Sampling

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

  1. Load the R package we will use. 
    library(tidyverse)
library(moderndive)

Question:

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

Segment 1: sample size = 26

1.a) Take 1100 samples of size of 26 instead of 1000 replicates of size 25 from the bowl dataset. Assign the output to virtual_samples_26

virtual_samples_26 <- bowl %>% 
  rep_sample_n(size = 26, reps = 1100)

1.b) Compute resulting 1100 replicates of proportion red

-start with virtual_samples_26 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 / 26 -Assign the output to virtual_prop_red_26

virtual_prop_red_26 <- virtual_samples_26 %>% 
  group_by(replicate) %>% 
  summarize(red = sum(color == "red")) %>% 
  mutate(prop_red = red / 26)

1.c) Plot distribution of virtual_prop_red_26 via a histogram

use labs to

-label x axis = “Proportion of 26 balls that were red” -create title = “26”

ggplot(virtual_prop_red_26, aes(x = prop_red)) +
  geom_histogram(binwidth = 0.05, boundary = 0.4, color = "white") +
  labs(x = "Proportion of 26 balls that were red", title = "26")

Segment 2: sample size = 57

2.a) Take 1100 samples of size of 57 instead of 1000 replicates of size 50. Assign the output to virtual_samples_57

virtual_samples_57 <- bowl %>% 
  rep_sample_n(size = 57, reps = 1100)

2.b) Compute resulting 1100 replicates of proportion red

-start with virtual_samples_57 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 / 57 -Assign the output to virtual_prop_red_57

virtual_prop_red_57 <- virtual_samples_57 %>% 
  group_by(replicate) %>% 
  summarize(red = sum(color == "red")) %>% 
  mutate(prop_red = red / 57)

2.c) Plot distribution of virtual_prop_red_57 via a histogram

use labs to

-label x axis = “Proportion of 57 balls that were red” -create title = “57”

ggplot(virtual_prop_red_57, aes(x = prop_red)) +
  geom_histogram(binwidth = 0.05, boundary = 0.4, color = "white") +
  labs(x = "Proportion of 57 balls that were red", title = "57")

Segment 3: sample size = 110

3.a) Take 1100 samples of size of 110 instead of 1000 replicates of size 50. Assign the output to virtual_samples_110

virtual_samples_110 <- bowl %>% 
  rep_sample_n(size = 110, reps = 1100)

3.b) Compute resulting 1100 replicates of proportion red

start with virtual_samples_110 group_by replicate THEN create variable red equal to the sum of all the red balls create variable prop_red equal to variable red / 110 Assign the output to virtual_prop_red_110

virtual_prop_red_110 <- virtual_samples_110 %>% 
  group_by(replicate) %>% 
  summarize(red = sum(color == "red")) %>% 
  mutate(prop_red = red / 110)

3.c) Plot distribution of virtual_prop_red_110 via a histogram

use labs to

-label x axis = “Proportion of 110 balls that were red” -create title = “110”

ggplot(virtual_prop_red_110, aes(x = prop_red)) +
  geom_histogram(binwidth = 0.05, boundary = 0.4, color = "white") +
  labs(x = "Proportion of 110 balls that were red", title = "110")

ggsave(filename = "preview.png",
       path = here::here("_posts", "2021-05-04-sampling"))

Calculate the standard deviations for your three sets of 1100 values of prop_red using the standard deviation

n = 26

virtual_prop_red_26 %>% 
  summarize(sd = sd(prop_red))

# A tibble: 1 x 1
      sd
   <dbl>
1 0.0959

n = 57

virtual_prop_red_57 %>% 
  summarize(sd = sd(prop_red))

# A tibble: 1 x 1
      sd
   <dbl>
1 0.0632

n = 110

virtual_prop_red_110 %>% 
  summarize(sd = sd(prop_red))

# A tibble: 1 x 1
      sd
   <dbl>
1 0.0458

The distribution with sample size, n = 110, has the smallest standard deviation (spread) around the estimated proportion of red balls.