1. More About ANOVA
BPS 7e Chapter 30
© 2015 W. H. Freeman and Company

2. Conditions for ANOVA The conditions for ANOVA require:
independent random samples from each of the K populations (or a randomized comparative experiment with K treatments).
Normal distributions for the response variable in each population.
a common standard deviation in all populations.
All of the above

3. Conditions for ANOVA (answer)
The conditions for ANOVA require:
independent random samples from each of the K populations (or a randomized comparative experiment with K treatments).
Normal distributions for the response variable in each population.
a common standard deviation in all populations.
All of the above

4. Hypothesis Testing
Researchers investigated how logging in a tropical rainforest affected the forest in later years. They compared forest plots in Borneo that had never been logged (group A) with similar plots nearby that had been logged 1 year earlier (group B) and 8 years earlier (group C).
What would be the null hypothesis?
H0: μA = μB = μC
H0: μA ≠ μB ≠ μC
H0: μA = 0
H0: μA ≠ μB = μC

5. Hypothesis Testing (answer)
Researchers investigated how logging in a tropical rainforest affected the forest in later years. They compared forest plots in Borneo that had never been logged (group A) with similar plots nearby that had been logged 1 year earlier (group B) and 8 years earlier (group C).
What would be the null hypothesis?
H0: μA = μB = μC
H0: μA ≠ μB ≠ μC
H0: μA = 0
H0: μA ≠ μB = μC

6. F Test
Given the output shown below, should researchers reject or retain the null hypothesis (at alpha p < 0.05)?
reject
retain
The information is incomplete.

7. F Test (answer)
Given the output shown below, should researchers reject or retain the null hypothesis (at alpha p < 0.05)?
reject
retain
The information is incomplete.

8. Two-Way ANOVA
True or False: In two-way ANOVA, we have two factors (explanatory variables) that form treatments in a two-way layout. Factor R has r values and factor C has c values so that there are r*c treatments.
True
False

9. Two-Way ANOVA (answer)
True or False: In two-way ANOVA, we have two factors (explanatory variables) that form treatments in a two-way layout. Factor R has r values and factor C has c values so that there are r*c treatments.
True
False

10. ANOVA F Test
There are three ANOVA F tests: for the __________ of no main effect for factor R, no main effect for factor C, and __________ between the two factors.
null hypotheses; interaction
null hypotheses; no interaction
alternative hypotheses; interaction
alternative hypotheses; no interaction

11. ANOVA F Test (answer)
There are three ANOVA F tests: for the __________ of no main effect for factor R, no main effect for factor C, and __________ between the two factors.
null hypotheses; interaction
null hypotheses; no interaction
alternative hypotheses; interaction
alternative hypotheses; no interaction

12. ANOVA
True or False: A factor has a main effect if the mean responses for each value of that factor, averaged over all values of the other factor, are the same.
True
False

13. ANOVA (answer)
True or False: A factor has a main effect if the mean responses for each value of that factor, averaged over all values of the other factor, are the same.
True
False

14. ANOVA Conditions
When we have the same number of individuals n in each treatment group or sample, such designs are called:
uniform.
balanced.
Normal.
fair.

15. ANOVA Conditions (answer)
When we have the same number of individuals n in each treatment group or sample, such designs are called:
uniform.
balanced.
Normal.
fair.

16. ANOVA
__________________ give(s) confidence intervals for all differences among treatment means with an overall level of confidence. That is, we can be (say) 95% confident that all the intervals simultaneously capture the true population differences between means.
One-way ANOVA
Tukey pairwise multiple comparisons
The F statistic
The center line

17. ANOVA (answer)
__________________ give(s) confidence intervals for all differences among treatment means with an overall level of confidence. That is, we can be (say) 95% confident that all the intervals simultaneously capture the true population differences between means.
One-way ANOVA
Tukey pairwise multiple comparisons
The F statistic
The center line

18. Population Contrast
Where L is a population contrast, to test the hypothesis H0: L = 0, we use the:
F statistic.
t statistic.
A or B is correct.
None of the above

19. Population Contrast (answer)
Where L is a population contrast, to test the hypothesis H0: L = 0, we use the:
F statistic.
t statistic.
A or B is correct.
None of the above

20. Population Contrast
In the ANOVA setting comparing the means μ1, μ2, ..., μI of I populations, a population contrast is a combination of the means
with numerical coefficients that add to: c1 + c2 + ··· + cl =:
100. 0. 1.
10.

21. Population Contrast (answer)
In the ANOVA setting comparing the means μ1, μ2, ..., μI of I populations, a population contrast is a combination of the means
with numerical coefficients that add to: c1 + c2 + ··· + cl =:
100. 0. 1.
10.

22. Two-Way ANOVA
Which of the following is NOT a condition for two-way ANOVA?
There are responses for all combinations of values of the two factors (no combinations are missing in data).
It is a completely randomized design.
The response variable has a Normal distribution in each population.
Treatment groups or samples have the same number of observations (n).
The population mean responses and all rc populations’ common standard deviations may differ.

23. Two-Way ANOVA (answer)
Which of the following is NOT a conditions for two-way ANOVA?
There are responses for all combinations of values of the two factors (no combinations are missing in data).
It is a completely randomized design.
The response variable has a Normal distribution in each population.
Treatment groups or samples have the same number of observations (n).
The population mean responses and all rc populations’ common standard deviations may differ.