---
title: "Hello Data"
subtitle: |
  | IMS1 Ch. 1 
  | Math 219
author: "Yurk"
format: 
  revealjs:
    theme: beige
editor: source
---

## Lending Club Loans

```{r}
#| include: false
#| echo: false

library(tidyverse)
library(openintro)
library(tidytuesdayR)
library(knitr)
library(kableExtra)
```

```{r}
#| include: true
#| echo: false
#| tbl-cap: Six loans from the loan50 dataset
loan50 |>
  select(loan_amount, interest_rate, term, grade, state, total_income, homeownership) |>
  head(6) |>
  kbl(booktabs = TRUE, escape = FALSE) |>
  kable_styling(font_size = 20)
```

- Random sample of 50 loans made through Lending Club platform
- A **sample** is a subset of a larger group (the **population**)
- The sample consists of the 50 loans. The population is all loans made through the platform 

---

```{r}
#| include: true
#| echo: false
#| tbl-cap: Six loans from the loan50 dataset
loan50 |>
  select(loan_amount, interest_rate, term, grade, state, total_income, homeownership) |>
  head(6) |>
  kbl(booktabs = TRUE, escape = FALSE) |>
  kable_styling(font_size = 20)
```

- Data organized in a table called a **data frame**

---

```{r}
#| include: true
#| echo: false
#| tbl-cap: Six loans from the loan50 dataset
loan50 |>
  select(loan_amount, interest_rate, term, grade, state, total_income, homeownership) |>
  head(6) |>
  kbl(booktabs = TRUE, escape = FALSE) |>
  kable_styling(font_size = 20)
```

- Each row represents a single **case** or **observational unit**
- Each column represents a **variable**, corresponding to a loan characteristic. E.g.,

  - `loan_amount` (amount of loan in USD)
  - `term` (number of months of the loan) 
  - `grade` (related to likelihood of being repaid)


## Summary Statistics

```{r}
#| include: false
#| echo: false

mean_loan <- loan50 |>
  summarize(mean = mean(loan_amount)) |>
  pull()
```

- A **summary statistic** is a single number that summarizes data from a sample
- Mean loan amount ($`r format(round(mean_loan, 2), nsmall=2, big.mark=",")`) is a summary statistic
- Summary statistics can be organized in tables

```{r}
#| include: true
#| echo: false

loan50 |>
  group_by(grade) |>
  summarize(mean = mean(interest_rate)) |>
  kbl(booktabs = TRUE, escape = FALSE, digits = 1,
      col.names = c("grade", "mean interest rate")) |>
  kable_styling(font_size = 24)
```

## Association

- If there is a relationship between two variables, we say that the variables are **associated**
- Interest rate and loan grade appear to be associated
- If there is no relationship between two variables, we say the variables are **independent**

## Variable Types

- A **numerical** variable takes on values that are described using numbers that make sense to add, subtract, average, etc
- A **categorical** variable takes on values that indicate different levels or categories 

---

```{r}
#| include: true
#| echo: false
#| tbl-cap: Six loans from the loan50 dataset
loan50 |>
  select(loan_amount, interest_rate, term, grade, state, total_income, homeownership) |>
  head(6) |>
kbl(booktabs = TRUE, escape = FALSE) |>
  kable_styling(font_size = 20)
```

Loan data variable types:

::: {style="font-size: 50%;"}

| Variable | Type |
|--|--|
| loan_amount | numerical |
| interest_rate | numerical |
| term | numerical |
| grade | categorical |
| state | categorical |
| total_income | numerical |
| homeownership | categorical |

:::

---

- Numerical variables can be further broken down into

  - **discrete**: takes on discrete values (with jumps between consecutive values)
  - **continuous**: can take on any value within a range

- Categorical variables can be further broken down into

  - **ordinal**: levels have a natural ordering
  - **nominal**: levels do not have a natural ordering

---

![Variable types. From IMS1 Fig. 1.1.](https://openintro-ims.netlify.app/01-data-hello_files/figure-html/variables-1.png)


---

```{r}
#| include: true
#| echo: false
#| tbl-cap: Six loans from the loan50 dataset
loan50 |>
  select(loan_amount, interest_rate, term, grade, state, total_income, homeownership) |>
  head(6) |>
kbl(booktabs = TRUE, escape = FALSE) |>
  kable_styling(font_size = 20)
```

Loan data variable types:

::: {style="font-size: 50%;"}

| Variable | Type |
|--|--|
| loan_amount | numerical, continuous |
| interest_rate | numerical, continuous |
| term | numerical, discrete |
| grade | categorical, ordinal |
| state | categorical, nominal |
| total_income | numerical, continuous |
| homeownership | categorical, nominal |

:::

## Scatterplots

- The relationship between two numerical variables can be visualized using a **scatterplot**

```{r}
#| include: true
#| echo: false
#| fig-cap: "Scatterplot showing loan amount vs. income."

loan50 |>
  ggplot(aes(total_income, loan_amount)) +
  geom_point() +
  theme_minimal() +
  theme(text = element_text(size=20))
```

## Direction of association

- Two numerical variables are said to have a **positive association** if the values of one variable tend to be higher when the values of the other variable are higher
- Two numerical variables are said to have a **negative association** if the values of one variable tend to be lower when the values of the other variable are higher
- Loan amount and total income appear top be positively associated

## Stents for Treating Strokes

```{r}
#| include: true
#| echo: false
#| tbl-cap: First five patients

set.seed(123)
stent365[sample(1:nrow(stent365)),] |>
  head(5) |>
  kbl(booktabs = TRUE, escape = FALSE) |>
  kable_styling(font_size = 22)
```

- Researchers designed a study to study the effectiveness of stents in preventing strokes
- 451 at-risk patients randomly assigned to receive stent (treatment) or not (control)
- Outcome ("stroke" or "no event") recorded after 365 days

---

```{r}
#| include: true
#| echo: false
#| tbl-cap: First five patients

set.seed(123)
stent365[sample(1:nrow(stent365)),] |>
  head(5) |>
  kbl(booktabs = TRUE, escape = FALSE) |>
  kable_styling(font_size = 22)
```

- What are the cases?
- What are the variables?
- What are the variable types?

---

```{r}
#| include: true
#| echo: false
#| tbl-cap: "Summary of results for stent study"

stent365 |>
  group_by(group) |>
  summarize(stroke = sum(outcome == "stroke"),
            nostroke = sum(outcome == "no event")) |>
  kbl(booktabs = TRUE, escape = FALSE, digits = 1,
      col.names = c("Group", "Stroke", "No Event")) |>
  kable_styling(font_size = 28)
```

- The proportion that had a stroke in the treatment group was 45/119 = 0.20
- The proportion that had a stroke in the control group was 45/119 = 0.12
- Does there appear to be an association between group and outcome?

## Variable Roles

- In some cases we may think that the one variable affects the other variable
- We say that the **explanatory variable** affects the **response variable**
- In the stent study, the group (treatment or control) is the explanatory variable, and the outcome is the response variable

## Experiment vs. Observational Study

- An **experiment** is a study in which researchers researchers manipulate or assign the values of the explanatory variable
- The stent study is an experiment, because the researchers assign patients to the treatment or control group
- When cases are randomly assigned to groups, the study is called a **randomized experiment**
- An **observational study** is a study without such manipulation. The cases are *observed* as they are
- The Lending Club data are from an observational study

```{r}
#| include: false
#| echo: false

#tt_out <- tt_load("2020-01-14")

# tt_out

#passwords <- tt_out |> 
#  pluck("passwords")
```