--- title: "Exploring Categorical Data" subtitle: | | IMS2 Ch. 4 | Math 115 author: "Yurk" format: revealjs: theme: beige embed-resources: true editor: source metadata: license: CC BY-SA --- ## Comic Characters ```{r} #| include: false #| echo: false library(tidyverse) library(openintro) library(tidytuesdayR) library(knitr) library(kableExtra) ``` ```{r} #| include: false #| echo: false comics <- read_csv("data/comics.csv") |> filter(!is.na(align), !is.na(id), !is.na(gender)) |> droplevels() ``` - 15,182 comic characters from DC and Marvel comics - 11 variables, including - name - identity (id) gives information about personal identity (e.g., identity is kept secret) - alignment (align) gives information about whether character is good, bad, etc ## CSV Data Files - In J Lab 1 we learned how to import data from a CSV file into Jamovi - The `comics` data set is also saved in a [CSV file](https://drive.google.com/file/d/1BbrTjI6uwcdod0wzLcyMYMzII5McEPHq/view?usp=share_link) - Let's download the file and explore it using a text editor - We can also open it with Jamovi --- - First 10 rows of the comics data ```{r} #| include: true #| echo: false comics |> slice_head(n = 10) |> kbl(booktabs = TRUE, escape = FALSE) |> kable_styling(font_size = 18) ``` ## Describing categorical data - We can summarize a single categorical variable using a **frequency table** - Counts the number of observations for each level of the variable ```{r} #| include: true #| echo: false comics |> count(id) |> bind_rows(tibble(id = "Total", n = 15128)) |> kbl(booktabs = TRUE, escape = FALSE, col.names = c("identity", "count"), format.args = list(big.mark = ',')) |> kable_styling(font_size = 28) |> row_spec(5, bold = T) ``` --- - We can also calculate proportions for each of the levels ```{r} #| include: true #| echo: false comics |> count(id) |> mutate(n = n/sum(n)) |> kbl(booktabs = TRUE, escape = FALSE, col.names = c("identity", "proportion"), digits = 3, format.args = list(big.mark = ',')) |> kable_styling(font_size = 28) ``` ## Visualizing categorical data - We can use a bar plot to visualize categorical data ```{r} #| include: true #| echo: false #| fig-cap: "Bar plot showing frequencies of levels of identity variable" ggplot(data = comics, mapping = aes(x = id, fill = id)) + geom_bar() + theme_minimal() + theme(text = element_text(size = 20)) ``` ## Summarizing two categorical variables - A **contingency table** is a table that can be used to summarize two categorical variables - Each value is a count of the number of times a variable outcome combination occurs - Usually includes row and column totals as well (**marginal totals**) --- ```{r} #| include: true #| echo: false #| tbl-cap: "Contingency table for identity and alignment" col_tots <- comics |> count(align, id) |> pivot_wider(names_from = id, values_from = n, values_fill = 0) |> mutate(Total = `No Dual` + Public + Secret + Unknown) |> summarize(align = "Total", `No Dual` = sum(`No Dual`), Public = sum(Public), Secret = sum(Secret), Unknown = sum(Unknown), Total = sum(Total)) comics |> count(align, id) |> pivot_wider(names_from = id, values_from = n, values_fill = 0) |> mutate(Total = `No Dual` + Public + Secret + Unknown) |> bind_rows(col_tots) |> kbl(booktabs = TRUE, escape = FALSE, digits = 0, format.args = list(big.mark = ',')) |> kable_styling(font_size = 28) |> row_spec(5, bold = T) |> column_spec(6, bold = T) ``` --- - It is also useful to create contingency tables with proportions - The simplest version is obtained by dividing each count by the grand total - In this case values in table sum to 1 --- ```{r} #| include: true #| echo: false #| tbl-cap: "Proportion of outcomes for each combination of allignment and identity" comics |> count(align, id) |> mutate(prop = n/sum(n)) |> pivot_wider(id_cols = align, names_from = id, values_from = prop, values_fill = 0) |> kbl(booktabs = TRUE, escape = FALSE, digits = 4, format.args = list(big.mark = ',', scientific= FALSE)) |> kable_styling(font_size = 28) ``` - What does the value 0.0299 mean? ## Conditional proportions - We can also create tables of **conditional proportions** than can be helpful to explore associations between the variables - We need to decide whether the proportions should be conditioned on rows (divide counts by row totals) or columns (divide counts by colum totals) - If conditioned on rows, proportions sum to 1 along rows - If conditioned on columns, proportions sum to 1 along columns --- - These proportions are conditioned on rows (alignment) - Allows us to compare proportions of identity types between different alignment groups - For example, we can see that about 63% of *bad* characters have *secret* identities whereas only about 41% of *good* characters have *secret* identities. ```{r} #| include: true #| echo: false comics |> count(align, id) |> group_by(align) |> mutate(prop = n/sum(n)) |> pivot_wider(id_cols = align, names_from = id, values_from = prop, values_fill = 0) |> kbl(booktabs = TRUE, escape = FALSE, digits = 4, format.args = list(big.mark = ',', scientific= FALSE)) |> kable_styling(font_size = 28) ``` --- - These proportions are conditioned on columns (identity) - Allows us to compare proportions of alignment types between different identity groups - For example, we can see that about 57% characters with *secret* identities are *bad*, whereas only about 32% of characters with *secret* identities are *good*. ```{r} #| include: true #| echo: false comics |> count(align, id) |> group_by(id) |> mutate(prop = n/sum(n)) |> pivot_wider(id_cols = align, names_from = id, values_from = prop, values_fill = 0) |> kbl(booktabs = TRUE, escape = FALSE, digits = 4, format.args = list(big.mark = ',', scientific= FALSE)) |> kable_styling(font_size = 28) ``` ## Visualizing two categorical variables - There are different ways to visualize two categorical variables using bar plots - We can create **stacked** bar plot - Colors show how composition varies within each group --- ```{r} #| include: true #| echo: false #| fig-cap: "Stacked bar plot showing alignment frequencies for different id levels" comics |> ggplot(aes(x = id, fill = align)) + geom_bar() + theme_minimal() + theme(text = element_text(size = 20)) ``` --- - We can also visualize the data using side-by-side (dodged) bar plots ```{r} #| include: true #| echo: false #| fig-cap: "Dodged bar plot showing alignment frequencies for different id levels" comics |> ggplot(aes(x = id, fill = align)) + geom_bar(position = "dodge") + labs(x = "Character's Personal Identity", fill = "Alignment of Character", y = "Number of Characters") + theme_minimal() + theme(text = element_text(size = 18)) ``` --- - Another alternative is to use **faceted** bar plots - Facet according to one of the variables - A facet (subplot) is created for each level of that variable --- ```{r} #| include: true #| echo: false #| fig-cap: "Faceted bar plot showing alignment frequencies for different id levels" comics |> ggplot(aes(x = id, fill = align)) + geom_bar() + facet_wrap(~align) + theme_minimal() + theme(text = element_text(size = 16)) ``` --- - A fourth type of bar plot we can use to visualize two categorical variables is a **standardized** (filled) bar plot - This shows conditional proportions (instead of counts) in a stacked format - The following proportions are conditioned on `id` --- ```{r} #| include: true #| echo: false #| fig-cap: "Standardized bar plot showing alignment proportions for different id levels" comics |> ggplot(aes(x = id, fill = align)) + geom_bar(position = "fill") + labs(y = "Proportion of Characters") + theme_minimal() + theme(text = element_text(size = 20)) ``` --- - We can take a different perspective by exchanging the roles of the variables - The following proportions are conditioned on `align` --- ```{r} #| include: true #| echo: false #| fig-cap: "Standardized bar plot showing id proportions for different alignment levels" comics |> ggplot(aes(x = align, fill = id)) + geom_bar(position = "fill") + labs(y = "Proportion of Characters") + theme_minimal() + theme(text = element_text(size = 20)) ```