When only two treatments are involved, ANOVA and the Student t test (Chapter 11)

Question

When only two treatments are involved, ANOVA and the Student t test (Chapter 11) result in the same conclusions. Also, . As an example, suppose that 14 randomly selected students were divided into two groups, one consisting of 6 students and the other of 8. One group was taught using a combination of lecture and programmed instruction, the other using a combination of lecture and television. At the end of the course, each group was given a 50-item test. The following is a list of the number correct for each of the two groups. Using analysis of variance techniques, test the null hypothesis, that the two mean test scores are equal.

Lecture and
Programmed
Instruction Lecture and
Television
15 34
15 22
23 39
27 21
16 27
13 28
24
24

Explanation / Answer

mean for Lecture and Programmed Instruction=(15+15+23+27+16+13+24+24)/8 =19.625
mean for Lecture and Television =(34+22+39+21+27+28)/6 =28.5

for Lecture and Programmed Instruction=(4.625+4.625+3.375+7.375+3.625+6.625+4.375+4.375)/8 =4.875 =2.2

for Lecture and Television=5.33 =2.3

to test for null hypothesis

z for Lecture and Programmed Instruction=19.625/ *8 =25.23

z for  Lecture and Television=28.5/ *6 =30.35

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