Mission443Solutions.Rmd

---
title: "Hypothesis Testing in R: Guided Project Solutions"
output: html_document
---

We would like to remind our students that our solutions represent just one of the many ways that a programmer might perform the analyses. This solution merely provides a platform for those who need a bit more guidance.

```{r setup }
library(tidyverse)
```

# Data Import

```{r}
jeopardy = read_csv("./data/jeopardy.csv")
```

```{r}
head(jeopardy)
```

```{r}
colnames(jeopardy)
```

```{r}
# the clean_names() function from the janitor package would have been great here too
colnames(jeopardy) = c("show_number", "air_date", "round", "category", "value", "question", "answer")
```

```{r}
sapply(jeopardy, typeof)
```

# Fixing Data Types

```{r}
unique(jeopardy$value)
```

```{r}
# Removing Nones, cleaning the text, and converting everything into numeric
jeopardy = jeopardy %>% 
  filter(value != "None") %>% 
  mutate(
    value = str_replace_all(value, "[$,]", ""),
    value = as.numeric(value)
  )
```

```{r}
unique(jeopardy$value)
```

# Normalizing Text

```{r}
# The stringr library is automatically brought in when tidyverse is brought in

# Notice how there is a space in the regular expression
jeopardy = jeopardy %>% 
  mutate(
    question = tolower(question),
    question = str_replace_all(question, "[^A-Za-z0-9 ]", ""),
    answer = tolower(answer),
    answer = str_replace_all(answer, "[^A-Za-z0-9 ]", ""),
    category = tolower(category),
    category = str_replace_all(category, "[^A-Za-z0-9 ]", "")
  )
```

```{r}
head(jeopardy)
```

# Making Dates More Accessible

```{r}
jeopardy = jeopardy %>% 
  separate(., air_date, into = c("year", "month", "day"), sep = "-") %>% 
  mutate(
    year = as.numeric(year),
    month = as.numeric(month),
    day = as.numeric(day)
  )
```

# Focusing On Particular Subject Areas

```{r}
n_questions = nrow(jeopardy)
p_category_expected = 1/3369 
p_not_category_expected = 3368/3369 
```

```{r}
categories = pull(jeopardy, category)
n_science_categories = 0

# Count how many times the word science appears in the categories
for (c in categories) {
  if ("science" %in% c) {
    n_science_categories = n_science_categories + 1
  }
}

science_obs = c(n_science_categories, n_questions - n_science_categories)
p_expected = c(1/3369, 3368/3369)
chisq.test(science_obs, p = p_expected)
```

```{r}
n_history_categories = 0

# Count how many times the word science appears in the categories
for (c in categories) {
  if ("history" %in% c) {
    n_history_categories = n_history_categories + 1
  }
}

history_obs = c(n_history_categories, n_questions - n_history_categories)
p_expected = c(1/3369, 3368/3369)
chisq.test(history_obs, p = p_expected)
```

```{r}
n_shakespeare_categories = 0

# Count how many times the word science appears in the categories
for (c in categories) {
  if ("shakespeare" %in% c) {
    n_shakespeare_categories = n_shakespeare_categories + 1
  }
}

shakespeare_obs = c(n_shakespeare_categories, n_questions - n_shakespeare_categories)
p_expected = c(1/3369, 3368/3369)
chisq.test(shakespeare_obs, p = p_expected)
```

We see p-values less than 0.05 for each of the hypothesis tests. From this, we would conclude that we should reject the null hypothesis that science doesn't have a higher prevalence than other topics in the Jeopardy data. We would conclude the same with history and Shakespeare.

# Unique Terms in Questions

```{r}
# Pull just the questions from the jeopardy data
questions = pull(jeopardy, question)
terms_used = character(0)

for (q in questions) {
  # Split the sentence into distinct words
  split_sentence = str_split(q, " ")[[1]]
  
  # Check if each word is longer than 6 and if it's currently in terms_used
  for (term in split_sentence) {
    if (!term %in% terms_used & nchar(term) >= 6) {
      terms_used = c(terms_used, term)
    }
  }
}
```

# Terms In Low and High Value Questions

```{r}
# Going only through the first 20 terms for shortness
# But you can remove the indexing to perform this code on all the terms
values = pull(jeopardy, value)
value_count_data = NULL

for (term in terms_used[1:20]) {
  n_high_value = 0
  n_low_value = 0
  
  for (i in 1:length(questions)) {
    # Split the sentence into a new vector
    split_sentence = str_split(questions[i], " ")[[1]]
    
    # Detect if the term is in the question and its value status
    if (term %in% split_sentence & values[i] >= 800) {
      n_high_value = n_high_value + 1
    } else if (term %in% split_sentence & values[i] < 800) { 
      n_low_value = n_low_value + 1
    }
  }
  
  # Testing if the counts for high and low value questions deviates from what we expect
  test = chisq.test(c(n_high_value, n_low_value), p = c(2/5, 3/5))
  new_row = c(term, n_high_value, n_low_value, test$p.value)
  
  # Append this new row to our
  value_count_data = rbind(value_count_data, new_row)
  
}
```

```{r}
# Take the value count data and put it in a better format
tidy_value_count_data = as_tibble(value_count_data)
colnames(tidy_value_count_data) = c("term", "n_high", "n_low", "p_value")

head(tidy_value_count_data)
```

We can see from the output that some of the values are less than 5. Recall that the chi-squared test is prone to errors when the counts in each of the cells are less than 5. We may need to discard these terms and only look at terms where both counts are greater than 5.

From the 20 terms that we looked at, it seems that the term "indian" is more associated with high value questions. Interesting!