Question

An independent-measures research study compares three treatment conditions using a sample of n = 5 in each treatment. For this study, the three sample means are, M1 = 1, M2 = 2, and M3 = 3. For the ANOVA, what value would be obtained for SSbetween?​

a. ​30b. ​20c. ​10d. 2

Answer 1

Answer: c. ​10

Explanation:

Given : An independent-measures research study compares three treatment conditions using a sample of n = 5 in each treatment.

For this study, the three sample means are, M1 = 1, M2 = 2, and M3 = 3.

Grand mean =
`\overline{X}=(M1+M2+M3)/(3)` [All sample have equal elements]

`=(1+2+3)/(3)=2`

For ANOVA,

`SS_(between)=n\sum(M_i-\overline{X})^2` , where i= 1, 2 , 3

`SS_(between)=5((1-2)^2+(2-2)^2+((3-2)^2)`

`SS_(between)=5((-1)^2+(0)^2+((1)^2)= 5(1+1)=10`

Hence,the value would be obtained for
`SS_(between)=10` .

hence, the correct answer = c. ​10