Conditioning

STAT 20: Introduction to Probability and Statistics

Concept Questions

This is a code heavy day, so it can be helpful to write up the names of the key dplyr verbs - mutate, arrange, select, filter, summarize, group_by - on side boards at the beginning when write short definitions as they come up. They can serve as references for the rest of the class period.

It can also be helpful to have RStudio open so that you can copy and paste from these cells into RStudio and run them.

c("fruit", "fruit", "vegetable") == "fruit"

What will this line of code return?

01:00

Evaluating equivalence, cont.

In R, this evaluation happens element-wise when operating on vectors.

c("fruit", "fruit", "vegetable") == "fruit"

[1]  TRUE  TRUE FALSE

c("fruit", "fruit", "vegetable") != "fruit"

[1] FALSE FALSE  TRUE

c("fruit", "vegetable", "boba") %in% c("fruit", "vegetable")

[1]  TRUE  TRUE FALSE

Question 2

class_survey |>
  filter(coding_exp_scale < 3,
         olympics %in% c("Ice skating", "Speed skating"),
         is_entrepreneur == TRUE)

Which observations will be included in the following data frame?

01:00

Question 3

Which data frame will have fewer rows?

# A
filter(class_survey, time_at_cal == "This is my first semester!")

# B
class_survey |>
  mutate(first_sem = (time_at_cal == "This is my first semester!")) |>
  filter(first_sem)

01:00

Building data pipelines

Consider the subset of students here:

class_survey |>
  filter(coding_exp_scale < 3,
         olympics %in% c("Ice skating", "Speed skating"),
         is_entrepreneur == TRUE)

How do we extract the average of these students’ chance that class will be disrupted by a new COVID variant?

Let’s look at three different ways to answer this question

Nesting

filter(class_survey, 
       coding_exp_scale < 3,
       olympics %in% c("Ice skating", "Speed skating"),
       is_entrepreneur == TRUE)

This set of slides walks through the three different approaches to stringing together functions in R, identifies the pros and cons of each, and encourages students to use the pipe.

Nesting

select(filter(class_survey, 
       coding_exp_scale < 3,
       olympics %in% c("Ice skating", "Speed skating"),
       is_entrepreneur == TRUE),
       coding_exp_xcale,
       olympics,
       is_entrepreneur,
       covid)

Nesting

summarize(select(filter(class_survey, 
       coding_exp_scale < 3,
       olympics %in% c("Ice skating", "Speed skating"),
       is_entrepreneur == TRUE),
       coding_exp_scale,
       olympics,
       is_entrepreneur,
       covid),
       covid_avg = mean(covid))

Nesting

summarize(select(filter(class_survey, 
       coding_exp_scale < 3,
       olympics %in% c("Ice skating", "Speed skating"),
       is_entrepreneur == TRUE),
       coding_exp_scale,
       olympics,
       is_entrepreneur,
       covid),
       covid_avg = mean(covid))

# A tibble: 1 × 1
  covid_avg
      <dbl>
1     0.428

Nesting

summarize(select(filter(class_survey, 
       coding_exp_scale < 3,
       olympics %in% c("Ice skating", "Speed skating"),
       is_entrepreneur == TRUE),
       coding_exp_scale,
       olympics,
       is_entrepreneur,
       covid),
       covid_avg = mean(covid))

Cons

• Must be read from inside out 👎
• Hard to keep track of arguments 👎

Pros

• All in one line of code 👍
• Only refer to one data frame 👍

Step-by-step

df1 <- filter(class_survey, 
              coding_exp_scale < 3,
              olympics %in% c("Ice skating", "Speed skating"),
              is_entrepreneur == TRUE)
df2 <- select(df1, 
              coding_exp_scale,
              olympics,
              is_entrepreneur,
              covid)
summarize(df2,
          covid_avg = mean(covid))

Cons

• Have to repeat data frame names 👎
• Creates unnecessary objects 👎

Pros

• Stores intermediate objects 👍
• Can be read top to bottom 👍

Using the pipe operator

class_survey |>
  filter(coding_exp_scale < 3,
         olympics %in% c("Ice skating", "Speed skating"),
         is_entrepreneur == TRUE) |>
  select(coding_exp_scale,
         olympics,
         is_entrepreneur,
         covid) |>
  summarize(covid_avg = mean(covid))

Cons

• 🤷

Pros

• Can be read like an english paragraph 👍
• Only type the data once 👍
• No leftovers objects 👍

Understanding your pipeline

It’s good practice to understand the output of each line of code by breaking the pipe.

class_survey |>
  select(covid) |>
  filter(time_at_cal == "It's my first time_at_cal.")

Error in `filter()`:
ℹ In argument: `time_at_cal == "It's my first time_at_cal."`.
Caused by error:
! object 'time_at_cal' not found

class_survey |>
  select(covid)

# A tibble: 816 × 1
   covid
   <dbl>
 1  0   
 2  0.5 
 3  0.6 
 4  0.7 
 5 NA   
 6  0.15
 7  0.7 
 8  0   
 9  0.8 
10 NA   
# ℹ 806 more rows

Concept Question

class_survey |> # A #<<
  filter(coding_exp_scale < 3,
         olympics %in% c("Ice skating", 
                         "Speed skating"),
         is_entrepreneur == TRUE) |> # B #<<
  select(coding_exp_scale,
         olympics,
         is_entrepreneur,
         covid) |> # C #<<
  summarize(covid_avg = mean(covid)) # D #<<

# note
dim(class_survey)

[1] 816  30

What are the dimensions (rows x columns) of the data frames output at each stage of this pipe?

01:00

summarize(class_survey,
          mean(time_at_cal == "I'm in my first year.", na.rm = TRUE))

What is will this line of code return?

01:00

This will return the proportion of students who answered “I’m in my first year”. This is surprising to students because it’s not immediately clear that a mean of a logical vector is the same as the proportion of cases that are true. ::

Boolean Algebra

Logical vectors have a dual representation as TRUE FALSE and 1, 0, so you can do math on logicals accordingly.

TRUE + TRUE

[1] 2

TRUE * TRUE

[1] 1

Taking the mean of a logical vector is equivalent to find the proportion of rows that are TRUE (i.e. the proportion of rows that meet the condition).

Worksheet: Conditioning

20:00

Break

05:00

Lab Part I: Flights

25:00