DI.qmd

---
format: html
editor: visual
theme: default
---

```{r setup, include=FALSE}

# Load required packages
library(dplyr)
library(ggplot2)
library(png)
library(ggimage)
library(ggwaffle) #devtools::install_github("liamgilbey/ggwaffle")
library(emojifont)
library(MetBrewer)
library(tidyverse)

```

::: {.content-visible when-profile="english"}
# About the Disproportionality Index

## Estimating Median Salary

[Median salaries](https://employment-equity.github.io/Visualizations.html#median-salary-tables) for each group were estimated using the following formula:

$$median = L + \frac{ (\frac{n}{2} – F) }{f}  * w$$

## Calculating DI

In this analysis, Disproportionality Index (DI) is used as a measure of equitable representation. It is calculated as below.

$$\frac{\%_{Group\: X; \:salary\: range \: i}}{\% _{All \:Employees; \:salary\: range \: i}} = DI _{Group\:X; \:salary\:range\:i}$$

For example, 23.51% of Black employees and 16.70% of all employees are are within the \<60K salary range. This gives us a DI of 1.41.

$$ DI_{Black \: employees; <60K } =\frac{23.51\%}{16.70\%} = 1.41$$

For a table of DI's per year, [please see here](https://employment-equity.github.io/Visualizations.html#disproportionality-tables).

## Understanding DI - An Example

Suppose that we have a department of 500 employees. There are two groups of self-identifying minority employees, A and B. Group C is composed of the majority at 460 employees. Groups A and B make up 4% of employees at 20 employees each, which happens to mirror the Canadian population. At a glance, representation seems equal.

```{r Plot-1, echo = FALSE}
# Create dataframe with group numbers repeated
Dept_data <- tibble(Group_count = rep("A", 20) %>% 
                      c(rep("B", 20)) %>% 
                      c(rep("C", 460)) )

# Move data to waffle object for plotting
Dept_data_waffle <- waffle_iron(Dept_data, 
                                aes_d(group = Group_count), 
                                rows = 20) %>% 
  mutate(label = fontawesome('fa-male'))


## Plot symbols -----------------------------------------------

# Create color palette 
colors <- c(met.brewer("Johnson", 5)[c(1,5)], "#808080")

# Plot as waffle   
ggplot(Dept_data_waffle, aes(x, y, colour = group)) + 
  geom_text(aes(label=label), 
            family = 'fontawesome-webfont', 
            size = 5) +
  coord_equal() + 
  scale_colour_manual(values = c(colors)) + 
  theme_waffle()  +
  theme(axis.title.x = element_blank(),
        axis.title.y = element_blank(), 
        text = element_text(size = 12)) + 
  guides(color = guide_legend(title="Group"))
  
  
```

However, if you take a closer look at how the 20 employees from group A and B are distributed across salary levels, a different story appears. Group A is equally distributed among salary level, but the majority of group B employees remain at the lowest salary levels.

![Salary Scaffold](images/salary-scaffold.png)

Calculating DI further illustrates the differences in salary distribution. Above a DI of 1, a group's representation at a salary level is higher than the average of all employees. Below a DI of 1, a group's representation at a salary level is lower than the average of all employees.

```{r Plot 2-DI Example, echo = FALSE, message = FALSE, warning = FALSE}
Group <- c(rep("A", 5), rep("B", 5))
Salary <- c("<60.0K", "60.0-69.9K", "70.0-84.9K", "85.0-99.9K", "100.0K+", "<60.0K", "60.0-69.9K", "70.0-84.9K", "85.0-99.9K", "100.0K+")
DI <- c(.75, 1, 1.25, 1, 1, 1.5, 1.5, 1, .75, .25)

Salary_di <- data.frame(Group, Salary, DI)

Salary_di$Salary <- factor(Salary_di$Salary, levels = c("<60.0K", "60.0-69.9K", "70.0-84.9K", "85.0-99.9K", "100.0K+"))

colors <- c(met.brewer("Johnson", 5)[c(1,5)])

ggplot(Salary_di) +
  geom_bar(stat = "identity",
           position = "dodge",
           aes(x = Group,
               y = DI,
               fill = Group, 
               alpha = Salary)) +
  theme_minimal() +
  theme(
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.background = element_blank(),
    axis.line = element_line(colour = "black"), 
    text = element_text(size = 15),
    legend.text = element_text(size = 12)
  ) +
  scale_fill_manual  (values = colors, 
  ) +
  labs(title = NULL,
       x = "Group",
       y = "Disproportionality Index",
       fill = NULL) + 
  guides(fill="none") +
    geom_hline(yintercept = 1, 
             linetype = "dashed")

```
:::

::: {.content-visible when-profile="french"}
# Sur l'indice de disproportionnalité

## Estimation du salaire médian

[Les salaires médians](https://employment-equity.github.io/Visualizations.html#median-salary-tables) pour chaque groupe ont été estimées à l'aide de la formule suivante:

$$médian = L + \frac{ (\frac{n}{2} – F) }{f}  * w$$

## Calcul de l'ID

Dans cette analyse, l'indice de disproportionnalité (ID) est utilisé comme mesure de la représentation équitable. Il est calculé comme suit.

$$\frac{\%_{Groupe\: X; \:échelle\: des \:salaires \: i}}{\% _{Tous \:les \:Employees; \:échelle\: des \:salaires \: i}} = DI _{Groupe\:X; \:échelle\: des \:salaires\:i}$$

Par exemple, 23,51 % des employés noirs et 16,70 % de l'ensemble des employés se situent dans la fourchette salariale \<60K. Cela nous donne un DI de 1,41.

$$ DI_{Employés \:de \:race \:noire \:<60K } =\frac{23.51\%}{16.70\%} = 1.41$$

Pour un tableau des DI par année, [voir ici](https://employment-equity.github.io/fr/Visualizations.html#tableau-des-salaires-m%C3%A9dians).

## Comprendre l'ID - Un exemple

Supposons que nous ayons un département de 500 employés. Il y a deux groupes d'employés s'identifiant comme des minorités, A et B. Le groupe C est composé de la majorité, soit 460 employés. Les groupes A et B représentent 4 % des employés, soit 20 employés chacun, ce qui correspond à la population canadienne. À première vue, la représentation semble égale.

```{r, echo = FALSE}
# Create dataframe with group numbers repeated
Dept_data <- tibble(Group_count = rep("A", 20) %>% 
                      c(rep("B", 20)) %>% 
                      c(rep("C", 460)) )

# Move data to waffle object for plotting
Dept_data_waffle <- waffle_iron(Dept_data, 
                                aes_d(group = Group_count), 
                                rows = 20) %>% 
  mutate(label = fontawesome('fa-male'))


## Plot symbols -----------------------------------------------

# Create color palette 
colors <- c(met.brewer("Johnson", 5)[c(1,5)], "#808080")

# Plot as waffle   
ggplot(Dept_data_waffle, aes(x, y, colour = group)) + 
  geom_text(aes(label=label), 
            family = 'fontawesome-webfont', 
            size = 5) +
  coord_equal() + 
  scale_colour_manual(values = c(colors)) + 
  theme_waffle()  +
  theme(axis.title.x = element_blank(),
        axis.title.y = element_blank(), 
        text = element_text(size = 12)) + 
  guides(color = guide_legend(title="Groupe"))
  
  
```

Toutefois, si l'on examine de plus près la répartition des 20 salariés des groupes A et B entre les différents niveaux de salaire, la situation est différente. Le groupe A est également réparti entre les niveaux de salaire, mais la majorité des salariés du groupe B restent aux niveaux de salaire les plus bas.

![Échafaudage salarial](images/salary-scaffold.png)

Le calcul de l'ID illustre davantage les différences dans la répartition des salaires. Au-dessus d'un ID de 1, la représentation d'un groupe à un niveau de salaire est supérieure à la moyenne de l'ensemble des salariés. En dessous de 1, la représentation d'un groupe à un niveau de salaire est inférieure à la moyenne de l'ensemble des salariés.

```{r, echo = FALSE, message = FALSE, warning = FALSE}
Group <- c(rep("A", 5), rep("B", 5))
Salary <- c("<60.0K", "60.0-69.9K", "70.0-84.9K", "85.0-99.9K", "100.0K+", "<60.0K", "60.0-69.9K", "70.0-84.9K", "85.0-99.9K", "100.0K+")
DI <- c(.75, 1, 1.25, 1, 1, 1.5, 1.5, 1, .75, .25)

Salary_di <- data.frame(Group, Salary, DI)

Salary_di$Salary <- factor(Salary_di$Salary, levels = c("<60.0K", "60.0-69.9K", "70.0-84.9K", "85.0-99.9K", "100.0K+"))

colors <- c(met.brewer("Johnson", 5)[c(1,5)])

ggplot(Salary_di) +
  geom_bar(stat = "identity",
           position = "dodge",
           aes(x = Group,
               y = DI,
               fill = Group, 
               alpha = Salary)) +
  theme_minimal() +
  theme(
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.background = element_blank(),
    axis.line = element_line(colour = "black"), 
    text = element_text(size = 15),
    legend.text = element_text(size = 12)
  ) +
  scale_fill_manual(values = colors, 
  ) +
  labs(title = NULL,
       x = "Groupe",
       y = "Indice de disproportionnalité",
       fill = NULL,
       alpha = "Salaire") + 
  guides(fill="none") +
    geom_hline(yintercept = 1, 
             linetype = "dashed")

```
:::