---
title: "Lab 2"
subtitle: "36-315: Statistical Graphics and Visualization, Summer 2026"
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---

\newpage

# Problem 1: Inference for 1D categorical data (35pts)

We will consider a dataset on IMDb rated movies, TV series, etc., which can be loaded with the code below.

```{r}
library(tidyverse)
theme_set(theme_light()) # feel free to set another theme
imdb <- read_csv("https://raw.githubusercontent.com/qntkhvn/36-315-summer26/refs/heads/master/data/imdb.csv")
```

Here is a description of the variables:

* `Title`: movie title
* `Directors`: movie director(s)
* `vote_date`: date of movie rating
* `day_of_week`: day of week for `vote_date`
* `weekend`: whether `vote_date` is on the weekend
* `ratings`: Low (0--4), Med (4--7), or High (8--10)
* `movie_period`: release period for movie: Retro (before 1981), Old (1981--2000), Modern (2001--2018)

## A (5pts) 

First, let us find the most frequent directors that appear in this dataset. Code is provided below.

```{r}
imdb |> 
  group_by(Directors) |> 
  summarize(count = n()) |> 
  filter(count == max(count))
```

What is the above code doing? In particular, what is the purpose of `filter(count == max(count))`?

**YOUR ANSWER HERE**

## B (5pts) 

We now examine the marginal distributions of the `movie_period` and `duration` variables. (A marginal distribution shows how a single variable is distributed on its own, ignoring any other variables in the dataset.)

First, let's calculate the counts, proportions, and percentages of each variable. 

The following code is provided for `duration`:

```{r}
# Get counts, proportions, and percentages for duration
duration_marginal <- imdb |>
  group_by(duration) |>
  summarize(count = n(), 
            total = nrow(imdb),
            proportion = round(count / total, 4),
            percentage = proportion * 100)
duration_marginal
```

Notice that within the `summarize()` function, we can sequentially define a new variable, and then refer to that new variable later on. For example, within `summarize()`, we first define a variable `total`, and then we refer to `total` when defining `proportion`.

Now write the same code for `movie_period`:

```{r}
# YOUR CODE HERE
```

Report your general observations in one sentence for each variable.

**YOUR ANSWER HERE**

## C (5pts) 

Besides frequency bar charts, marginal distributions are often communicated with proportions or percentages.

Modify the template code below to create a bar chart with one bar for each `duration`, where the bar length corresponds to the `percentage` of each duration. (Note that from part B, the percentages are stored in `duration_marginal`.)

Also, add appropriate titles, labels, and a non-default color.

```{r}
# fill in the ?s below to make the desired plot
# ? |>
#   ggplot(aes(x = ?, y = ?)) + 
#   geom_col()
```

Note that the code above uses `geom_col()`, since we want the lengths of the bars to represent values in the data. Read more about the differences between `geom_bar()` and `geom_col()` [here](https://ggplot2.tidyverse.org/reference/geom_bar.html).

## D (5pts) 

Your friend thinks there are equal proportions of short, medium, and long movies in this dataset. Using your bar chart from Part C, do you think your friend is right? (Use your common statistical sense. Given the sample size and the difference in the bars, is there possibly a significant difference?)

**YOUR ANSWER HERE**

## E (10pts) 

Let's test this statistically. Run a chi-squared test using `chisq.test(duration_marginal$?)` to check your friend's assertion. (Replace `?` with an appropriate variable.)

```{r}
# YOUR CODE HERE
```

* What is the p-value for this test?  

**YOUR ANSWER HERE**

* What is the formal conclusion (in-context) from this test?

**YOUR ANSWER HERE**

## F (5pts) 

It can be helpful to report p-values on graphs so it is clear whether the observed differences are statistically significant.

To annotate the p-value on the plot from Part C:

* Add `geom_text(x = ?, y = ?, label = ?)`. 

* Specify `x` and `y` as the x- and y-coordinates for the text, and `label` as the text itself in quotes. (Note: If one axis is categorical, specify the text coordinate as either one of the categories or as a number.)

* Specify `label` as the p-value from Part E (e.g., `label = "Chi-squared test p-value = ?"`), with ? appropriately specified. If the p-value is extremely small, it is fine to simply state `"Chi-squared test p-value approximately zero"`. If the text is too long, simply add `\n` somewhere inside the string to create a line break.

```{r}
# YOUR CODE HERE
```

\newpage

# Problem 2: Faceting (20 points)

In addition to visualizing a single categorical variable, we can also create the same visualization for different categories, thereby allowing for flexible multivariate graphics. This is known as "faceting," where the data is grouped according to some categorical variable, and then we create the same graphic for each group. The resulting graphs are typically displayed in a grid, where each graph is a single "facet" of the full graphic.

This is a popular way to show how the features of the variable(s) being displayed in a particular graphic can change depending on some other variable (usually a categorical variable).

## A (10pts) 

To create a bar chart of `ratings` faceted by `weekend`:

* First, create a bar chart of `ratings` the standard way (also use `royalblue` as the interior color for all bars).

* Then, add `facet_grid(~ weekend)`.

```{r}
# YOUR CODE HERE
```

In 2--3 sentences, briefly summarize the graph.

**YOUR ANSWER HERE**

## B (10pts) 

Next, use the code from Part A and add `margin = TRUE` within `facet_grid()`.

```{r}
# YOUR CODE HERE
```

The resulting plot should display a third facet with a bar chart, labeled as `(all)`. This displays the marginal distribution for which variable?

**YOUR ANSWER HERE**

\newpage

# Problem 3: Baby names (15 points)

The [`babynames`](https://hadley.github.io/babynames) package contains a dataset (also) named `babynames`, which contains information on baby names of each sex given each name from 1880 to 2017, provided by the United States Social Security Administration.

```{r}
# make sure to install the package by typing this into the Console
# install.packages("babynames")
library(babynames)
head(babynames)
```

## A (5pts)

Answer the following questions:

* How many observations and variables are in this dataset?

```{r}
# YOUR CODE HERE
```

**YOUR ANSWER HERE**

* How many columns are categorical? What are they?

**YOUR ANSWER HERE**

## B (10pts)

Use what you've learned from lectures so far about data wrangling and visualization to make the following plot:

* Display the popularity (in terms of frequency) of your own name (combination of first name and sex) over time. (Hint: use `geom_point()` and `geom_line()`).

* On the same plot, stick a thick, red, vertical dashed line at your birth year (Hint: look up the help documentation for `geom_vline()`).

```{r}
# YOUR CODE HERE
```

\newpage

# Problem 4: Functions (30 points)

Functions can be very useful when making visualizations, especially as the data structures get more complex.

The structure of a function has three basic parts:

* Inputs (or arguments)
* Body (code that is executed)
* Output (or return value)

In `R`, a function can be created using the following template:

```{r}
#| eval: false
name <- function(input1, input2, ...) {
  # body with code statements
  return(output)
}
```

## A (5pts)

Write a function called `abssum` that takes four inputs: `a`, `b`, `x`, and `y`, and returns the quantity $ax + b|y|$. Test your function and demonstrate that it works for three different combinations of the inputs.

```{r}
# YOUR CODE HERE
```

## B (5pts)

Type `abssum(x = 1, y = 1)` into the Console. What happens when you only specify these two arguments?

**YOUR ANSWER HERE**

## C (5pts)

Create a new function, `abssum2`, that has default values for `a = 1`, `b = 1`. Type `abssum2(x = 1, y = 1)` into your code block. What happens when you only specify the two arguments now?

```{r}
# YOUR CODE HERE
```

**YOUR ANSWER HERE**

## D (5pts)

Note that typing `1:10` in `R` produces a sequence of numbers from 1 to 10. (Try this in the Console.) What happens when you call the function with the following input: `abssum2(x = 1:10, y = 1:10)`? Why does this happen?

```{r}
# YOUR CODE HERE
```

**YOUR ANSWER HERE**

## E (5pts)

Use `help(rnorm)` to learn about the function `rnorm`, which generates normal random variables.

First, generate 5000 independent standard normal random variables (i.e., a normal distribution with mean 0 and variance 1) and assign them to a variable called `Z`.

```{r}
# YOUR CODE HERE
```

Next, repeat the same procedure and generate another 5000 independent standard normal random variables. Assign them to a variable called `W`.

```{r}
# YOUR CODE HERE
```

Then, uncomment the following code, which uses the base `R` `plot()` function to produce a scatterplot.

```{r}
# plot(W, abssum2(x = Z, y = W), cex = 0.5, pch = 16, xlab = "W", ylab = "Z + |W|")
```

Describe the graph that shows up, and explain why this happens.

**YOUR ANSWER HERE**

## F (5pts)

Now use `ggplot()` to create the same plot in Part E. Be sure to include a proper title and axis labels in your plot.

**Hint**: `ggplot()` requires all variables to be contained in a single dataset. So, create a data frame `D` with `D <- data.frame(V1 = W, V2 = abssum2(x = Z, y = W))`. Then, use this to make the scatterplot with `ggplot()`.

```{r}
# YOUR CODE HERE
```