6: Analysis of Variance (ANOVA)

Question 1

___ is used to test whether two samples are from populations having equal variances.

Answer 1

F Distribution

Question 2

What are the characteristics of the F distribution?

1. ___
2. ___
3. ___
4. ___
5. ___

Answer 2

1. There is a family of F distributions.**
2. The F distribution is continuous.
3. The F statistic cannot be negative.
4. The F distribution is positively skewed.
5. The F distribution is asymptotic.

Question 3

The ___ is a technique used to test simultaneously whether the means of several populations are equal; uses the F distribution to test; both samples must be at least interval scale.

Answer 3

Analysis of variance (ANOVA)

Question 4

The ANOVA used to test the equality of three or more population means requires that three assumptions are true:

1. ___
2. ___
3. ___

Answer 4

1. The populations follow the normal distribution.
2. The populations have equal standard deviations (σ).
3. The populations are independent.

Question 5

How does ANOVA work?

Answer 5

If the ratio of two population variances is about 1, then we conclude that the population means are the same. If the ratio is quite different from 1, then we conclude that the population means are not the same.

Question 6

___ is the sum of the squared differences between each observation and the overall mean.

Answer 6

Total variation

Question 7

___ is the sum of the squared differences between each treatment mean and the grand or overall mean.

Answer 7

Treatment variation

Question 8

___ is the sum of the squared differences between each observation and its treatment mean.

Answer 8

Random variation

Question 9

Recall the 6-Step Procedure for Testing a Hypothesis:

1. ___
2. ___
3. ___
4. ___
5. ___
6. ___

Answer 9

Step 1: State the Null Hypothesis (H0) and the Alternate Hypothesis (H1).
Step 2: Select a Level of Significance
Step 3: Select the Test Statistic
Step 4: Formulate the Decision Rule
Step 5: Make a Decision
Step 6: Interpret the Result

Question 10

How does one calculate the df to formulate the decision rule in the analysis of variance?

Answer 10

The df in the numerator is k - 1

The df in the denominator n - k

Question 11

The term ___ is used to identify the different populations being examined.

Answer 11

Treatment

Question 12

___ is a second treatment variable that when included in the ANOVA analysis will have the effect of reducing the SSE term.

Answer 12

Blocking variable

Question 13

___ occurs when the effect of one factor on a response variable differs depending on the value of another factor.

Answer 13

Interaction