STAT 5372 -- HOMEWORK SET #4 --- KEY
Due March 24, 2005
Analyze the following two data sets:
(a) sunscreen data on page 994
(b) data in problem 18.3, page 1039
In each case:
(a) State the type of analysis that should be run (e.g. 2-factor ANOVA with
type of inspection fixed and inspector random.)
(b) Use SAS to obtain an appropriate ANOVA table
(c) On the SAS output or on attached sheets:
(i) write the hypotheses to be tested
(ii) give the F-value and P-value from the SAS output and draw
conclusions
(iii) provide estimates of variance components or perform multiple
comparisons that are needed
SUNSCREEN DATA (p.994)
2-Factor Mixed Effects ANOVA - Sunscreen Data
The GLM Procedure
Dependent Variable: burn
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 19 527.9510000 27.7868947 210.51 <.0001
Error 20 2.6400000 0.1320000
Corrected Total 39 530.5910000
R-Square Coeff Var Root MSE burn Mean
0.995024 4.853948 0.363318 7.485000
Source DF Type I SS Mean Square F Value Pr > F
sun 1 4.4890000 4.4890000 34.01 <.0001
tech 9 517.4860000 57.4984444 435.59 <.0001
sun*tech 9 5.9760000 0.6640000 5.03 0.0013
The GLM Procedure
Source Type III Expected Mean Square
sun Var(Error) + 2 Var(sun*tech) + Q(sun)
tech Var(Error) + 2 Var(sun*tech) + 4 Var(tech)
sun*tech Var(Error) + 2 Var(sun*tech)
The GLM Procedure
Tests of Hypotheses for Mixed Model Analysis of Variance
Dependent Variable: burn
Source DF Type III SS Mean Square F Value Pr > F
sun 1 4.489000 4.489000 6.76 0.0287
tech 9 517.486000 57.498444 86.59 <.0001
Error: MS(sun*tech) 9 5.976000 0.664000
Source DF Type III SS Mean Square F Value Pr > F
sun*tech 9 5.976000 0.664000 5.03 0.0013
Error: MS(Error) 20 2.640000 0.132000
Cell Means for Sunscreen Data
The MEANS Procedure
Variable Mean Std Dev
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
burn 7.8200000 3.6592493
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
------sun=2 ------
Variable Mean Std Dev
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
burn 7.1500000 3.7814645
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
Problem 18.3, page 1039
2-Factor Repeated Measures - Antihistamine
The GLM Procedure
Dependent Variable: percent
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 27 13885.29480 514.27018 3.56 <.0001
Error 72 10394.40360 144.36672
Corrected Total 99 24279.69840
R-Square Coeff Var Root MSE percent Mean
0.571889 57.77683 12.01527 20.79600
Source DF Type I SS Mean Square F Value Pr > F
treat 1 3994.240000 3994.240000 27.67 <.0001
patient(treat) 18 5553.206400 308.511467 2.14 0.0124
time 4 3466.997400 866.749350 6.00 0.0003
treat*time 4 870.851000 217.712750 1.51 0.2089
2-Factor Repeated Measures – Antihistamine
The GLM Procedure
Source Type III Expected Mean Square
treat Var(Error) + 5 Var(patient(treat)) + Q(treat,treat*time)
patient(treat) Var(Error) + 5 Var(patient(treat))
time Var(Error) + Q(time,treat*time)
treat*time Var(Error) + Q(treat*time)
2-Factor Repeated Measures - Antihistamine Data
The GLM Procedure
Tests of Hypotheses for Mixed Model Analysis of Variance
Dependent Variable: percent
Source DF Type III SS Mean Square F Value Pr > F
* treat 1 3994.240000 3994.240000 12.95 0.0021
Error 18 5553.206400 308.511467
Error: MS(patient(treat))
* This test assumes one or more other fixed effects are zero.
Source DF Type III SS Mean Square F Value Pr > F
patient(treat) 18 5553.206400 308.511467 2.14 0.0124
* time 4 3466.997400 866.749350 6.00 0.0003
treat*time 4 870.851000 217.712750 1.51 0.2089
Error: MS(Error) 72 10394 144.366717
* This test assumes one or more other fixed effects are zero.
.
Means for Treatment
Mean N treat
27.116 50 1
14.476 50 2
No LSD performed for treatments. SAS would have done it incorrectly since the MSAB was used as error term. Also, there are only 2 groups. All we need to note here is that treatment 1 produces more inhibition than treatment 2.
LSD Results for Time
2-Factor Repeated Measures - Antihistimine
t Tests (LSD) for percent
NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate.
Alpha 0.05
Error Degrees of Freedom 72
Error Mean Square 144.3667
Critical Value of t 1.99346
Least Significant Difference 7.5743
Means with the same letter are not significantly different.
t Grouping Mean N time
A 27.115 20 4
A
A 24.735 20 3
A
A 21.600 20 8
A
A 20.560 20 2
B 9.970 20 1