Pool of Questions for the In-Class Quiz

PLS205, Winter 2014

Pool of questions for the in-class quiz

The in-class quiz scheduled for Thursday, January 30, will consist of 5 of the following 30 short questions. The 5 chosen questions for the quiz will be worded exactly as shown here, though specific numbers/data may be different.

1. What is the name of this quantity? In plain language, what does it estimate?

2. What is the expected value for the Treatment1-Block1 cell? What is its residual?

3. For a given a and a given detection distance, state two general strategies for decreasing the Type II error rate of an experiment. (Very brief, a couple of words each will do).

4. A T-test is used for comparing the difference between two treatment effects. Can we use ANOVA? What is the relationship between F and t in this case?

5. You perform an ANOVA and obtain an F value for treatment of 7.5. In plain language, what does this mean?

6. For a normally distributed variable Y, suppose that P(Y ≤ Y0) = 0.30. In plain language, what is Y0? Draw a diagram to support your explanation.

7. State the Central Limit Theorem and briefly explain its relevance to ANOVA.

8. Rank by sensitivity (power) the following four methods for comparing means (most sensitive à least sensitive): Tukey, orthogonal contrasts, Scheffe, Dunnett. In one sentence, why would you ever choose a less sensitive method?

9. In no more than two sentences, explain why the MSE may actually increase when blocks are introduced.

10. What do we mean when we say that a difference is "significant"?

11. What determines the Type I error in an experiment?

12. In plain language, how does an ANOVA partition the treatment sum of squares? How do orthogonal contrasts partition the treatment sum of squares?

13. What is the generic equation for the boundaries of a confidence interval around a distribution of individuals? Around a distribution of sample means?

14. Determine the minimum significant difference and assign groups (A, B, C, etc.) for the following Tukey table:

Tukey's Studentized Range (HSD) Test for Growth

Alpha 0.05

Error Degrees of Freedom 18

Error Mean Square 18

Critical Value of Studentized Range 4.5 (Table 8)

Minimum Significant Difference

Tukey Grouping Mean Practice

55 1n2

46 ShW

42 STr

37 GLo

28 ClF

26 Sel

15. You perform a t-test for two independent samples and find p = 0.051. In plain language, what does this mean?

16. We say that ANOVA assumes homogeneity of variance. In a sentence or two, explain a) where this assumption is made in the analysis and b) in which part of the analysis is more critical.

17. We say that ANOVA assumes normality. In a sentence or two, explain where this assumption is made in the analysis.

18. In an RCBD with one replication per block-treatment combination, we say that ANOVA assumes additivity of effects. In a sentence or two, explain where this assumption is made in the analysis.

19. List three functions of replication in an experiment. Which, if any, of these functions are also functions of subsamples?

20. You measure the performance of 20 students in standardized tests before and after trying a new teaching method. Which statistical test would you use to see if there is a significant improvement in the scores after the test? Justify your selection.

21. Provide the general expression for the minimum significant difference used in the Tukey method of means separation and explain, in plain language, how it controls the EER.

22. Even if the overall F-test for Treatment is not significant (NS), orthogonal contrasts among treatment means may still be significant. Describe a simple way of testing for the possibility of significant contrasts when FTRT is NS (one sentence).

23. When designing an experiment, what information is required to determine the number of needed replications?

24. The table below contains three sets of coefficients (ci) for making three group comparisons among 4 treatment means. a) Show that each set is a contrast. b) Show that the three sets are orthogonal to one another. c) State in plain language the comparison being made by each of the three sets of coefficients.

25. For a given sample size, fixed variance, and fixed Type I error rate, briefly explain how changes in the true difference between population means will affect the probability of a Type II error. Use a diagram to help support your argument.

26. For a given pair-wise Type I error rate of 0.01, how many a posteriori mean comparisons can be made while keeping the experiment wise error rate (EER) less than 0.05? Show your work.

27. You conduct an experiment to compare the effect of different treatments on fruit weight. Explain one thing you could do to increase the accuracy of this experiment (one sentence). Explain two things you could do to increase its precision (one sentence each).

28. Assume that in a CRD ANOVA have the all the degrees of freedom, the total sum of squares and the treatment sum of squares. a) How do you calculate the F value? b) Indicate why the treatment sum of square formula includes a multiplication by r.

29. A normally-distributed population has one true parametric mean and one true parametric variance. How many true parametric standard errors does it have? Refer to the definition of standard error to justify your answer.

30. The method of ANOVA relies on two independent estimates of experimental error for testing the significance of treatment effects. In plain language, where do these two estimates come from?