Analysis

Warning: package 'brms' was built under R version 4.4.1

Warning: package 'tidybayes' was built under R version 4.4.1

Rows: 6325 Columns: 6
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
dbl (6): race, classtype, yearssmall, hsgrad, g4math, g4reading

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: g4math ~ kinder 
   Data: x (Number of observations: 1582) 
  Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
         total post-warmup draws = 4000

Regression Coefficients:
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept       709.18      1.56   706.13   712.31 1.00     4180     2899
kinderregular     0.38      2.14    -3.86     4.50 1.00     4811     3382

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma    42.25      0.75    40.80    43.75 1.00     4523     3151

Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

Using 10 posterior draws for ppc type 'dens_overlay' by default.

# A tibble: 8,000 × 6
# Groups:   kinder, .row [2]
   kinder  .row .chain .iteration .draw .epred
   <chr>  <int>  <int>      <int> <int>  <dbl>
 1 small      1     NA         NA     1   709.
 2 small      1     NA         NA     2   708.
 3 small      1     NA         NA     3   711.
 4 small      1     NA         NA     4   709.
 5 small      1     NA         NA     5   707.
 6 small      1     NA         NA     6   707.
 7 small      1     NA         NA     7   710.
 8 small      1     NA         NA     8   710.
 9 small      1     NA         NA     9   710.
10 small      1     NA         NA    10   709.
# ℹ 7,990 more rows

Formula: \[ score_i = \beta_0 + \beta_1 class\_size \]

Question: How does class size in K-4 school classes affect student performances? (Causal Affect)

Quantity of Interest: Student Scores

Preceptor Table: Units- Each Student Outcome- g4math Covariate- YearsSmall, classtype Treatment- Different Class Size

Population Table: Time- Year

4 Key Assumptions with one counter for each: Validity- Math scores calculated differently across schools in the US Stability- Education System is different in diffferent schools and times Unconfoundedness- Schools selected are schools in districts that have better grades Representativeness- Only data in Tenessee which doesn’t represent the US