Análise estatística descritiva com uso de R

class: center, middle, inverse, title-slide

# Análise estatística descritiva com uso de R
## Análise bidimensional: Correlação linear e chi-quadrado
### Marília Melo Favalesso

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background-image: url(fig/background.png)
background-size: cover

.center[
## .big-text[Hola!]

### Marília Melo Favalesso

.pull-left[
<img style="border: 2px solid #555; border-radius: 70%;" src="fig/me.png" width="200px"/>

.pull-right[
.center[**Educação**]

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## Lembre-se!

### **Pergunte, pergunte & perguntas!** ✋🎤 💬
<br>

### **Aula de revisão de conteúdos e exercícios!** ✏️
<br>

### **De preferência, mantenha a câmera ligada** 📷
<br>

### **Respeitar os colegas e a profa.** 👊
<br>

### **Tentar se divertir durante a aula.** 🥳
<br>

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## Conteúdo programático da mini-aula

- [O que é correlação](#correlation)
   - [Correlação ≠ Causalidade](#causalidade)

- [Correlação linear](#cor_linear)
   - [Coeficiente de correlação produto-momento (r)](#dir)
   - [Exercício](#exe1)

- `$\chi^2$` [de associação](#qui)
   - [Resíduos ajustados](#qui)
   - [Exercício](#exe2)

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name: correlation
class: middle, center

# O que é correlação?

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## O que é correlação?

> Em estatística, a **correlação** mede a **direção** e a **intensidade** de uma relação entre duas variáveis.

- Por exemplo:

- **↑**🌡️ **↑**🍧**?**
  
  - **↑**📚 **↑**💰**?**
  
  - **↑**🍆 **↓**🐷**?**
  
  - **↑**🚴 **↓**💨**?**
  
  - **↑**🙋  **↑**🦵**?**
  
  - **↑**🚬  **↑**👃**?**
  
> Quando se pode demonstrar que existe associação entre duas variáveis, isto é, quando se constata que elas variam juntas, diz-se que as variáveis estão **correlacionadas**.

---
## O que é correlação?

### Correlação ≠ Causalidade

.center[
### **↑**🦵 ~ **↑**🙋 **?**

![](slides_files/figure-html/unnamed-chunk-1-1.png)
]

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name: cor_linear
class: middle, center

# Correlação linear
---
name: dir
## Correlação linear

### Coeficiente de correlação produto-momento (r)

- O **r** (*rhô*) é uma medida da força e direção da correlação entre duas variáveis quantitativas e também é conhecido como **coeficiente de correlação de Pearson**.

.center[<img src="fig/corplot4.png" style="width: 38%;">]

---
## Correlação linear

### Direção da correlação

.center[<img src="fig/regua2.png" style="width: 40%;">]

<small>
> A partir dos diagramas de dispersão, já temos uma indicação se a relação entre as variáveis é **positiva** (quando as duas crescem juntas), **negativa** (quando uma aumenta e a outra diminui) ou se **não há correlação**.
</small>

---
## Correlação linear

### Intensidade da correlação

.center[<img src="fig/inter.png" style="width: 50%;">]

---
name: exe1

## Correlação linear

### Exercício 💻

Existe associação entre o PIB total (R$) dos municípios brasileiros e o tamanho de suas populações?

```r
## Pacotes ----
library(tidyverse) # manipulação dos dados
library(janitor) # limpeza dos dados

## Importar os dados ----
# • Para importar os dados em .csv, utilizamos a função "read.csv". 
dados_socio_economicos <- 
  read_csv("dados_socio_economicos.csv") %>% # importação da tabela
  clean_names # examinar e limpar os nomes das colunas

dados_socio_economicos %>% names # Consultar as variáveis contidas na tabela
```

<small>
\#\# [1] "uf" "cod_uf" "cod_municipio" "nome_do_municipio" "populacao_estimada" "pib_per_capita" "pib_total_em_r_mi" <br>
\#\# [2] "atividade_economica" "ranking_pib_per_capita" "ranking_pib_total" 
</small>

---
## Correlação linear

### Exercício 💻

```r
## Plotar os dados em um gráfico de dispersão ---
dados_socio_economicos %>% # tabela de dados
  ggplot(aes(x = populacao_estimada, y = pib_total_em_r_mi)) + # var linha e colunax
  geom_point() + # transparência e tamanho dos pontos 
  xlab("População estimada") + # nome do eixo X
  ylab("PIB total (R$)") # nome do eixo Y
```

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</center>

---
## Correlação linear

### Exercício 💻

```r
## Plotar os dados com transformação nos eixos  ---
dados_socio_economicos %>% 
  ggplot(aes(x = populacao_estimada, y = pib_total_em_r_mi)) + 
  geom_point() +  
* scale_x_log10() +
* scale_y_log10() +
  xlab("População estimada") + ylab("PIB total (R$)") 
```

---
## Correlação linear

### Exercício 💻

```r
## Plotar os dados com transformação nos eixos  ---
dados_socio_economicos %>% 
  ggplot(aes(x = populacao_estimada, y = pib_total_em_r_mi)) + 
  geom_point() +  
  scale_x_log10() + # transformação log dados do eixo x
  scale_y_log10() + # transformação log dados do eixo y
  xlab("População estimada") + ylab("PIB total (R$)") 
```

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</center>

---
## Correlação linear

### Exercício 💻

- Para finalizar, precisamos calcular o **r** para os nossos dados:

```r
cor(
  dados_socio_economicos$populacao_estimada, 
  dados_socio_economicos$pib_total_em_r_mi
  )
```

```
## [1] 0.9621635
```

> Existe uma correlação **\_\_\_\_\_\_\_\_\_\_**  e **\_\_\_\_\_\_\_\_\_\_** entre a população estimada e o PIB total (r = **\_\_\_\_**).

---
## Correlação linear

### Exercício 💻

- Para finalizar, precisamos calcular o **r** para os nossos dados:

```r
cor(
  dados_socio_economicos$populacao_estimada, 
  dados_socio_economicos$pib_total_em_r_mi
  )
```

```
## [1] 0.9621635
```

> Existe uma correlação **positiva**  e **muito forte** entre a população estimada e o PIB total (r = **0,96**).

---
name: qui
class: middle, center

# `$\chi^2$` de associação
## Resíduos ajustados

---
## `$\chi^2$` de associação

### Resíduos ajustados

- Os resíduos do `$\chi^2$` (qui-quadrado) de associação ou de independência são utilizados para avaliar a correlação entre **variáveis categóricas**, assim como o coeficiente **r** é usado para o mesmo fim com variáveis quantitativas.

- **Exemplo:** 
  - A presença de doenças respiratórias está associado ao tabagismo? (amostra: n = 40).

.center[<img src="fig/cont2.png" style="width: 43%;">]

---
## `$\chi^2$` de associação

### Gráfico de barras empilhadas

.center[
![](slides_files/figure-html/unnamed-chunk-11-1.png)
]

---
## `$\chi^2$` de associação

### Resíduos ajustados

.center[<img src="fig/cont3.png" style="width: 35%;">]

> No **R** usamos a função `chisq.test(X, Y)$stdres` para obter os `$R_{aj}$`.

---
name: exe2
## `$\chi^2$` de associação

### Exercício 💻

- Existe associação entre raça e identificação partidária para os entrevistados pelo *US General Social Survey*?

```r
## Pacotes ----
library(tidyverse) # manipulação de dados + gráficos
library(janitor) # limpeza nos dados
library(dados) # onde está a tabela de dados
library(viridis) # para usar a paleta de cores viridis
```

```
## Carregando pacotes exigidos: viridisLite
```

```r
library(corrplot) # usaremos para plotar os resíduos
```

```
## corrplot 0.90 loaded
```

```r
## Chamar os dados da tabela 'questionario'{dados} ----
questionario <- questionario %>% clean_names

questionario %>% names # variáveis da tabela
```

```
## [1] "ano"          "estado_civil" "idade"        "raca"         "renda"       
## [6] "partido"      "religiao"     "denominacao"  "horas_tv"
```

---
## `$\chi^2$` de associação

### Exercício 💻

.pull-left[
**Gráfico de barras empilhadas**

```r
## Para criar o gráfico usamos o pacote 'ggplot'

questionario %>% # incluimos nossos dados
  ggplot(aes(y = raca, # raça vai no eixo "y"
             fill = partido)) + # as barras empilhadas correspondem a partido
  geom_bar( # usamos a função "geom_bar" para criar o grafico
    position = "fill" # posição das barras no gráfico
    ) + 
  scale_fill_viridis( # usamos a paletta de cores 'viridis'...
    discrete = TRUE, # ... para dados discretos
    name = "Partido") + # título da legenda
  xlab("Frequência relativa") + # nome do eixo x
  ylab("Raça") # nome do eixo y
```
]

.pull-right[
![](slides_files/figure-html/unnamed-chunk-14-1.png)
]

---
## `$\chi^2$` de associação

### Exercício 💻

**Análise dos resíduos**

```r
chisq.test(questionario$raca, 
           questionario$partido)$stdres %>%
  corrplot(is.cor = FALSE)
```

![](slides_files/figure-html/unnamed-chunk-16-1.png)

```
## NULL
```

> Observamos que há uma associação **positiva** entre a raça preta e o <br>
partido democrata; e entre brancos e o partido republicano.

---
## Dúvidas?

.center[<img src="fig/qr.png" style="width: 35%;">

<https://www.menti.com/hs6etjj2u9> (cod: 7513-1177)
]

---
class: center

<br>
## FIM!

<br>
.center[<img src="fig/ms.gif" style="width: 60%;">]