Pres.Rmd

---
title: "A Shiny App for Introductory Statistics Concepts"
author: "Chelsey Legacy"
date: "April 7, 2017"
output: ioslides_presentation
runtime: shiny
---


## Outline

  - Technology in Statistics Education
  - Availible Options
  - Shiny App
  - Worksheets
  - Conclusions & Future Work

## Cognitive technologies
  
  - Pea explains cognitive technology as: "any medium that helps transcend the limitations of the mind.." 
  - Technology helps make complex concepts accessible to more people
  - Help students go beyond following formulas and returning answers
  

## Impact of Technology on Pededagogy

  - Focus more on selcting the right tools, than on formulas and calculations
  - Try to select straightforward software

## Availible Options & Drawbacks

  - Software: JMP, Fathom, Minitab, SPSS
    - Expensive
    - Learning curve
  - Web-based Java platforms: StatKey, Rossman Chance applets
    - Not suitable for all courses
    - Java loading issues
 

## Shiny by RStudio

  - Avaliable for free
  - User only needs to know programming in R
  - Easily custimizable 
  - Interactive
  

## Shiny App for Intro Stat Concepts
##
```{r, echo = FALSE}
shinyAppFile("combined.R",
  options=list(
    width=600, height=600
  )
)

```

##
```{r, echo = FALSE, message=FALSE, warning = FALSE}
#Shiny for inference for ONE PROPORTION
#Load Libraries
library(markdown)
library(ggplot2)
library(shinydashboard)
library(datasets)
library(shinythemes)
shinyApp(
  
  ui =     
    navbarPage(h6("Stats"),theme = shinytheme("flatly"),
               tabPanel("Sampling Distribution for One Proportion",
                                     column(width = 2,
                                            
                                            numericInput("popProp", "Population Proportion",
                                                         value = 0.3,min = 0, max = 1, step = 0.01),
                                            numericInput("sampleSize", "Sample Size", value = 100, min = 1),
                                            numericInput( "numSamp", "Number of Samples", value = 100, min = 1),
                                            actionButton("goProp", "Draw",class="btn btn-success btn")
                                            
                                     ),
                                     
                                     column(width = 5,
                                            
                                            tableOutput("sampSumDat"),
                                            tableOutput("popSumDat")
                                            
                                     ),
                                     
                                     column(width = 5, 
                                            verbatimTextOutput("sdist"),
                                            plotOutput("sampleDist", width = "auto", height = 200),
                                            verbatimTextOutput("singdist"),
                                            plotOutput("samplingDist", width = "auto", height = 200)
                                     )
                            )),
  server =  function(input, output, session) {
    # Create a single sample distribution 
  # Get a sample from a binomial distribution
  pickVect = eventReactive(input$goProp,{
    pickf = rbinom(input$sampleSize,1, input$popProp)
    return(pickf)
  })
  
  # Count the number of "successes" and put it over the sample size to make p_hat
  pickProp = eventReactive(input$goProp,{
    pickprop = length(which(pickVect() == 1))/input$sampleSize
    return(pickprop)
  })
  
  
  #Sample Distribution bar graph
  output$sampleDist = renderPlot({
    qplot(as.character(pickVect()), xlab = "Category", ylab = "Count")
  })
  
  #Sample summary information to be put into a table
  samplesum = eventReactive(input$goProp,{data.frame(
    Category = c( "Yes = 1", "No = 0"),
    Count =c( length(which(pickVect() == 1)), length(which(pickVect() == 0))),
    Prop = c(format(round(length(which(pickVect() == 1))/input$sampleSize,digits = 4),4), format(round(length(which(pickVect() == 0))/input$sampleSize,4),4))
  )
  })
  
  #Sample summary table output
  output$sampSumDat  = renderTable(caption = "Sample Summary Statistics",caption.placement = getOption("xtable.caption.placement", "top"),{
    samplesum()
  })
  
  #Calculations to make a sampling distribution
  samples = eventReactive(input$goProp,{
    # If one sample is needed use only the one p_hat from above
    if(input$numSamp == 1){
      return(pickProp())
    }
    # If many samples are needed, generate a vector of p_hats by the above method
    if(input$numSamp > 1){
      v = c(pickProp())
      for(i in 2:input$numSamp){
        # Generate a sample
        npick = reactive({
          newpick = rbinom(input$sampleSize, 1,input$popProp)
          newprop = length(which(newpick == 1))/input$sampleSize
          return(newprop)
          
        })
        # Store the generated sample in a vector
        v = c(v,npick())
        
      }}
    # Return to 
    return(v)
  })
  
  # Histogram of the sampling distribution
  output$samplingDist =renderPlot({
    ggplot(data = data.frame(samples()),aes(samples()))+ geom_histogram(binwidth = 0.01) +xlab("Sample Proportion") +ylab("Number of Samples")
  })
  
  # Population summary info to be displayed in a table
  popSum = eventReactive(input$goProp,{data.frame(
    Mean = mean(samples()),
    "Standard Deviation" = sd(samples())
  )
  })
  
  #Population summary table output
  output$popSumDat  = renderTable(caption = "Sampling Distribution Summary Statistics",caption.placement = getOption("xtable.caption.placement", "top"),{
    popSum()
  })
  
  # Add the text for "Sample/Sampling Distribution" to the Shiny display
  output$sdist <- renderText({ "Sample Distribution" })
  output$singdist <- renderText({ "Sampling Distribution" })
  
  }
  
)

```


##
```{r, echo = FALSE, warning=FALSE, message = FALSE}
# Shiny for confidence intervals
library(shinythemes)

shinyApp(
  
  ui = 
    navbarPage(h6("Stats"),theme = shinytheme("flatly"),
    tabPanel("Confidence Interval",
             fluidRow(
               box(width = 4, title = NULL, status = "primary",
                   sliderInput("cIDemoCL", "Confidence Level %", value = 80, min = 80, max = 99, step = 5)
               ),
               box(width = 4, title = NULL, status = "primary",
                   sliderInput("cIDemoSampSize", "Sample Size", value = 25, min = 25, max = 500, step = 5)
               )
               
             ),
             fluidRow(
               box(width = 10, title = NULL, status = "primary",
                   plotOutput("sampCLPlot")
               )
             )
    )),
  
  server = function(input, output, session){
      
  # Generate 20 sample p_hats to create confidence intervals around
  twSamps = eventReactive(input$cIDemoSampSize,{
    tsampCL = NULL
    for(i in 1:20){
      tsCL = rbinom(input$cIDemoSampSize, 1, 0.5)
      # Get the proportion of "successes" for the generated sample
      countPropCL = length(which(tsCL == 1 ))/ input$cIDemoSampSize
      tsampCL = c(tsampCL,countPropCL)
    }
    return(tsampCL)
  })
  
  # Create a sample vector of y values so that the confidence intervals can be stacked in the plot
  ysCLDemo = reactive({
    yy = seq(from = 1, by = 0.5, length.out = length(twSamps()))
    return(yy)
  })
  
  # Set the z-value to be the value input by the user
  zlev = reactive({
    if(input$cIDemoCL  == 80){
      zlev = 1.282
    }
    if(input$cIDemoCL == 85){
      zlev = 1.44
    }
    if(input$cIDemoCL == 90){
      zlev = 1.645
    }
    if(input$cIDemoCL == 95){
      zlev = 1.96
    }
    if(input$cIDemoCL == 99){
      zlev = 2.576
    }
    return(zlev)
  })
  
  # Calculate the upper bounds for the confidence intervals
  upCLDemo = reactive({
    usd = twSamps() + zlev()*(sqrt(twSamps()*(1-twSamps())/input$cIDemoSampSize))
    return(usd)
  })
  
  # Calculate the lower bounds for the confidence intervals
  lowCLDemo = reactive({
    lsd =  twSamps() - zlev()*(sqrt(twSamps()*(1-twSamps())/input$cIDemoSampSize))
    return(lsd)
  })
  
  # Color the interval based on whether or not they capture the true population proportion
  colorCLDemo = reactive({
    coldemo = NULL
    for(i in 1:20){
      # Color the intervals blue if they contain 0.4 (the set value for the population parameter)
      if(lowCLDemo()[i] <= 0.5 && 0.5  <= upCLDemo()[i]   ){
        
        colne = "steelblue1"
        coldemo = c(coldemo,colne)
        
      }
      # Color the intervals orange if they do not contain 0.4 (the set value for the population parameter)
      else{
        
        colne = "tan1"
        coldemo = c(coldemo,colne)
        
      }
    }
    # Return the vector of colors to be added to the plot
    return(coldemo)
  })
  
  # Graph the confidence intervals stacked on one plot to display how many captured the population proportion 
  output$sampCLPlot = renderPlot({
    qplot(x = twSamps(), y = ysCLDemo(), xlab = "Confidence Intervals")+xlim(0,1)+
      geom_segment(aes(x = lowCLDemo(), xend = upCLDemo(), y = ysCLDemo(), yend = ysCLDemo()), colour = colorCLDemo())+
      theme(axis.title.y=element_blank(), axis.text.y=element_blank(), axis.ticks.y=element_blank())+geom_vline(xintercept = 0.5, color = "slategray4")
  })
  
    
  }
)

```


##
```{r,echo=FALSE,warning=FALSE, message = FALSE}
#Shiny for difference in Proportions

```
## Worksheets

  - Pre/Post Questions
    - Undegrads:
        - Confidence level
        - ANOVA
    - Math educators:
        - Sample/Sampling Distribution for proportions
        - Regression
  - Worksheets for every section
    


## Conclusions and Future Work

  - Shiny app easily customizable, easy to use, free
  - Tests on the Shiny app forthcoming
    - Undergraduates
    - High school and college math teachers