N <- 40
post_test <- 
c(92.8, 104.9, 88.9, 109.9, 98.9, 113.1, 114.1, 114, 114, 92.4,
111.1, 98.9, 112.2, 114.5, 110.3, 103.7, 110.8, 108.9, 109.6, 107.2, 110.6,
107.6, 90.5, 105.8, 110.6, 111.3, 107.1, 105.8, 111, 91.7, 102.9, 110.4, 115.3,
114.7, 110.2, 98.3, 101.9, 100.8, 111.6, 105.4)
pre_test <- 
c(77.6, 96.5, 64.2, 88.3, 88.6, 102.4, 105, 101.4, 102.6, 76.4, 98,
83.3, 100.8, 103.8, 100.7, 97, 97.3, 94.5, 97.7, 93.9, 103.7, 95.4, 68.6, 91.1,
97.8, 100.6, 99.6, 98.7, 104, 78, 95.3, 103.6, 108.1, 109.1, 98.9, 87.4, 92.5,
89, 100.6, 94)
grade <- 
c(3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3)
treatment <- 
c(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)