Question

4. A potions instructor wants to investigate how he could reduce the number of explosions that occur in his class. He takes a single sample of students (n =13), and uses 3 different teaching methods on them throughout the semester. First, they experience teaching as usual, second, they experience teaching combined with examples of proper brewing procedure, and third, they experience teaching combined with a workshop on lab safety. The goal of the study was to see if any of the teaching methods differ from each other, and, if so, which ones are significantly different from each other (Tukey⁰sHSD = ±5.03). Conduct the appropriate ANOVA for these data (α =0.05) and calculate the percentage of variance explained by the IV (partial − η²). Assume that all assumptions for the test are met. (See table below for sample data.)

Teaching as usual	Teaching+examples	Teaching+safety training	General+Person totals
T =220	T =162	T =117	Σx2 =7753
SS =264.92	SS =113.23	SS =580	G =499
n =13	n =13	n =13	N =39
M =16.92	M =12.46	M =9	k =3 P2 Σ k =6644.33

Given all of this informations, the researchers obtained the following results table:

Source	SS	df	MS	F
Between treatments	410.21	2	136.74	4.7
Within	958.15	36
Between subjects	259.69	12
Error	698.46	24	29.1
Total	1368.36	38

They also found an effect size of partial − η² =0.37.

Answer 1

Null Hypothesis H0: The mean number of explosions are equal for all teaching methods.

Alternative Hypothesis Ha: Not all the mean number of explosions are equal for teaching methods.

Critical value of F at df = 2, 36 and 0.05 is 3.26

Since the observed test statistic (4.7) is greater than the critical value (3.26) , we reject H0 and conclude that there is a significant evidence that not all the mean number of explosions are equal for teaching methods.

Mean difference between Teaching as usual and Teaching+examples is 16.92 - 12.46 = 4.46

Mean difference between Teaching as usual and Teaching+safety training is 16.92 - 9 = 7.92

Mean difference between Teaching as usual and Teaching+examples is 12.46 - 9 = 3.46

Since the mean difference between Teaching as usual and Teaching+safety training is greater than Tukey0sHSD value of 5.03, there is significant difference in mean number of explosions between Teaching as usual and Teaching+safety training methods.

partial − η2 =0.37

The percentage of variance of number of explosions explained by the IV is 37%