William H. Knapp III

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This homework was due on Friday, November 23 at 06:00 a.m. Turkish time. Late submissions receive half credit.

By checking the box below, you certify that the answers you will submit here represent your own work.

1. Analysis of variance divides total variance in to portions related to effects and error.
True
False

2. Error variance and effect variance are correlated in ANOVA.
True
False

3. When sampling from a normal population, the sums of squares of samples are distributed according to which distribution?
Binomial
Chi-square
F
Normal

4. When sampling from normal populations, the ratios of different mean squares are distributed according to which distribution?
Binomial
Chi-square
F
Normal

5. As the sample size increases, which distribution approaches the normal distribution?
Binomial
Chi-square
F
All of the above.

6. Which assumption does ANOVA depend on? (Choose all that apply)
That the different populations sampled are normally distributed.
That the different populations sampled have the same variance.
That the observations in each sample were made independently of the others.
That the population variances are known.
That the sample sizes for each group are equal.

7. When the results of an ANOVA involving three groups are significant, what claims are reasonable to make?
That the highest mean is greater than the middle mean.
The means of the groups were not all equal.
The variance of some particular group were different from the mean of some other group.
The variances of the groups were not all equal.
The variance of the effect was large compared to the variance of the error.

8. Imagine you had a study with 8 groups and 20 observations per group. How many degrees of freedom do you have total?

9. How many degrees of freedom do you have for the effect?

10. How many degrees of freedom do you have for the error?

11. If the sum of squares for the effect was 86, what is the mean square for the effect?

12. If the sum of squares for the error was 789, what is the mean square for the error?

13. What would the observed F statistic be for the previous information?

14. What is the critical value for F in this example? Use the traditional alpha level.

15. What should you do?
Fail to reject the null.
Reject the null.
Not enough information to tell.

16. What is probability of observing an F that or more extreme? If you're getting this wrong, make sure it's not due to a silly rounding error by using variables instead of copied and pasted values.

17. For the rest set of questions, you need the data from the last homework.
If you forgot how to get the data from the different samples out, you can use the following code. We're only using sample 1 and 2 so I've only provided the code for those two samples.
s1=data$observations[data$sample==1]
s2=data$observations[data$sample==2]
What's the mean square for the effect of 'sample'?

18. What's the mean square for the error?

19. What's the F ratio?

20. If your alpha is .01, what should you do?
Fail to reject the null.
Reject the null.
Not enough information to tell.