Survei Sosial Umum

Inferensi untuk Data Kategorik di R

Andrew Bray

Assistant Professor of Statistics at Reed College

Penjelajah Data GSS, hanya footer

Penjelajah Data GSS, dengan orang mengobrol

Penjelajah Data GSS, dengan dunia

Penjelajah Data GSS, dunia dan panah

Penjelajah Data GSS, dengan orang

Menjelajahi GSS

library(dplyr)
glimpse(gss)

Observations: 3,300
Variables: 25
$ id       <dbl> 518, 1092, 2094, 229, 979, 554, 491, 319, 3143, 1...
$ year     <dbl> 1982, 1982, 1982, 1982, 1982, 1982, 1982, 1982, 1...
$ age      <fct> 49, 22, 26, 75, 71, 33, 56, 33, 69, 40, 44, 42, 5...
$ class    <fct> WORKING CLASS, WORKING CLASS, WORKING CLASS, LOWE...
$ degree   <fct> HIGH SCHOOL, HIGH SCHOOL, HIGH SCHOOL, LT HIGH SC...
$ sex      <fct> MALE, MALE, MALE, MALE, FEMALE, FEMALE, MALE, FEM...

$ happy    <fct> HAPPY, HAPPY, HAPPY, HAPPY, HAPPY, HAPPY, HAPPY, ...

Menjelajahi GSS

gss2016 <- filter(gss, year == 2016)

ggplot(gss2016, aes(x = happy)) +
  geom_bar()

Menjelajahi GSS

gss2016 <- filter(gss, year == 2016)

ggplot(gss2016, aes(x = happy)) +
  geom_bar()

Menjelajahi GSS

p_hat <- gss2016 %>%
  summarize(prop_happy = mean(happy == "HAPPY")) %>%
  pull()

p_hat

0.7733333

Interval kepercayaan 95% umum

$$(\hat{p} - 2 \times SE, \hat{p} + 2 \times SE)$$

Proporsi sampel plus/minus dua galat baku

Bootstrap

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Interval Kepercayaan Bootstrap

library(infer)
boot <- gss2016 %>%
  specify(response = happy, 
          success = “HAPPY”) %>%
  generate(reps = 500, 
           type = "bootstrap") %>%
  calculate(stat = "prop")

boot

Response: happy (factor)
# A tibble: 500 x 2
   replicate  stat
       <int> <dbl>
 1         1 0.827
 2         2 0.740
 3         3 0.780
 4         4 0.773
 5         5 0.747
 6         6 0.753

Interval Kepercayaan Bootstrap

ggplot(boot, aes(x = stat)) +
  geom_density()

Plot kerapatan stat bootstrap

Interval Kepercayaan Bootstrap

SE <- boot %>%
  summarize(sd(stat)) %>%
  pull()

SE

0.03482251

$$(\hat{p} - 2 \times SE, \hat{p} + 2 \times SE)$$

c(p_hat - 2 * SE, p_hat + 2 * SE)

0.7051883 0.8412784

Ayo berlatih!

Inferensi untuk Data Kategorik di R