Categorical Data Analysis

library(tidyverse)

1 Goal

• Visualization Methods
  • for EDA: visualize patterns, trends, anomalies in data
  • for model diagnostic methods: visualize to assess violations of assumptions
  • for summary methods: visualize to provide an interpretable summary of data
• apply theory to practice
  • conert research questions into statistical hypotheses and models
  • look into the difference between non-parametric (ex. fisher exact test) vs parametric (ex. \(\chi^2 test for independence\)) vs model-based methods (ex. logistic regression)
  • for summary methods: visualize to provide an interpretable summary of data

2 Definition of Categorical Data

• categorical (or frequency) data consist of a discrete set of categories, which may be ordered or unordered.
  • unordered
    • gener: {male, female, transgender}
    • marital status: {never married, married, separated, divorced, widowed}
    • party preference: {NDP, liberal, conservative, green}
    • treatment improvement: {none, some, marked}
  • ordered
    • age group: {0s,10s,20s,30s, …}
    • number of children: {0, 1 , 2 ,3, …} ## Structures

Categorical data appears in various forms like:

• tables

  • one way

  table(sample(LETTERS[1:4], 100, TRUE))    

  • two way
  • three way

• matrices ```r

  ```

• array ```r

  ```

• data frames

  • case form

  #| include: false
  
  data.frame(subject=1:1000,
  height=sample(170:210,1000,replace=TRUE),
  weight=sample(50:100,1000,replace=TRUE))%>%
  head(10)%>%
  knitr::kable()

  • frequency form

  #| include: false
  data.frame(subject=1:1000,
  height=sample(170:210,1000,replace=TRUE),
  weight=sample(50:100,1000,replace=TRUE))%>%
  group_by(weight)%>%
  summarise(n=n())%>%head(10)%>%
  knitr::kable()