Given four classes, each with a different number of students: Class A: 41 students; Class B: 39 students; Class C: 38 students; Class D: 30 students; Each class took an exam and garnered the following average scores: Class A: 27.80; Class B: 18.87; Class C: 19.24; Class D: 21.00; If each class were ranked according to who got the highest average score, how should the calculation go about? P.S. It's fairly obvious that Class A would be ranked as first. However, I can't say the same for the other three. Though Class D has the second highest average, it has only 30 students, which may make a direct comparison with Classses B and C unfair.
asked Feb 9, 2018 at 5:48 John Vincent Rañopa John Vincent Rañopa 21 1 1 bronze badgeThis question conflates population and sample.
If your question is, as you state what order they would be in by average score then that is easy: A, D, C, B. Class size doesn't matter and no inferential statistics need be done as you have the whole populations. You've already done all the necessary calculations.
Proposals about ANOVA or whatever would be about whether the differences are significant, and about how much sampling error there is. These are inferential questions, they presuppose that the classes are random samples from four different populations. That seems unlikely, but possible: If, every year, classes are split according to the same formula, then I guess it's possible to argue that these are a sample.
answered Jan 8 at 23:17 Peter Flom Peter Flom 125k 36 36 gold badges 182 182 silver badges 414 414 bronze badges $\begingroup$Since your smallest sample size for a group is 30, you can probably just use ANOVA first to establish there is a difference in average score between classes, as your unequal sample size is not a huge departure from the model assumptions. Once you have this, you can conduct pair-wise t-test between classes, adjusted for multiple comparison (Tukey, Bonferonni, etc).
If you want to be really rigorous, you can conduct the nonparametric "ANOVA" -- Kruskal-wallis test, followed by pair-wise rank-sum test between classes, adjusting for multiple comparison.
answered Feb 9, 2018 at 6:33 161 8 8 bronze badgesTo subscribe to this RSS feed, copy and paste this URL into your RSS reader.
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