By NEAS - 7/2/2024 3:46:43 PM
MS Module 11 Single-Factor ANOVA practice exam questions
(The attached PDF file has better formatting.)
[The practice problems in the 24 modules explain the statistical procedures; the practice exam questions in this thread shows what you will be asked on the final exam.]
A experiment has three groups and four observations in each group.
obsv → 1 2 3 4
group 1 14 22 16 14
group 2 12 15 14 25
group 3 7 17 24 32
The groups are normally distributed with the same variance.
The null hypothesis is that the means of the groups are the same: H0: μ1 = μ2 = μ3
Question 10.1: Square of the sum of the observations
What is the square of the sum of all the observations, or x..2 ?
Answer 10.1: (14 + 22 + 16 + 14 + 12 + 15 + 14 + 25 + 7 + 17 + 24 + 32)2 = 44,944
Question 10.2: Sum of the squares of the observations
What is the sum of the squares of all the observations, or i j xij2 ?
Answer 10.2: 142 + 222 + 162 + 142 + 122 + 152 + 142 + 252 + 72 + 172 + 242 + 322 = 4,260
Question 10.3: Total sum of squares
What is SST, the total sum of squares?
Answer 10.3: 4,260 – 44,944 / 12 = 514.67
(the total sum of squares = the sum of the squares of all the observations – the square of the sum of all the observations / the number of observations)
Question 10.4: Sums of squares of group totals
What is the sum of squares of the group totals?
Answer 10.4: (14 + 22 + 16 + 14)2 + (12 + 15 + 14 + 25)2 + (7 + 17 + 24 + 32)2 = 15,112
Question 10.5: Treatment sums of squares
What is SSTr, the treatment sum of squares?
Answer 10.5: 15,112 / 4 – 44,944 / 12 = 32.67
(treatment sums of squares = the sum of squares of the group totals / the number of observations per group – the square of the sum of all the observations / the total number of observations)
Question 10.6: Error sum of squares
What is SSE, the error sum of squares?
Answer 10.6: 514.67 – 32.67 = 482.00
(error sum of squares = total sum of squares – treatment sums of squares)
Question 10.7: Total degrees of freedom
What are the total degrees of freedom?
Answer 10.7: 12 – 1 = 11
(total degrees of freedom = number of observations – 1)
Question 10.8: Degrees of freedom for the groups
What are the degrees of freedom for the groups?
Answer 10.8: 3 – 1 = 2
(degrees of freedom for the groups = number of groups – 1)
Question 10.9: Degrees of freedom for the error sum of squares
What are the degrees of freedom for the error sum of squares?
Answer 10.9: 11 – 2 = 9
(degrees of freedom for the error sum of squares = total degrees of freedom – degrees of freedom for the groups)
Question 10.10: Mean squared deviation for the groups
What is MSTr, the mean squared deviation for the groups?
Answer 10.10: 32.667 / 2 = 16.33
(mean squared deviation for the groups = treatment sums of squares / degrees of freedom for the groups)
Question 10.11: Mean squared error
What is MSE, the mean squared error?
Answer 10.11: 482 / 9 = 53.556
(mean squared error = error sum of squares / degrees of freedom for the error sum of squares)
Question 10.12: F value
What is the F value for testing the null hypothesis?
Answer 10.12: 16.333 / 53.556 = 0.305
( F value = treatment mean square / mean squared error)
|
|