Question

An oxperiment has a single factor wth three groups and three values in each group. In determining the among-group variation, there are 2 degrees of freedom. in determining the wtin-group variation, there are 6 degrees of freedom. In delermining the total variation, there are 8 degrees of freedom

a. If SSA=36 and SST=72. what is SSW ?
b. What is MSA?
c. What is MSW?
d. What is the value of Fswe?

Answer 1

To solve the ANOVA problem, SSW is computed to be 36, MSA is 18, MSW is 6, and the F statistic is 3.

Step-by-step explanation:

The student is asking a one-way Analysis of Variance (ANOVA) question. To find the within-group variation (SSW), total variation (SST), and the among-group variation (SSA), the following formulas and concepts from ANOVA are used:

• SST = SSA + SSW (Total Sum of Squares = Sum of Squares Among + Sum of Squares Within)
• MSA = SSA / dfamong (Mean Square Among = Sum of Squares Among / degrees of freedom among)
• MSW = SSW / dfwithin (Mean Square Within = Sum of Squares Within / degrees of freedom within)
• Fstatistic = MSA / MSW (F Ratio = Mean Square Among / Mean Square Within)

Given that SSA = 36 and SST = 72, and using the degrees of freedom provided:

1. SSW (Sum of Squares Within) is found using the equation SST = SSA + SSW. Since SST = 72 and SSA = 36, SSW = SST - SSA, which gives SSW = 72 - 36 = 36.
2. MSA (Mean Square Among) is found by dividing SSA by its degrees of freedom (dfamong). Since SSA = 36 and dfamong = 2, MSA = 36 / 2 = 18.
3. MSW (Mean Square Within) is calculated by dividing SSW by its degrees of freedom (dfwithin). Since SSW = 36 and dfwithin = 6, MSW = 36 / 6 = 6.
4. Fstatistic is calculated as MSA / MSW. Therefore, F = 18 / 6 = 3.