Sampling

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

Intro

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

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7.24 in ModernDive

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 30

1.a) Take 1200 samples of size of 30 instead of 1000 replicates of size 25 from the bowl dataset. Assign the output to virtual_samples_30

virtual_samples_30 <- bowl %>%
  rep_sample_n(size=30, reps = 1200)

1.b) Compute resulting 1200 replicates of proportion red

• start with virtual_samples_30 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 / 30
• Assign the output to virtual_prop_red_30

virtual_prop_red_30 <- virtual_samples_30 %>%
  group_by(replicate) %>%
  summarize(red = sum(color == "red")) %>%
  mutate(prop_red = red / 30)

1.c) Plot distribution of virtual_prop_red_30 via a histogram use labs to

• Label x axis = “Proportion of 30 balls that were red”
• create title = “30”

ggplot(virtual_prop_red_30, aes(x=prop_red)) + 
  geom_histogram(binwidth = 0.05, boundary = 0.4, color = "white") +
  labs(x = "Proportion of 30 balls that were red", title = "30")

ggsave(filename= "preview.png",
       path = here::here("_posts", "2022-04-19-sampling"))

---

Segment 2: Sample size = 55

2.a) Take 1200 samples of size of 55 instead of 1000 replicates of size 50. Assign the output to virtual_samples_55

virtual_samples_55 <- bowl %>%
  rep_sample_n(size = 55, reps = 1200)

2.b) Computer resulting 1200 replicates of proportion red

• start with virtual_samples_55 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 / 55
• Assign the output to virtual_prop_red_55

virtual_prop_red_55 <- virtual_samples_55 %>%
  group_by(replicate) %>%
  summarize(red = sum(color == "red")) %>%
  mutate(prop_red = red / 55)

2.c) Plot distribution of virtual_prop_red_55 via a histogram

use labs to

• Label x axis = “Proportion of 55 balls that were red”
• create title = “55”

ggplot(virtual_prop_red_55, aes(x= prop_red)) +
  geom_histogram(binwidth = 0.05, boundary = 0.4, color = "white") +
  labs(x = "Proportion of 55 balls that were red", title = "55")

---

Segment 3: sample size = 120

3.a) Take 1200 samples of size of 120 instead of 1000 replicates of size 50. Assign the output to virtual_samples_120

virtual_samples_120 <- bowl %>%
  rep_sample_n(size=120, reps = 1200)

3.b) Compute resulting 1200 replicates of proportion red

• Start with virtual_samples_120 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 / 120
• Assign the output to virtual_prop_red_120

virtual_prop_red_120 <- virtual_samples_120 %>%
  group_by(replicate) %>%
  summarize(red = sum(color == "red")) %>%
  mutate(prop_red = red / 120 )

3.c) Plot distribution of virtual_prop_red_120 via a histogram use labs to

• label x axis = “Proportion of 120 balls that were red”
• create title = “120”

ggplot(virtual_prop_red_120, aes(x = prop_red)) +
  geom_histogram(binwidth = 0.05, boundary = 0.4, color = "white") + 
  labs(x = "Proportion of 120 balls that were red", title = "120")

---

Standard Dev

Calculate the standard deviations for your three sets of 1200 values of prop_red using the standard deviation

n = 30

virtual_prop_red_30 %>%
  summarize(sd = sd(prop_red))

# A tibble: 1 x 1
      sd
   <dbl>
1 0.0868

n = 55

virtual_prop_red_55 %>%
  summarize(sd = sd(prop_red))

# A tibble: 1 x 1
      sd
   <dbl>
1 0.0652

n=120

virtual_prop_red_120 %>%
  summarize(sd = sd(prop_red))

# A tibble: 1 x 1
      sd
   <dbl>
1 0.0429

The distribution with sample size, n=120, has the smallest standard deviation (spread) around the estimated proportion of balls.