EDA for vocabulary score vs. social class

Before we conduct inference, we should take a look at the distributions of vocabulary scores across the levels of 
(self identified) social class.

* Make this a histogram, using an appropriate binwidth. Facet this histogram, wrapping by social class level.


>
glimpse(gss)
Rows: 795
Columns: 2
$ wordsum <int> 6, 9, 6, 5, 6, 6, 8, 10, 8, 9, 7, 10, 3, 8, 3, 2, 6, 1, 9, ...
$ class   <chr> "MIDDLE", "WORKING", "WORKING", "WORKING", "WORKING", "WORK...

# Using gss, plot wordsum
ggplot(gss, mapping = aes(x = wordsum)) +
  # Add a histogram layer
  geom_histogram(binwidth = 1) +
  # Facet by class
  facet_wrap(~class)

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ANOVA for vocabulary score vs. (self identified) social class

Let's conduct the ANOVA for evaluating whether there is a difference in the average vocabulary scores between the levels of (self identified) social class.


# Run an analysis of variance on wordsum vs. class
aov_wordsum_class <- aov(wordsum ~ class, gss)

# Tidy the model
tidy(aov_wordsum_class)

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Checking the constant variance condition

In addition to checking the normality of distributions of vocabulary scores across levels of social class, we need to check that the
variances from each are roughly constant.

gss %>%
  # Group by class
  group_by(class) %>%
  # Calculate the std dev of wordsum as std_dev_wordsum
  summarize(std_dev_wordsum = sd(wordsum))

# A tibble: 4 x 2
  class   std_dev_wordsum
  <chr>             <dbl>
1 LOWER              2.24
2 MIDDLE             1.89
3 UPPER              2.34
4 WORKING            1.87

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Compare pairwise means

Compare means of vocabulary scores using the pairwise.t.test() function for all pairings of social classes.

* Conduct a pairwise t-test on vocabulary scores and social class. Set p.adjust.method to "none" 
  (we'll adjust the significance level, not the p-value).


# Run a pairwise t-test on wordsum and class, without adjustment
t_test_results <- pairwise.t.test(gss$wordsum, gss$class, p.adjust.method = "none")

# Tidy the result
tidy(t_test_results)