Introduction

If a student has previous knowledge in a topic that they are going to take a class on, then we would assume that they would perform better than those who do not have that knowledge. Here we will explore if this is the case in anatomy. To do this, we will compare the different test scores of students that said they have taken a class on anatomy before with those who say they have not.

anatomy <- read.csv("../Data/anatomy.csv", na.strings = c("", " ", "N/A"))

anatomyInPast <- filter(anatomy, anatomy.past %in% c("Yes","No") & 
                                 !is.na(Score.Exam.1) &
                                 !is.na(Score.Exam.2) &
                                 !is.na(In.Class.Exam))

Exam 1 Scores

palette(c("red", "green"))
boxplot(Score.Exam.1 ~ anatomy.past,
        data = anatomyInPast,
        ylim = c(0,100),
        col  = palette(),
        main = "Previous Experience with Anatomy\nIncreases Average Exam 1 Score",
        ylab = "Score",
        xlab = "Has Student Taken an Anatomy Class Before?")

anatomyInPast  %>% 
    group_by(anatomy.past)  %>% 
    summarise(Min    =      min(Score.Exam.1),  
              Q1     = quantile(Score.Exam.1, 0.25),
              Median =   median(Score.Exam.1),
              Q3     = quantile(Score.Exam.1, 0.75),
              Max    =      max(Score.Exam.1),
              "Sample Size" = n()) %>% 
   pander(caption = "Numerical Summary of Above")
Numerical Summary of Above
anatomy.past Min Q1 Median Q3 Max Sample Size
No 2 26 48 64 86 81
Yes 14 42 60 78 96 77 
pander(wilcox.test(Score.Exam.1 ~ anatomy.past,
                   data = anatomyInPast,
                   alternative = "less"))
Wilcoxon rank sum test with continuity correction: Score.Exam.1 by anatomy.past
Test statistic P value Alternative hypothesis
2110 0.000227 * * * less

The results of this test give us sufficient evidence to believe that students who have taken anatomy before will perform better on the first exam on average. Within this sample, those who had previous knowledge had a median score 12 points higher than those who did not—more than a whole letter grade better.


Exam 2 Scores

boxplot(Score.Exam.2 ~ anatomy.past,
        data = anatomyInPast,
        ylim = c(0,100),
        col  = palette(),
        main = "Previous Experience with Anatomy\nIncreases Average Exam 2 Score",
        ylab = "Score",
        xlab = "Has Student Taken an Anatomy Class Before?")

anatomyInPast  %>% 
    group_by(anatomy.past)  %>% 
    summarise(Min    =      min(Score.Exam.2),  
              Q1     = quantile(Score.Exam.2, 0.25),
              Median =   median(Score.Exam.2),
              Q3     = quantile(Score.Exam.2, 0.75),
              Max    =      max(Score.Exam.2),
              "Sample Size" = n()) %>% 
   pander(caption = "Numerical Summary of Above")
Numerical Summary of Above
anatomy.past Min Q1 Median Q3 Max Sample Size
No 0 16 26 42 74 81
Yes 6 28 40 58 86 77 
pander(wilcox.test(Score.Exam.2 ~ anatomy.past,
                   data = anatomyInPast,
                   alternative = "less"))
Wilcoxon rank sum test with continuity correction: Score.Exam.2 by anatomy.past
Test statistic P value Alternative hypothesis
2036 8.34e-05 * * * less

The results of this test are nearly the same. Just as it was with the first exam, on average, students with knowledge of anatomy before beginning the class performed significantly better on the second exam than others did. They performed so much better that their median score was 14 points higher than the others.


In-Class Exam Scores

boxplot(In.Class.Exam ~ anatomy.past,
        data = anatomyInPast,
        ylim = c(0,104),
        col  = palette(),
        main = "Previous Experience with Anatomy\nHas No Effect on Average In-Class Exam Score",
        ylab = "Score",
        xlab = "Has Student Taken an Anatomy Class Before?")

anatomyInPast  %>% 
    group_by(anatomy.past)  %>% 
    summarise(Min    =      min(In.Class.Exam),  
              Q1     = quantile(In.Class.Exam, 0.25),
              Median =   median(In.Class.Exam),
              Q3     = quantile(In.Class.Exam, 0.75),
              Max    =      max(In.Class.Exam),
              "Sample Size" = n()) %>% 
   pander(caption = "Numerical Summary of Above")
Numerical Summary of Above
anatomy.past Min Q1 Median Q3 Max Sample Size
No 22 74 92 96 104 81
Yes 20 75 88 97 104 77 
pander(wilcox.test(In.Class.Exam ~ anatomy.past,
                   data = anatomyInPast))
Wilcoxon rank sum test with continuity correction: In.Class.Exam by anatomy.past
Test statistic P value Alternative hypothesis
3357 0.4074 two.sided

Here, the results are a bit more interesting. Our results here tell us that there is no significant difference in the median scores between the two groups of students. In other words, if a student has taken a class on anatomy before, they are likely going to perform just as well as if they did not have previous experience. Interestingly, students who did not take an anatomy class before had a median score 4 points higher than those who did. However, this difference is very small and is not significant.

Possible reasons why both groups performed about the same might be because by the time the course was ending (assuming the in-class exam was towards the end of the semester) the students without experience “caught-up” to the others. Or perhaps the material on the in-class exam was simply more easily understood by all the students and the fact that some had over full marks didn’t allow for differences to appear. That is to say, if the exam was more difficult perhaps we would see differences similar to the first two exams.