Assignment #9 Sketch of Solutions
#1
General Linear Model: time versus trt, blk
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
trt 2 3169 1584.7 15.63 0.001 small P-Value evidence for Mercury effect
blk 5 15574 3114.7 30.72 0.000 small P-Value evidence for Litter (Block) effect
Error 10 1014 101.4
Total 17 19757
Control Mean < Means of mercuric-chloride, methyl-mercury
Tukey Pairwise Comparisons: Response = time, Term = trt
Grouping Information Using the Tukey Method and 95% Confidence
trt N Mean Grouping
mercuric-chloride 6 104.167 A
methyl-mercury 6 88.333 A
control 6 71.667 B
Means that do not share a letter are significantly different.
Tukey Simultaneous Tests for Differences of Means
Difference SE of Simultaneous Adjusted
Difference of trt Levels of Means Difference 95% CI T-Value P-Value
mercuric-chloride - control 32.50 5.81 ( 16.55, 48.45) 5.59 0.001
methyl-mercury - control 16.67 5.81 ( 0.72, 32.62) 2.87 0.041
methyl-mercury - mercuric-chloride -15.83 5.81 (-31.78, 0.12) -2.72 0.051
Individual confidence level = 97.93%
#2
General Linear Model: algae versus depth, blk
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
depth 2 178188 89094 17.63 0.003 small P-Value evidence of depth effect
blk 3 84247 28082 5.56 0.036 small P-Value evidence of lake (block) effect
Error 6 30321 5054
Total 11 292757
Mean – Algae Concentration
Means of 1m, 3m < Mean of Surface
Tukey Pairwise Comparisons: Response = algae, Term = depth
Grouping Information Using the Tukey Method and 95% Confidence
depth N Mean Grouping
surface 4 337.50 A
1m 4 118.75 B
3m 4 52.25 B
Means that do not share a letter are significantly different.
Tukey Simultaneous Tests for Differences of Means
Difference of Difference SE of Simultaneous Adjusted
depth Levels of Means Difference 95% CI T-Value P-Value
3m - 1m -66.5 50.3 (-220.8, 87.8) -1.32 0.434
surface - 1m 218.7 50.3 ( 64.5, 373.0) 4.35 0.011
surface - 3m 285.3 50.3 ( 131.0, 439.5) 5.67 0.003
Individual confidence level = 97.80%
#3
General Linear Model: sbp versus sex, agegrp
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
sex 1 616.5 616.53 8.68 0.007
agegrp 2 6661.7 3330.83 46.90 0.000
sex*agegrp 2 622.1 311.03 4.38 0.024 small P-Value – evidence for interaction
Error 24 1704.4 71.02 comparison of 6 treatment means
Total 29 9604.7
#3 continued …
Tukey Pairwise Comparisons: Response = sbp, Term = sex*agegrp
Grouping Information Using the Tukey Method and 95% Confidence
sex*agegrp N Mean Grouping
male old 5 144.0 A
female old 5 128.0 A B
male mature 5 125.0 B C
female mature 5 110.0 C D
female adolescent 5 101.4 D
male adolescent 5 97.6 D
Means that do not share a letter are significantly different.
Tukey Simultaneous Tests for Differences of Means
Difference SE of Simultaneous Adjusted
Difference of sex*agegrp Levels of Means Difference 95% CI T-Value P-Value
(female mature) - (female adolescent) 8.60 5.33 ( -7.87, 25.07) 1.61 0.598
(female old) - (female adolescent) 26.60 5.33 ( 10.13, 43.07) 4.99 0.001
(male adolescent) - (female adolescent) -3.80 5.33 (-20.27, 12.67) -0.71 0.978
(male mature) - (female adolescent) 23.60 5.33 ( 7.13, 40.07) 4.43 0.002
(male old) - (female adolescent) 42.60 5.33 ( 26.13, 59.07) 7.99 0.000
(female old) - (female mature) 18.00 5.33 ( 1.53, 34.47) 3.38 0.027
(male adolescent) - (female mature) -12.40 5.33 (-28.87, 4.07) -2.33 0.222
(male mature) - (female mature) 15.00 5.33 ( -1.47, 31.47) 2.81 0.089
(male old) - (female mature) 34.00 5.33 ( 17.53, 50.47) 6.38 0.000
(male adolescent) - (female old) -30.40 5.33 (-46.87, -13.93) -5.70 0.000
(male mature) - (female old) -3.00 5.33 (-19.47, 13.47) -0.56 0.993
(male old) - (female old) 16.00 5.33 ( -0.47, 32.47) 3.00 0.061
(male mature) - (male adolescent) 27.40 5.33 ( 10.93, 43.87) 5.14 0.000
(male old) - (male adolescent) 46.40 5.33 ( 29.93, 62.87) 8.71 0.000
(male old) - (male mature) 19.00 5.33 ( 2.53, 35.47) 3.56 0.017
Individual confidence level = 99.50%
Means -- sbp
Male – Mean Adolescent < Mean Mature < Mean Old
Female – Mean Adolescent, Mean Mature < Mean Old
#4
General Linear Model: activity versus virus, strain
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
virus 2 58569.9 29284.9 99.07 0.000 small P-Value – Virus Effect
strain 2 19683.6 9841.8 33.30 0.000 small P-Value – Strain Effect
virus*strain 4 407.3 101.8 0.34 0.844 large P-Value … weak evidence for interaction
Error 18 5320.7 295.6
Total 26 83981.4
#4 continued …
Tukey Pairwise Comparisons: Response = activity, Term = virus
Grouping Information Using the Tukey Method and 95% Confidence
virus N Mean Grouping
TMV-infected 9 212.667 A
TRSV-infected 9 116.222 B
noninfected 9 111.667 B
Means that do not share a letter are significantly different.
Tukey Simultaneous Tests for Differences of Means
Difference SE of Simultaneous Adjusted
Difference of virus Levels of Means Difference 95% CI T-Value P-Value
TMV-infected - noninfected 101.00 8.10 ( 80.31, 121.69) 12.46 0.000
TRSV-infected - noninfected 4.56 8.10 ( -16.13, 25.24) 0.56 0.842
TRSV-infected - TMV-infected -96.44 8.10 (-117.13, -75.76) -11.90 0.000
Individual confidence level = 98.00%
Means noninfected, TRSV-infected < Mean TMV-infected
#4 continued …
Tukey Pairwise Comparisons: Response = activity, Term = strain
Grouping Information Using the Tukey Method and 95% Confidence
strain N Mean Grouping
Strain C 9 180.444 A
Strain A 9 145.778 B
Strain B 9 114.333 C
Means that do not share a letter are significantly different.
Tukey Simultaneous Tests for Differences of Means
Difference of Difference SE of Simultaneous Adjusted
strain Levels of Means Difference 95% CI T-Value P-Value
Strain B - Strain A -31.44 8.10 (-52.13, -10.76) -3.88 0.003
Strain C - Strain A 34.67 8.10 ( 13.98, 55.36) 4.28 0.001
Strain C - Strain B 66.11 8.10 ( 45.42, 86.80) 8.16 0.000
Individual confidence level = 98.00%
Mean Strain B < Mean Strain A < Mean Strain C