Sampling

Based on Chapter 7 of ModernDive. Code for Quiz 11.

1. Load the R packages we will use.

library(tidyverse)
library(moderndive) 

2. Quiz questions

• Replace all the instances of ‘SEE QUIZ’. These are inputs from your moodle quiz.
• Replace all the instances of ‘???’. These are answers on your moodle quiz.
• Run all the individual code chunks to make sure the answers in this file correspond with your quiz answers
• After you check all your code chunks run then you can knit it. It won’t knit until the ??? are replaced
• The quiz assumes that you have watched the videos and worked through the examples in Chapter 7 of ModernDive

---

Question: 7.2.4 in Modern Dive with different sample sizes and repetitions

• Make sure you have installed and loaded the tidyverse and the moderndive packages
• Fill in the blanks
• Put the command you use in the Rchunks in your Rmd file for this quiz.

Modify the code for comparing different sample sizes from the virtual bowl

Segment 1: sample size = 28

1.a) Take 1150 samples of size of 28 instead of 1000 replicates of size 25 from the bowl dataset. Assign the output to virtual_samples_28

virtual_samples_28  <- bowl  %>% 
rep_sample_n(size = 28, reps = 1150)

1.b) Compute resulting 1150 replicates of proportion red

• start with virtual_samples_28 THEN

• group_by replicate THEN

• create variable red equal to the sum of all the red balls

• create variable prop_red equal to variable red / 28

• Assign the output to virtual_prop_red_28

virtual_prop_red_28 <- virtual_samples_28 %>% 
  group_by(replicate) %>% 
  summarize(red = sum(color == "red")) %>% 
  mutate(prop_red = red / 28)

1.c) Plot distribution of virtual_prop_red_28 via a histogram use labsto label

• x axis = “Proportion of 28 balls that were red”

• create title =“28”

ggplot(virtual_prop_red_28, aes(x = prop_red)) +
  geom_histogram(binwidth = 0.05, boundary = 0.4, color = "white") +
  labs(x = "Proportion of 28 balls that were red", title = "28") 

---

Segment 2: sample size = 53

2.a) Take 1150 samples of size of 53 instead of 1000 replicates of size 50.

Assign the output to virtual_samples_53

virtual_samples_53  <- bowl  %>% 
rep_sample_n(size = 53, reps = 1150)

2.b) Compute resulting 1150 replicates of proportion red

• start with virtual_samples_53 THEN

• group_by replicate THEN

• create variable red equal to the sum of all the red balls

• create variable prop_red equal to variable red / 53

• Assign the output to virtual_prop_red_53

virtual_prop_red_53 <- virtual_samples_53 %>% 
  group_by(replicate) %>% 
  summarize(red = sum(color == "red")) %>% 
  mutate(prop_red = red / 53)

2.c) Plot distribution of virtual_prop_red_53 via a histogram use labs to

• label x axis = “Proportion of 53 balls that were red”

• create title = “53”

ggplot(virtual_prop_red_53, aes(x = prop_red)) +
  geom_histogram(binwidth = 0.05, boundary = 0.4, color = "white") +
  labs(x = "Proportion of 53 balls that were red", title = "53")

---

Segment 3: sample size = 118

3.a) Take 1150 samples of size of 118 instead of 1000 replicates of size 50.

Assign the output to virtual_samples_118

virtual_samples_118  <- bowl  %>% 
rep_sample_n(size = 118, reps = 1150)

3.b) Compute resulting 1150 replicates of proportion red

• start with virtual_samples_118 THEN

• group_by replicate THEN

• create variable red equal to the sum of all the red balls

• create variable prop_red equal to variable red / 118

• Assign the output to virtual_prop_red_118

virtual_prop_red_118 <- virtual_samples_118 %>% 
  group_by(replicate) %>% 
  summarize(red = sum(color == "red")) %>% 
  mutate(prop_red = red / 118)

3.c) Plot distribution of virtual_prop_red_118 via a histogram use labs to

• label x axis = “Proportion of 118 balls that were red”

• create title = “118”

ggplot(virtual_prop_red_118, aes(x = prop_red)) +
  geom_histogram(binwidth = 0.05, boundary = 0.4, color = "white") +
  labs(x = "Proportion of 118 balls that were red", title = "118")

ggsave(filename = "preview.png", 
       path = here::here("_posts", "2022-04-14-sampling"))

---

Calculate the standard deviations for your three sets of 1150 values of prop_red using the standard deviation

n = 28

virtual_prop_red_28 %>% 
  summarize(sd = sd(prop_red))

# A tibble: 1 × 1
      sd
   <dbl>
1 0.0916

n = 53

virtual_prop_red_53 %>% 
  summarize(sd = sd(prop_red))

# A tibble: 1 × 1
      sd
   <dbl>
1 0.0667

n = 118

virtual_prop_red_118 %>% 
  summarize(sd = sd(prop_red))

# A tibble: 1 × 1
      sd
   <dbl>
1 0.0443

The distribution with sample size, n = 118, has the smallest standard deviation (spread) around the estimated proportion of red balls.