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Statistical Analysis Assignment 4: Analyzing Experimental Data with CRD Design - Prof. Tre, Assignments of Statistics

University of Florida (UF)Statistics
Prof. Trevor Park

Instructions for assignment 4 of stat 6208, a spring 2009 course. Students are required to analyze experimental data using a completely randomized design (crd) and perform various statistical tests, including normal probability plots, residual plots, levene test, and confidence intervals. They will be using sas or r for computations.

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Pre 2010

Uploaded on 09/17/2009

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STA 6208 — Section 0015 — Spring 2009
Assignment 4
1. Use the data set after your name below to complete the following parts. Assume yij
represents the response of unit jin treatment group ifrom an experiment using a CRD.
y11 y12 y13 y14 y15 y21 y22 y23 y24 y25 y31 y32 y33 y34 y35
BAI LEI 56 63 75 58 60 2 1 2 1 2 14 7 21 18 19
BOHRMANN THOMAS 57 50 56 63 55 3 2 1 1 4 13 14 17 9 16
CHANG CHE-SHUN 62 51 60 78 77 2 1 0 1 3 13 13 10 12 11
CHEN OU 73 66 60 67 86 4 3 2 0 1 22 10 16 18 23
GAO HAIBING 71 58 71 60 62 5 1 5 5 3 13 24 15 11 15
GLUCK MATHEW R 52 62 67 76 61 3 3 1 1 1 13 12 16 19 9
GORDON ROBERT F 58 72 72 57 71 5 3 1 0 3 13 18 10 13 11
HUANG LEI 74 58 76 57 60 1 6 1 2 1 11 21 17 15 14
JARINA EMILY J 64 72 58 74 53 1 3 1 2 3 10 17 16 16 15
KIM CHANMIN 67 60 56 66 62 0 3 5 5 6 12 14 15 17 6
KIRPICH ALEX 63 62 72 63 67 2 3 4 1 2 20 13 7 15 13
LEARY EMILY V 65 59 54 55 52 1 2 0 2 3 19 13 10 11 17
LI KE 71 49 76 68 56 2 1 4 1 2 13 12 17 20 13
LIU MINZHAO 75 73 62 61 63 2 3 2 3 4 15 8 15 20 22
LUO XUAN 66 67 69 56 65 3 2 2 3 3 17 9 14 12 13
MA LU 80 65 76 58 70 1 0 1 1 3 19 16 28 18 8
NEAL DANIEL W 53 51 76 66 64 1 2 0 1 2 18 11 19 17 13
PRANO BRIJIDA A 65 55 68 58 61 4 0 6 1 1 18 12 18 16 12
SUN WAN 63 67 55 72 63 4 3 4 1 1 15 12 14 20 10
THAYER LAURA K 72 53 59 72 65 0 0 2 3 0 16 18 19 8 15
ZHU XIAOYU 45 57 69 64 68 2 0 1 3 3 23 11 12 11 11
demo 63 45 66 52 65 1 3 2 4 0 11 14 16 20 12
Using SAS R
or R, fit the usual model, then do the following:
(a) Produce a normal probability plot of the standardized residuals. Comment on whether
the plot shows evidence that your data do not follow the usual model assumptions, and,
if so, in what way.
[Note: Comparison with the sample normal probability plots posted on the course web
site may help you to judge whether your plot shows sufficiently strong evidence of
deviation from the usual model assumptions.]
(b) Produce a plot of residuals versus fitted (predicted) values. Comment on whether the
plot shows evidence that your data do not follow the usual model assumptions, and, if
so, in what way.
(c) Perform a modified Levene test for homogeneity of group variances (α= 0.05).
2. Perform Exercise 6.4 from Section 6.8 in the textbook. (You may use SASR
or R to perform
the computations.) In addition, decide which transformation power you would use.
3. Perform Exercise 6.5 in your textbook, Section 6.8.
pf2

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Download Statistical Analysis Assignment 4: Analyzing Experimental Data with CRD Design - Prof. Tre and more Assignments Statistics in PDF only on Docsity!

STA 6208 — Section 0015 — Spring 2009

Assignment 4

1. Use the data set after your name below to complete the following parts. Assume yij

represents the response of unit j in treatment group i from an experiment using a CRD.

y11 y12 y13 y14 y15 y21 y22 y23 y24 y25 y31 y32 y33 y34 y BAI LEI 56 63 75 58 60 2 1 2 1 2 14 7 21 18 19 BOHRMANN THOMAS 57 50 56 63 55 3 2 1 1 4 13 14 17 9 16 CHANG CHE-SHUN 62 51 60 78 77 2 1 0 1 3 13 13 10 12 11 CHEN OU 73 66 60 67 86 4 3 2 0 1 22 10 16 18 23 GAO HAIBING 71 58 71 60 62 5 1 5 5 3 13 24 15 11 15 GLUCK MATHEW R 52 62 67 76 61 3 3 1 1 1 13 12 16 19 9 GORDON ROBERT F 58 72 72 57 71 5 3 1 0 3 13 18 10 13 11 HUANG LEI 74 58 76 57 60 1 6 1 2 1 11 21 17 15 14 JARINA EMILY J 64 72 58 74 53 1 3 1 2 3 10 17 16 16 15 KIM CHANMIN 67 60 56 66 62 0 3 5 5 6 12 14 15 17 6 KIRPICH ALEX 63 62 72 63 67 2 3 4 1 2 20 13 7 15 13 LEARY EMILY V 65 59 54 55 52 1 2 0 2 3 19 13 10 11 17 LI KE 71 49 76 68 56 2 1 4 1 2 13 12 17 20 13 LIU MINZHAO 75 73 62 61 63 2 3 2 3 4 15 8 15 20 22 LUO XUAN 66 67 69 56 65 3 2 2 3 3 17 9 14 12 13 MA LU 80 65 76 58 70 1 0 1 1 3 19 16 28 18 8 NEAL DANIEL W 53 51 76 66 64 1 2 0 1 2 18 11 19 17 13 PRANO BRIJIDA A 65 55 68 58 61 4 0 6 1 1 18 12 18 16 12 SUN WAN 63 67 55 72 63 4 3 4 1 1 15 12 14 20 10 THAYER LAURA K 72 53 59 72 65 0 0 2 3 0 16 18 19 8 15 ZHU XIAOYU 45 57 69 64 68 2 0 1 3 3 23 11 12 11 11 demo 63 45 66 52 65 1 3 2 4 0 11 14 16 20 12

Using SAS ©R or R, fit the usual model, then do the following:

(a) Produce a normal probability plot of the standardized residuals. Comment on whether

the plot shows evidence that your data do not follow the usual model assumptions, and,

if so, in what way.

[Note: Comparison with the sample normal probability plots posted on the course web

site may help you to judge whether your plot shows sufficiently strong evidence of

deviation from the usual model assumptions.]

(b) Produce a plot of residuals versus fitted (predicted) values. Comment on whether the

plot shows evidence that your data do not follow the usual model assumptions, and, if

so, in what way.

(c) Perform a modified Levene test for homogeneity of group variances (α = 0.05).

2. Perform Exercise 6.4 from Section 6.8 in the textbook. (You may use SAS ©R or R to perform

the computations.) In addition, decide which transformation power you would use.

3. Perform Exercise 6.5 in your textbook, Section 6.8.

4. Suppose you are designing an experiment to compare five different treatments in a CRD. A

pilot study suggests that the mean treatment responses μ 1 ,... , μ 5 and the response error

variance σ^2 are as listed after your name in the following table.

mu.1 mu.2 mu.3 mu.4 mu.5 sigma BAI LEI 60 64 50 37 40 36. BOHRMANN THOMAS 46 42 54 49 24 32. CHANG CHE-SHUN 58 50 55 57 61 27. CHEN OU 28 59 42 54 71 36. GAO HAIBING 48 64 60 45 47 37. GLUCK MATHEW R 47 50 47 51 58 34. GORDON ROBERT F 42 56 36 55 67 35. HUANG LEI 52 44 50 49 49 31. JARINA EMILY J 29 72 43 54 56 33. KIM CHANMIN 43 30 54 50 40 39. KIRPICH ALEX 36 45 42 39 42 36. LEARY EMILY V 54 40 59 65 33 40. LI KE 68 55 41 50 44 38. LIU MINZHAO 31 49 39 55 46 34. LUO XUAN 52 41 57 39 48 36. MA LU 37 40 50 51 60 24. NEAL DANIEL W 35 46 39 46 47 34. PRANO BRIJIDA A 51 61 44 37 75 36. SUN WAN 58 49 38 71 46 30. THAYER LAURA K 46 51 55 49 44 31. ZHU XIAOYU 46 60 46 45 36 46. demo 61 64 41 56 36 37.

Assume that the experiment will be designed with equal numbers of experimental units per

treatment group. You may use SAS ©R or R to complete the following parts:

(a) What is the minimum number of experimental units per treatment group required so

that an individual (not simultaneous) 95% two-sided confidence interval for a difference

between two treatment response means will have width no greater than

approximately 8? (Use the value of σ^2 suggested by the pilot study as your guess for the

estimated error variance.)

(b) What is the power of the ANOVA F -test for treatment effects using α = 0.05 when

there are 3 experimental units per treatment group and the alternative is the one

suggested by the pilot study?

[Note: If you use the power curves in textbook Table D.10 to answer this part, beware

of a mistake in the description on p. 621 — the formula for the noncentrality parameter

is missing a factor of n.]

(c) What is the minimum number of experimental units per treatment group required so

that, at the alternative suggested by the pilot study, the power of the ANOVA F -test

using α = 0.01 is at least 0.95? (Note that the α level is 0.01, not 0.05.)