N <- 42
post_test <- 
c(116.2, 116.9, 106.9, 104.6, 114.2, 113.6, 116.6, 114.8, 114.9,
111, 113.9, 115.6, 116.2, 119.6, 109.6, 122, 109.7, 112.4, 115.5, 119.7, 111.5,
95.5, 109.4, 94, 101, 115.3, 110.6, 96, 111.7, 115.9, 113.9, 114.4, 116.2,
115.7, 118, 110.9, 113.4, 111.2, 113.3, 115.9, 115.2, 110)
pre_test <- 
c(105.9, 100.8, 91.7, 97.5, 106.5, 107.4, 111.4, 110, 106.9, 106.7,
104.1, 109.7, 110.6, 115.2, 101.9, 119.8, 108.8, 104.6, 111.1, 115.5, 107.2,
81.2, 102.5, 78.4, 91.9, 110.3, 104.9, 89.7, 106.2, 106.2, 111.9, 109.4, 111.8,
112.1, 113.9, 106.3, 110.8, 107.5, 110, 111.6, 109.8, 102.6)
grade <- 
c(4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4)
treatment <- 
c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)