a variable as a geometric entity. We define
the variance this way, as the average of areas of N squares, because the 'formula' for variance
involves a squared value. Textbook definitions of Sample Variance label it in various ways, including:
\\(S^2\\) (an upper case S), \\(SD^2\\). amd \\(VAR_X\\) "),
br(),
p("This sample variance is usally defined with this expression:
\\(\\frac{{\\sum\\limits_{i = 1}^n {({X_i} - \\bar X)^2} }}{{N}}\\)
"),
p("Expansion of the numerator permits a rewrite:
\\(\\frac{{\\sum\\limits_{i = 1}^n {({X_i} - \\bar X)({X_i} - \\bar X)} }}{{N}}\\)
"),
p("Either of these expressions make it clear that the deviation of each X value from its mean is
multiplied by itself, yielding the 'area of a geometric square'
perspective that the plots in this app emphasize. When this is done for each X value and the N quantities are summed,
that gives us the numerator of the expression. This numerator is usally give a shorthand notation of SS. This is because it is the
'sum of squared deviations from the mean'. So we can write the variance expression a third way:
\\(\\frac{{SS}}{{N}}\\)"
),
br(),
p("Students are encouraged to obtain the data values from the 'show the data' tab of this app and perform the calculations for these
expressions in Excel, or a with a calculator."),
br(),
p("Some users of this app may have been taught to compute the Variance a different way. This expression is similar to the ones above,
differing only in the denominator: \\(\\frac{{\\sum\\limits_{i = 1}^n {({X_i} - \\bar X)^2} }}{{N-1}}\\)."),
br(),
p("The numerator is still called Sum of Squares (SS), but the expression is no longer the arithmetic average of the squared deviations.
It is close, but will be slightly larger.
"),
p("This modified version of the expression is usually denoted as \\(s^2\\), with a lower case s. It is the more commonly used
variance expression. This preference is because it is an unbiased estimate of the variance in the population from which the N X scores
were randomly sampled. Although it is no longer exactly the arithmetic average of areas of squares it is close, especially for larger
sample sizes (N).
"),
p("Introductory Statistics coursework will expand on the difference in these two variance compuations.
In this app we used the first of the two versions which is typicalled the sample variance.
Since the 'area of a square' concept is related to the numerator, the distinction in the two
expressions doesn't alter they way we understand Sum of Squares.
")
),
tabPanel("About the App",
includeMarkdown('about.md')
)
)#finish tabsetpanel
)#finish mainpanel
))
# Define server logic required to draw a histogram
server <- function(input, output, session) {
#################################################################
# first for an n of five, with relatively large variance
set.seed(25)
x <-runif(5,min=82, max=118)+.9025
y <- rep(0,5)
y
xbar <- mean(x)
xdev <- x-xbar
maxxdev <- abs(max(xdev))
rangex <- max(x)-min(x)
xdevsq <- xdev^2
base <- as.data.frame(cbind(y,x,xdev))
basehigh <- as.data.frame(cbind(x,xdev,xdevsq))
colnames(basehigh) <- c("X","X Dev from Mean", "X Dev Squared")
#str(base)
#sd(x)**2
#(var(x)*4/5)**.5
SD1 <- 10.89265
SS <- (SD1**2)*5
halfsd1 <- SD1/2
sampsize <- 5
highstats <- as.data.frame(cbind(xbar, SS, SD1**2))
colnames(highstats) <- c("Mean of X","Sum of Squares", "Sample Variance")
#################################################################
# now repeat the whole thing with a smaller variance
set.seed(3)
x2 <-runif(5,min=92,max=108)
y2 <- rep(0,5)
y2
xbar2 <- mean(x2)
xdev2 <- x2-xbar2
xdevsq2 <- xdev2^2
maxxdev2 <- abs(max(xdev2))
rangex2 <- max(x2)-min(x2)
base2 <- as.data.frame(cbind(y2,x2,xdev2))
baselow <- as.data.frame(cbind(x2,xdev2,xdevsq2))
colnames(baselow) <- c("X","X Dev from Mean", "X Dev Squared")
# str(base2)
#sd(x2)**2
#(var(x2)*4/5)**.5
SD2 <- 3.572762
SS2 <- (SD2**2)*5
halfsd2 <- SD2/2
lowstats <- as.data.frame(cbind(xbar2, SS2, SD2**2))
colnames(lowstats) <- c("Mean of X","Sum of Squares", "Sample Variance")
################################################################
# plots for high dispersion data
# Basic stripchart
p <- ggplot(base, aes(x = x, y=y)) +
geom_dotplot(binwidth=.7) +
xlim(min(x), max(x)) +
ylim(0,rangex) +
labs(y=NULL) + labs(x="X") +
theme(axis.text.y = element_blank())+
theme(aspect.ratio=1)+
theme(axis.title.x=element_text(size=rel(1.3)))+
theme(axis.text.x=element_text(size=rel(1.5)))
p2 <- p + geom_vline(aes(xintercept=xbar),linetype=2)
# depict the x deviation from the mean for the largest data point
p3 <- p2 +
geom_segment(x=max(x), xend=xbar,y=0,yend=0,colour="blue")
# do the same xdeviation in the vertical orientation
p4 <- p3 +
geom_segment(x=max(x), xend=max(x),y=0,yend=maxxdev,colour="blue")
#view it as a square
p5 <- p4 +
geom_segment(x=max(x), xend=xbar, y=maxxdev, yend=maxxdev,colour="blue")+
geom_rect(xmin=mean(x),xmax=max(x), ymin=0,ymax=maxxdev,
fill="skyblue",alpha=.05)
# show all the squares
p6 <- p2 +
geom_segment(x=x, xend=xbar, y=0, yend=0,colour="blue")+ # bottom
geom_segment(x=x, xend=x,y=0,yend=abs(xdev),colour="blue")+ #side
geom_segment(x=x, xend=xbar, y=abs(xdev), yend=abs(xdev),colour="blue") + #top
geom_segment(x=xbar, xend=xbar, y=0, yend=abs(xdev),colour="blue") + #mean
geom_rect(xmin=x,xmax=xbar, ymin=0,ymax=abs(xdev),
fill="skyblue",alpha=.05)
# add a square for the average, the sample variance (SD squared)
p7 <- p6 +
geom_segment(x=xbar-halfsd1, xend=xbar+halfsd1, y=18, yend=18,colour="orange")+ # bottom
geom_segment(x=xbar-halfsd1, xend=xbar+halfsd1, y=18+SD1,yend=18+SD1,colour="orange")+ #top
geom_segment(x=xbar-halfsd1, xend=xbar-halfsd1, y=18, yend=18+SD1, colour="orange") + #left
geom_segment(x=xbar+halfsd1, xend=xbar+halfsd1, y=18, yend=18+SD1, colour="orange") + #right
geom_rect(xmin=xbar-halfsd1, xmax=xbar+halfsd1, ymin=18,ymax=18+SD1,
fill="orange",alpha=.02)
###############################################################
# low dispersion plotting
# Basic stripchart
ps <- ggplot(base2, aes(x = x2, y=y2)) +
geom_dotplot(binwidth=.7)+
xlim(min(x),max(x)) +
ylim(0,rangex) +
labs(y=NULL, x="X") +
theme(axis.text.y = element_blank())+
theme(aspect.ratio=1)+
theme(axis.title.x=element_text(size=rel(1.3)))+
theme(axis.text.x=element_text(size=rel(1.5)))
ps2 <- ps + geom_vline(aes(xintercept=xbar2),linetype=2)
# depict the x deviation from the mean for the largest data point
ps3 <- ps2 +
geom_segment(x=max(x2), xend=xbar2,y=0,yend=0,colour="blue")
# do the same xdeviation in the vertical orientation
ps4 <- ps3 +
geom_segment(x=max(x2), xend=max(x2),y=0,yend=maxxdev2,colour="blue")
#view it as a square
ps5 <- ps4 +
geom_segment(x=max(x2), xend=xbar2, y=maxxdev2, yend=maxxdev2,colour="blue")+
geom_rect(xmin=mean(x2),xmax=max(x2), ymin=0,ymax=maxxdev2,
fill="skyblue",alpha=.05)
# show all the rectangles
ps6 <- ps2 +
geom_segment(x=x2, xend=xbar2, y=0, yend=0,colour="blue")+ # bottom
geom_segment(x=x2, xend=x2,y=0,yend=abs(xdev2),colour="blue")+ #side
geom_segment(x=x2, xend=xbar2, y=abs(xdev2), yend=abs(xdev2),colour="blue") + #top
geom_segment(x=xbar2, xend=xbar2, y=0, yend=abs(xdev2),colour="blue") + #mean
geom_rect(xmin=x2,xmax=xbar2, ymin=0,ymax=abs(xdev2),
fill="skyblue",alpha=.05)
ps7 <- ps6 +
geom_segment(x=xbar2-halfsd2, xend=xbar2+halfsd2, y=18, yend=18,colour="orange")+ # bottom
geom_segment(x=xbar2-halfsd2, xend=xbar2+halfsd2, y=18+SD2,yend=18+SD2,colour="orange")+ #top
geom_segment(x=xbar2-halfsd2, xend=xbar2-halfsd2, y=18, yend=18+SD2, colour="orange") + #left
geom_segment(x=xbar2+halfsd2, xend=xbar2+halfsd2, y=18, yend=18+SD2, colour="orange") + #right
geom_rect(xmin=xbar2-halfsd2, xmax=xbar2+halfsd2, ymin=18,ymax=18+SD2,
fill="orange",alpha=.02)
##############################################################
output$highfigplot <- renderPlot(
if(input$high & input$highfig == 'data'){
p
}
else if(input$high & input$highfig == 'mean'){
p2
}
else if(input$high & input$highfig == 'xdev'){
p3
}
else if(input$high & input$highfig == 'xdevvert'){
p4
}
else if(input$high & input$highfig == 'square'){
p5
}
else if(input$high & input$highfig == 'squares'){
p6
}
else if(input$high & input$highfig == 'variance'){
p7
}
) # end renderplot
###############################################################
output$lowfigplot <- renderPlot(
if(input$low & input$lowfig == 'data'){
ps
}
else if(input$low & input$lowfig == 'mean'){
ps2
}
else if(input$low & input$lowfig == 'xdev'){
ps3
}
else if(input$low & input$lowfig == 'xdevvert'){
ps4
}
else if(input$low & input$lowfig == 'square'){
ps5
}
else if(input$low & input$lowfig == 'squares'){
ps6
}
else if(input$low & input$lowfig == 'variance'){
ps7
}
) # end renderplot
observeEvent(input$high,{
removePopover(session, 'highfigplot')
if (input$high){
addPopover(
session,
"highfigplot",
"What Does the Plot Show?",
content = "Squaring an X value deviation from its mean can be thought of as computing a
the area of a square. This figure shows those squares for all the X values.
When those areas are summed, we call it the Sum of Squares. The average of these square areas
is shown with the orange square and this average defines the Sample Variance, often denoted as S-squared or SD-squared. <BR><BR>
The user should compare the size of these squares for this 'high dispersion' variable with the 'low dispersion' variable shown
in the figure below.",
trigger = 'click',placement="left"
)
}#end if for high fig
})#end observeEvent
observeEvent(input$low,{
removePopover(session, 'lowfigplot')
if (input$low){
addPopover(
session,
"lowfigplot",
"What Does the Plot Show?",
content = "Notice in this figure, where the data points are less dispersed (closer to the mean), that
the squares are smaller and their average (orange - the variance) is considerable smaller.
<br><br>
The user should compare the size of these squares for this 'low dispersion' variable with the 'high dispersion' variable shown
in the figure above.",
trigger = 'click',placement="left"
)
}#end if for low fig
})#end observeEvent
output$dtable <- renderTable({
basehigh
})
output$dtable2 <- renderTable({
baselow
})
output$stattable <- renderTable({
highstats
})
output$stattable2 <- renderTable({
lowstats
})
}# end server
# Run the application
shinyApp(ui = ui, server = server)
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