Sampling

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

  1. Load the R packages we will use.
  1. Quiz Questions

Question:

7.2.4 in ModernDive with different sample sizes and repetitions

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

Segment 1: Sample size = 26

1a.) Take 1180 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 = 1180)

1b.) Compute resulting 1180 replicates of proportion red

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

1c.) Plot distribution of virtual_prop_red_26 via a histogram use labs to

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 = 55

2a.) Take 1180 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 = 1180)

2b.) Compute resulting 1180 replicates of proportion red

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

2c.) Plot distribution of virtual_prop_red_55 via a histogram uses labs to

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 = 110

3a.) Take 1180 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 = 1180)

3b.) Compute resulting 1180 replicates of proportion red

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

3c.) Plot distribution of virtual_prop_red_110 via a histogram use labs to

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", "2022-04-12-sampling"))

Calculate the standard deviations for your three sets of 1180 values of prop_red using the standard deviation

n = 26

virtual_prop_red_26  %>%
  summarize(sd = sd(prop_red))
# A tibble: 1 × 1
      sd
   <dbl>
1 0.0930

n = 55

virtual_prop_red_55  %>%
  summarize(sd = sd(prop_red))
# A tibble: 1 × 1
      sd
   <dbl>
1 0.0649

n = 110

virtual_prop_red_110  %>%
  summarize(sd = sd(prop_red))
# A tibble: 1 × 1
      sd
   <dbl>
1 0.0454

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