Midterms Comparison

midterm1 <- c(33, 50, 51, 53, 54, 55, 57, 61, 62, 63, 63, 65, 67, 70, 72, 73, 
    73, 76, 77, 77, 79, 79, 79, 79, 80, 82, 83, 85, 87, 87, 88, 91, 92, 93, 
    94, 96, 96, 97, 98, 99, 99)
midterm2 <- c(19, 36, 46, 49, 49, 52, 60, 60, 61, 62, 65, 66, 66, 66, 66, 67, 
    67, 68, 69, 69, 70, 73, 76, 77, 78, 79, 79, 80, 82, 82, 83, 84, 84, 86, 
    87, 90, 96, 97)
midterm3 <- c(49, 61, 62, 65, 66, 68, 73, 73, 74, 74, 79, 79, 79, 80, 81, 83, 
    83, 84, 85, 85, 86, 86, 86, 87, 88, 89, 89, 92, 92, 92, 92, 93, 94, 95, 
    96, 100)


boxplot(midterm1, midterm2, midterm3, names = c("Midterm 1", "Midterm 2", "Midterm 3"), 
    xlab = "Grades", horizontal = TRUE, col = "lightgray")

Data <- data.frame(Grades = c(midterm1, midterm2, midterm3), Midterm = factor(rep(c("Midterm 1", 
    "Midterm 2", "Midterm 3"), times = c(length(midterm1), length(midterm2), 
    length(midterm3)))))
fm1 <- aov(Grades ~ Midterm, data = Data)
anova(fm1)

## Analysis of Variance Table
## 
## Response: Grades
##            Df Sum Sq Mean Sq F value Pr(>F)   
## Midterm     2   2684    1342    6.09 0.0031 **
## Residuals 112  24664     220                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

ANOVA Re-considered

Here is the same analysis with all of the grades from students who dropped the course removed.

midterm1 <- c(53, 54, 55, 57, 61, 63, 65, 67, 70, 72, 73, 73, 76, 77, 77, 79, 
    79, 79, 79, 80, 82, 83, 85, 87, 87, 88, 91, 92, 93, 94, 96, 96, 97, 98, 
    99, 99)
midterm2 <- c(36, 46, 49, 49, 60, 60, 61, 62, 65, 66, 66, 66, 66, 67, 67, 68, 
    69, 69, 70, 73, 76, 77, 78, 79, 79, 80, 82, 82, 83, 84, 84, 86, 87, 90, 
    96, 97)
midterm3 <- c(49, 61, 62, 65, 66, 68, 73, 73, 74, 74, 79, 79, 79, 80, 81, 83, 
    83, 84, 85, 85, 86, 86, 86, 87, 88, 89, 89, 92, 92, 92, 92, 93, 94, 95, 
    96, 100)


boxplot(midterm1, midterm2, midterm3, names = c("Midterm 1", "Midterm 2", "Midterm 3"), 
    xlab = "Grades", horizontal = TRUE, col = "lightgray")

Data <- data.frame(Grades = c(midterm1, midterm2, midterm3), Midterm = factor(rep(c("Midterm 1", 
    "Midterm 2", "Midterm 3"), times = c(length(midterm1), length(midterm2), 
    length(midterm3)))))
fm1 <- aov(Grades ~ Midterm, data = Data)
anova(fm1)

## Analysis of Variance Table
## 
## Response: Grades
##            Df Sum Sq Mean Sq F value Pr(>F)   
## Midterm     2   2030    1015    6.01 0.0034 **
## Residuals 105  17745     169                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1