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

Step-by-step 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 = $\overline{X}=\dfrac{M1+M2+M3}{3}$ [All sample have equal elements]

$=\dfrac{1+2+3}{3}=2$

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