STAT 370: Homework 4 Fall 2017 Page 1 of 17 1. Consider the Spirituality and Depression study discussed in class. Create a report for the client to address their research question.
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STAT 370: Homework 4 Fall 2017
Page 1 of 17
1. Consider the Spirituality and Depression study discussed in class. Create a report for
the client to address their research question.
STAT 370: Homework 4 Fall 2017
Page 2 of 17
Model Information
Data Set WORK.LEE
Dependent Variable growth
Covariance Structure Variance
Components
Estimation Method Type 3
Residual Variance Method Factor
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Containment
Class Level Information
Class Levels Values
trial 4 1 2 3 4
conc 5 100 25 5 50 control
dish 3 1 2 3
seed 4 alfalfa lettuce mustard
wheat
Dimensions
Covariance Parameters 3
Columns in X 30
Columns in Z 64
Subjects 1
Max Obs Per Subject 240
Number of Observations
Number of Observations Read 240
Number of Observations Used 240
Number of Observations Not Used 0
STAT 370: Homework 4 Fall 2017
Page 3 of 17
Type 3 Analysis of Variance
Source DF
Sum of
Squares
Mean
Square Expected Mean Square Error Term
Error
DF
F
Value
conc 4 219.9256
36
54.981409 Var(Residual) + 4
Var(dish(trial*conc)) +
Q(conc,conc*seed)
MS(dish(trial*co
nc))
52 30.54
seed 3 432.1544
70
144.05149
0
Var(Residual) + Q(seed,conc*seed) MS(Residual) 165 188.8
8
conc*seed 12 92.95003
4
7.745836 Var(Residual) + Q(conc*seed) MS(Residual) 165 10.16
trial 3 65.83150
3
21.943834 Var(Residual) + 4
Var(dish(trial*conc)) + 60 Var(trial)
MS(dish(trial*co
nc))
52 12.19
dish(trial*conc) 52 93.61585
1
1.800305 Var(Residual) + 4
Var(dish(trial*conc))
MS(Residual) 165 2.36
Residual 16
5
125.8389
46
0.762660 Var(Residual) . . .
Type 3 Analysis of
Variance
Source Pr > F
conc <.0001
seed <.0001
conc*seed <.0001
trial <.0001
dish(trial*conc) <.0001
Residual .
Covariance Parameter
Estimates
Cov Parm Estimate
trial 0.3357
dish(trial*conc) 0.2594
Residual 0.7627
STAT 370: Homework 4 Fall 2017
Page 4 of 17
Fit Statistics
-2 Res Log Likelihood 669.2
AIC (smaller is better) 675.2
AICC (smaller is better) 675.3
BIC (smaller is better) 673.3
Type 3 Tests of Fixed Effects
Effect
Num
DF
Den
DF F Value Pr > F
conc 4 52 30.54 <.0001
seed 3 165 188.88 <.0001
conc*seed 12 165 10.16 <.0001
Least Squares Means
Effect conc seed
Estimat
e
Standa
rd
Error DF
t Valu
e Pr > |t|
conc*seed 100 alfalfa 1.0533 0.4112 165 2.56 0.0113
conc*seed 100 lettuce 5.33E-
15
0.4112 165 0.00 1.0000
conc*seed 100 mustard 0.9742 0.4112 165 2.37 0.0190
conc*seed 100 wheat 0.6158 0.4112 165 1.50 0.1362
conc*seed 25 alfalfa 3.2958 0.4112 165 8.01 <.0001
conc*seed 25 lettuce 0.07750 0.4112 165 0.19 0.8507
conc*seed 25 mustard 3.5417 0.4112 165 8.61 <.0001
conc*seed 25 wheat 4.6158 0.4112 165 11.22 <.0001
conc*seed 5 alfalfa 3.5950 0.4112 165 8.74 <.0001
conc*seed 5 lettuce 0.2458 0.4112 165 0.60 0.5508
conc*seed 5 mustard 4.0117 0.4112 165 9.76 <.0001
conc*seed 5 wheat 5.8492 0.4112 165 14.22 <.0001
conc*seed 50 alfalfa 2.7408 0.4112 165 6.67 <.0001
conc*seed 50 lettuce 0.05083 0.4112 165 0.12 0.9018
STAT 370: Homework 4 Fall 2017
Page 5 of 17
Least Squares Means
Effect conc seed
Estimat
e
Standa
rd
Error DF
t Valu
e Pr > |t|
conc*seed 50 mustard 2.7983 0.4112 165 6.80 <.0001
conc*seed 50 wheat 3.1775 0.4112 165 7.73 <.0001
conc*seed contr
ol
alfalfa 3.4250 0.4112 165 8.33 <.0001
conc*seed contr
ol
lettuce 0.3058 0.4112 165 0.74 0.4581
conc*seed contr
ol
mustard 4.0217 0.4112 165 9.78 <.0001
conc*seed contr
ol
wheat 3.7642 0.4112 165 9.15 <.0001
Differences of Least Squares Means
Effect conc seed _conc _seed Estimate
Standard
Error DF t Value Pr > |t|
conc*seed 100 alfalfa 100 lettuce 1.0533 0.3565 16
5
2.95 0.0036
conc*seed 100 alfalfa 100 mustar
d
0.07917 0.3565 16
5
0.22 0.8245
conc*seed 100 alfalfa 100 wheat 0.4375 0.3565 16
5
1.23 0.2215
conc*seed 100 alfalfa 25 alfalfa -2.2425 0.4127 16
5
-5.43 <.0001
conc*seed 100 alfalfa 25 lettuce 0.9758 0.4127 16
5
2.36 0.0192
conc*seed 100 alfalfa 25 mustar
d
-2.4883 0.4127 16
5
-6.03 <.0001
conc*seed 100 alfalfa 25 wheat -3.5625 0.4127 16
5
-8.63 <.0001
conc*seed 100 alfalfa 5 alfalfa -2.5417 0.4127 16
5
-6.16 <.0001
conc*seed 100 alfalfa 5 lettuce 0.8075 0.4127 16
5
1.96 0.0521
STAT 370: Homework 4 Fall 2017
Page 6 of 17
Differences of Least Squares Means
Effect conc seed _conc _seed Estimate
Standard
Error DF t Value Pr > |t|
conc*seed 100 alfalfa 5 mustar
d
-2.9583 0.4127 16
5
-7.17 <.0001
conc*seed 100 alfalfa 5 wheat -4.7958 0.4127 16
5
-11.62 <.0001
conc*seed 100 alfalfa 50 alfalfa -1.6875 0.4127 16
5
-4.09 <.0001
conc*seed 100 alfalfa 50 lettuce 1.0025 0.4127 16
5
2.43 0.0162
conc*seed 100 alfalfa 50 mustar
d
-1.7450 0.4127 16
5
-4.23 <.0001
conc*seed 100 alfalfa 50 wheat -2.1242 0.4127 16
5
-5.15 <.0001
conc*seed 100 alfalfa contr
ol
alfalfa -2.3717 0.4127 16
5
-5.75 <.0001
conc*seed 100 alfalfa contr
ol
lettuce 0.7475 0.4127 16
5
1.81 0.0719
conc*seed 100 alfalfa contr
ol
mustar
d
-2.9683 0.4127 16
5
-7.19 <.0001
conc*seed 100 alfalfa contr
ol
wheat -2.7108 0.4127 16
5
-6.57 <.0001
conc*seed 100 lettuce 100 mustar
d
-0.9742 0.3565 16
5
-2.73 0.0070
conc*seed 100 lettuce 100 wheat -0.6158 0.3565 16
5
-1.73 0.0860
conc*seed 100 lettuce 25 alfalfa -3.2958 0.4127 16
5
-7.99 <.0001
conc*seed 100 lettuce 25 lettuce -
0.07750
0.4127 16
5
-0.19 0.8513
conc*seed 100 lettuce 25 mustar
d
-3.5417 0.4127 16
5
-8.58 <.0001
conc*seed 100 lettuce 25 wheat -4.6158 0.4127 16
5
-11.18 <.0001
conc*seed 100 lettuce 5 alfalfa -3.5950 0.4127 16
5
-8.71 <.0001
STAT 370: Homework 4 Fall 2017
Page 7 of 17
Differences of Least Squares Means
Effect conc seed _conc _seed Estimate
Standard
Error DF t Value Pr > |t|
conc*seed 100 lettuce 5 lettuce -0.2458 0.4127 16
5
-0.60 0.5522
conc*seed 100 lettuce 5 mustar
d
-4.0117 0.4127 16
5
-9.72 <.0001
conc*seed 100 lettuce 5 wheat -5.8492 0.4127 16
5
-14.17 <.0001
conc*seed 100 lettuce 50 alfalfa -2.7408 0.4127 16
5
-6.64 <.0001
conc*seed 100 lettuce 50 lettuce -
0.05083
0.4127 16
5
-0.12 0.9021
conc*seed 100 lettuce 50 mustar
d
-2.7983 0.4127 16
5
-6.78 <.0001
conc*seed 100 lettuce 50 wheat -3.1775 0.4127 16
5
-7.70 <.0001
conc*seed 100 lettuce contr
ol
alfalfa -3.4250 0.4127 16
5
-8.30 <.0001
conc*seed 100 lettuce contr
ol
lettuce -0.3058 0.4127 16
5
-0.74 0.4597
conc*seed 100 lettuce contr
ol
mustar
d
-4.0217 0.4127 16
5
-9.74 <.0001
conc*seed 100 lettuce contr
ol
wheat -3.7642 0.4127 16
5
-9.12 <.0001
conc*seed 100 mustar
d
100 wheat 0.3583 0.3565 16
5
1.01 0.3163
conc*seed 100 mustar
d
25 alfalfa -2.3217 0.4127 16
5
-5.63 <.0001
conc*seed 100 mustar
d
25 lettuce 0.8967 0.4127 16
5
2.17 0.0312
conc*seed 100 mustar
d
25 mustar
d
-2.5675 0.4127 16
5
-6.22 <.0001
conc*seed 100 mustar
d
25 wheat -3.6417 0.4127 16
5
-8.82 <.0001
conc*seed 100 mustar
d
5 alfalfa -2.6208 0.4127 16
5
-6.35 <.0001
STAT 370: Homework 4 Fall 2017
Page 8 of 17
Differences of Least Squares Means
Effect conc seed _conc _seed Estimate
Standard
Error DF t Value Pr > |t|
conc*seed 100 mustar
d
5 lettuce 0.7283 0.4127 16
5
1.76 0.0795
conc*seed 100 mustar
d
5 mustar
d
-3.0375 0.4127 16
5
-7.36 <.0001
conc*seed 100 mustar
d
5 wheat -4.8750 0.4127 16
5
-11.81 <.0001
conc*seed 100 mustar
d
50 alfalfa -1.7667 0.4127 16
5
-4.28 <.0001
conc*seed 100 mustar
d
50 lettuce 0.9233 0.4127 16
5
2.24 0.0266
conc*seed 100 mustar
d
50 mustar
d
-1.8242 0.4127 16
5
-4.42 <.0001
conc*seed 100 mustar
d
50 wheat -2.2033 0.4127 16
5
-5.34 <.0001
conc*seed 100 mustar
d
contr
ol
alfalfa -2.4508 0.4127 16
5
-5.94 <.0001
conc*seed 100 mustar
d
contr
ol
lettuce 0.6683 0.4127 16
5
1.62 0.1073
conc*seed 100 mustar
d
contr
ol
mustar
d
-3.0475 0.4127 16
5
-7.38 <.0001
conc*seed 100 mustar
d
contr
ol
wheat -2.7900 0.4127 16
5
-6.76 <.0001
conc*seed 100 wheat 25 alfalfa -2.6800 0.4127 16
5
-6.49 <.0001
conc*seed 100 wheat 25 lettuce 0.5383 0.4127 16
5
1.30 0.1939
conc*seed 100 wheat 25 mustar
d
-2.9258 0.4127 16
5
-7.09 <.0001
conc*seed 100 wheat 25 wheat -4.0000 0.4127 16
5
-9.69 <.0001
conc*seed 100 wheat 5 alfalfa -2.9792 0.4127 16
5
-7.22 <.0001
conc*seed 100 wheat 5 lettuce 0.3700 0.4127 16
5
0.90 0.3713
STAT 370: Homework 4 Fall 2017
Page 9 of 17
Differences of Least Squares Means
Effect conc seed _conc _seed Estimate
Standard
Error DF t Value Pr > |t|
conc*seed 100 wheat 5 mustar
d
-3.3958 0.4127 16
5
-8.23 <.0001
conc*seed 100 wheat 5 wheat -5.2333 0.4127 16
5
-12.68 <.0001
conc*seed 100 wheat 50 alfalfa -2.1250 0.4127 16
5
-5.15 <.0001
conc*seed 100 wheat 50 lettuce 0.5650 0.4127 16
5
1.37 0.1729
conc*seed 100 wheat 50 mustar
d
-2.1825 0.4127 16
5
-5.29 <.0001
conc*seed 100 wheat 50 wheat -2.5617 0.4127 16
5
-6.21 <.0001
conc*seed 100 wheat contr
ol
alfalfa -2.8092 0.4127 16
5
-6.81 <.0001
conc*seed 100 wheat contr
ol
lettuce 0.3100 0.4127 16
5
0.75 0.4537
conc*seed 100 wheat contr
ol
mustar
d
-3.4058 0.4127 16
5
-8.25 <.0001
conc*seed 100 wheat contr
ol
wheat -3.1483 0.4127 16
5
-7.63 <.0001
conc*seed 25 alfalfa 25 lettuce 3.2183 0.3565 16
5
9.03 <.0001
conc*seed 25 alfalfa 25 mustar
d
-0.2458 0.3565 16
5
-0.69 0.4915
conc*seed 25 alfalfa 25 wheat -1.3200 0.3565 16
5
-3.70 0.0003
conc*seed 25 alfalfa 5 alfalfa -0.2992 0.4127 16
5
-0.72 0.4696
conc*seed 25 alfalfa 5 lettuce 3.0500 0.4127 16
5
7.39 <.0001
conc*seed 25 alfalfa 5 mustar
d
-0.7158 0.4127 16
5
-1.73 0.0847
conc*seed 25 alfalfa 5 wheat -2.5533 0.4127 16
5
-6.19 <.0001
STAT 370: Homework 4 Fall 2017
Page 10 of 17
Differences of Least Squares Means
Effect conc seed _conc _seed Estimate
Standard
Error DF t Value Pr > |t|
conc*seed 25 alfalfa 50 alfalfa 0.5550 0.4127 16
5
1.34 0.1806
conc*seed 25 alfalfa 50 lettuce 3.2450 0.4127 16
5
7.86 <.0001
conc*seed 25 alfalfa 50 mustar
d
0.4975 0.4127 16
5
1.21 0.2298
conc*seed 25 alfalfa 50 wheat 0.1183 0.4127 16
5
0.29 0.7747
conc*seed 25 alfalfa contr
ol
alfalfa -0.1292 0.4127 16
5
-0.31 0.7547
conc*seed 25 alfalfa contr
ol
lettuce 2.9900 0.4127 16
5
7.24 <.0001
conc*seed 25 alfalfa contr
ol
mustar
d
-0.7258 0.4127 16
5
-1.76 0.0805
conc*seed 25 alfalfa contr
ol
wheat -0.4683 0.4127 16
5
-1.13 0.2581
conc*seed 25 lettuce 25 mustar
d
-3.4642 0.3565 16
5
-9.72 <.0001
conc*seed 25 lettuce 25 wheat -4.5383 0.3565 16
5
-12.73 <.0001
conc*seed 25 lettuce 5 alfalfa -3.5175 0.4127 16
5
-8.52 <.0001
conc*seed 25 lettuce 5 lettuce -0.1683 0.4127 16
5
-0.41 0.6839
conc*seed 25 lettuce 5 mustar
d
-3.9342 0.4127 16
5
-9.53 <.0001
conc*seed 25 lettuce 5 wheat -5.7717 0.4127 16
5
-13.98 <.0001
conc*seed 25 lettuce 50 alfalfa -2.6633 0.4127 16
5
-6.45 <.0001
conc*seed 25 lettuce 50 lettuce 0.02667 0.4127 16
5
0.06 0.9486
conc*seed 25 lettuce 50 mustar
d
-2.7208 0.4127 16
5
-6.59 <.0001
STAT 370: Homework 4 Fall 2017
Page 11 of 17
Differences of Least Squares Means
Effect conc seed _conc _seed Estimate
Standard
Error DF t Value Pr > |t|
conc*seed 25 lettuce 50 wheat -3.1000 0.4127 16
5
-7.51 <.0001
conc*seed 25 lettuce contr
ol
alfalfa -3.3475 0.4127 16
5
-8.11 <.0001
conc*seed 25 lettuce contr
ol
lettuce -0.2283 0.4127 16
5
-0.55 0.5809
conc*seed 25 lettuce contr
ol
mustar
d
-3.9442 0.4127 16
5
-9.56 <.0001
conc*seed 25 lettuce contr
ol
wheat -3.6867 0.4127 16
5
-8.93 <.0001
conc*seed 25 mustar
d
25 wheat -1.0742 0.3565 16
5
-3.01 0.0030
conc*seed 25 mustar
d
5 alfalfa -
0.05333
0.4127 16
5
-0.13 0.8973
conc*seed 25 mustar
d
5 lettuce 3.2958 0.4127 16
5
7.99 <.0001
conc*seed 25 mustar
d
5 mustar
d
-0.4700 0.4127 16
5
-1.14 0.2565
conc*seed 25 mustar
d
5 wheat -2.3075 0.4127 16
5
-5.59 <.0001
conc*seed 25 mustar
d
50 alfalfa 0.8008 0.4127 16
5
1.94 0.0540
conc*seed 25 mustar
d
50 lettuce 3.4908 0.4127 16
5
8.46 <.0001
conc*seed 25 mustar
d
50 mustar
d
0.7433 0.4127 16
5
1.80 0.0735
conc*seed 25 mustar
d
50 wheat 0.3642 0.4127 16
5
0.88 0.3789
conc*seed 25 mustar
d
contr
ol
alfalfa 0.1167 0.4127 16
5
0.28 0.7778
conc*seed 25 mustar
d
contr
ol
lettuce 3.2358 0.4127 16
5
7.84 <.0001
conc*seed 25 mustar
d
contr
ol
mustar
d
-0.4800 0.4127 16
5
-1.16 0.2465
STAT 370: Homework 4 Fall 2017
Page 12 of 17
Differences of Least Squares Means
Effect conc seed _conc _seed Estimate
Standard
Error DF t Value Pr > |t|
conc*seed 25 mustar
d
contr
ol
wheat -0.2225 0.4127 16
5
-0.54 0.5905
conc*seed 25 wheat 5 alfalfa 1.0208 0.4127 16
5
2.47 0.0144
conc*seed 25 wheat 5 lettuce 4.3700 0.4127 16
5
10.59 <.0001
conc*seed 25 wheat 5 mustar
d
0.6042 0.4127 16
5
1.46 0.1451
conc*seed 25 wheat 5 wheat -1.2333 0.4127 16
5
-2.99 0.0032
conc*seed 25 wheat 50 alfalfa 1.8750 0.4127 16
5
4.54 <.0001
conc*seed 25 wheat 50 lettuce 4.5650 0.4127 16
5
11.06 <.0001
conc*seed 25 wheat 50 mustar
d
1.8175 0.4127 16
5
4.40 <.0001
conc*seed 25 wheat 50 wheat 1.4383 0.4127 16
5
3.48 0.0006
conc*seed 25 wheat contr
ol
alfalfa 1.1908 0.4127 16
5
2.89 0.0044
conc*seed 25 wheat contr
ol
lettuce 4.3100 0.4127 16
5
10.44 <.0001
conc*seed 25 wheat contr
ol
mustar
d
0.5942 0.4127 16
5
1.44 0.1519
conc*seed 25 wheat contr
ol
wheat 0.8517 0.4127 16
5
2.06 0.0406
conc*seed 5 alfalfa 5 lettuce 3.3492 0.3565 16
5
9.39 <.0001
conc*seed 5 alfalfa 5 mustar
d
-0.4167 0.3565 16
5
-1.17 0.2442
conc*seed 5 alfalfa 5 wheat -2.2542 0.3565 16
5
-6.32 <.0001
conc*seed 5 alfalfa 50 alfalfa 0.8542 0.4127 16
5
2.07 0.0401
STAT 370: Homework 4 Fall 2017
Page 13 of 17
Differences of Least Squares Means
Effect conc seed _conc _seed Estimate
Standard
Error DF t Value Pr > |t|
conc*seed 5 alfalfa 50 lettuce 3.5442 0.4127 16
5
8.59 <.0001
conc*seed 5 alfalfa 50 mustar
d
0.7967 0.4127 16
5
1.93 0.0553
conc*seed 5 alfalfa 50 wheat 0.4175 0.4127 16
5
1.01 0.3132
conc*seed 5 alfalfa contr
ol
alfalfa 0.1700 0.4127 16
5
0.41 0.6810
conc*seed 5 alfalfa contr
ol
lettuce 3.2892 0.4127 16
5
7.97 <.0001
conc*seed 5 alfalfa contr
ol
mustar
d
-0.4267 0.4127 16
5
-1.03 0.3028
conc*seed 5 alfalfa contr
ol
wheat -0.1692 0.4127 16
5
-0.41 0.6824
conc*seed 5 lettuce 5 mustar
d
-3.7658 0.3565 16
5
-10.56 <.0001
conc*seed 5 lettuce 5 wheat -5.6033 0.3565 16
5
-15.72 <.0001
conc*seed 5 lettuce 50 alfalfa -2.4950 0.4127 16
5
-6.05 <.0001
conc*seed 5 lettuce 50 lettuce 0.1950 0.4127 16
5
0.47 0.6372
conc*seed 5 lettuce 50 mustar
d
-2.5525 0.4127 16
5
-6.18 <.0001
conc*seed 5 lettuce 50 wheat -2.9317 0.4127 16
5
-7.10 <.0001
conc*seed 5 lettuce contr
ol
alfalfa -3.1792 0.4127 16
5
-7.70 <.0001
conc*seed 5 lettuce contr
ol
lettuce -
0.06000
0.4127 16
5
-0.15 0.8846
conc*seed 5 lettuce contr
ol
mustar
d
-3.7758 0.4127 16
5
-9.15 <.0001
conc*seed 5 lettuce contr
ol
wheat -3.5183 0.4127 16
5
-8.52 <.0001
STAT 370: Homework 4 Fall 2017
Page 14 of 17
Differences of Least Squares Means
Effect conc seed _conc _seed Estimate
Standard
Error DF t Value Pr > |t|
conc*seed 5 mustar
d
5 wheat -1.8375 0.3565 16
5
-5.15 <.0001
conc*seed 5 mustar
d
50 alfalfa 1.2708 0.4127 16
5
3.08 0.0024
conc*seed 5 mustar
d
50 lettuce 3.9608 0.4127 16
5
9.60 <.0001
conc*seed 5 mustar
d
50 mustar
d
1.2133 0.4127 16
5
2.94 0.0038
conc*seed 5 mustar
d
50 wheat 0.8342 0.4127 16
5
2.02 0.0449
conc*seed 5 mustar
d
contr
ol
alfalfa 0.5867 0.4127 16
5
1.42 0.1571
conc*seed 5 mustar
d
contr
ol
lettuce 3.7058 0.4127 16
5
8.98 <.0001
conc*seed 5 mustar
d
contr
ol
mustar
d
-
0.01000
0.4127 16
5
-0.02 0.9807
conc*seed 5 mustar
d
contr
ol
wheat 0.2475 0.4127 16
5
0.60 0.5496
conc*seed 5 wheat 50 alfalfa 3.1083 0.4127 16
5
7.53 <.0001
conc*seed 5 wheat 50 lettuce 5.7983 0.4127 16
5
14.05 <.0001
conc*seed 5 wheat 50 mustar
d
3.0508 0.4127 16
5
7.39 <.0001
conc*seed 5 wheat 50 wheat 2.6717 0.4127 16
5
6.47 <.0001
conc*seed 5 wheat contr
ol
alfalfa 2.4242 0.4127 16
5
5.87 <.0001
conc*seed 5 wheat contr
ol
lettuce 5.5433 0.4127 16
5
13.43 <.0001
conc*seed 5 wheat contr
ol
mustar
d
1.8275 0.4127 16
5
4.43 <.0001
conc*seed 5 wheat contr
ol
wheat 2.0850 0.4127 16
5
5.05 <.0001
STAT 370: Homework 4 Fall 2017
Page 15 of 17
Differences of Least Squares Means
Effect conc seed _conc _seed Estimate
Standard
Error DF t Value Pr > |t|
conc*seed 50 alfalfa 50 lettuce 2.6900 0.3565 16
5
7.55 <.0001
conc*seed 50 alfalfa 50 mustar
d
-
0.05750
0.3565 16
5
-0.16 0.8721
conc*seed 50 alfalfa 50 wheat -0.4367 0.3565 16
5
-1.22 0.2224
conc*seed 50 alfalfa contr
ol
alfalfa -0.6842 0.4127 16
5
-1.66 0.0993
conc*seed 50 alfalfa contr
ol
lettuce 2.4350 0.4127 16
5
5.90 <.0001
conc*seed 50 alfalfa contr
ol
mustar
d
-1.2808 0.4127 16
5
-3.10 0.0023
conc*seed 50 alfalfa contr
ol
wheat -1.0233 0.4127 16
5
-2.48 0.0142
conc*seed 50 lettuce 50 mustar
d
-2.7475 0.3565 16
5
-7.71 <.0001
conc*seed 50 lettuce 50 wheat -3.1267 0.3565 16
5
-8.77 <.0001
conc*seed 50 lettuce contr
ol
alfalfa -3.3742 0.4127 16
5
-8.18 <.0001
conc*seed 50 lettuce contr
ol
lettuce -0.2550 0.4127 16
5
-0.62 0.5375
conc*seed 50 lettuce contr
ol
mustar
d
-3.9708 0.4127 16
5
-9.62 <.0001
conc*seed 50 lettuce contr
ol
wheat -3.7133 0.4127 16
5
-9.00 <.0001
conc*seed 50 mustar
d
50 wheat -0.3792 0.3565 16
5
-1.06 0.2891
conc*seed 50 mustar
d
contr
ol
alfalfa -0.6267 0.4127 16
5
-1.52 0.1308
conc*seed 50 mustar
d
contr
ol
lettuce 2.4925 0.4127 16
5
6.04 <.0001
conc*seed 50 mustar
d
contr
ol
mustar
d
-1.2233 0.4127 16
5
-2.96 0.0035
STAT 370: Homework 4 Fall 2017
Page 16 of 17
Differences of Least Squares Means
Effect conc seed _conc _seed Estimate
Standard
Error DF t Value Pr > |t|
conc*seed 50 mustar
d
contr
ol
wheat -0.9658 0.4127 16
5
-2.34 0.0205
conc*seed 50 wheat contr
ol
alfalfa -0.2475 0.4127 16
5
-0.60 0.5496
conc*seed 50 wheat contr
ol
lettuce 2.8717 0.4127 16
5
6.96 <.0001
conc*seed 50 wheat contr
ol
mustar
d
-0.8442 0.4127 16
5
-2.05 0.0424
conc*seed 50 wheat contr
ol
wheat -0.5867 0.4127 16
5
-1.42 0.1571
conc*seed contr
ol
alfalfa contr
ol
lettuce 3.1192 0.3565 16
5
8.75 <.0001
conc*seed contr
ol
alfalfa contr
ol
mustar
d
-0.5967 0.3565 16
5
-1.67 0.0961
conc*seed contr
ol
alfalfa contr
ol
wheat -0.3392 0.3565 16
5
-0.95 0.3428
conc*seed contr
ol
lettuce contr
ol
mustar
d
-3.7158 0.3565 16
5
-10.42 <.0001
conc*seed contr
ol
lettuce contr
ol
wheat -3.4583 0.3565 16
5
-9.70 <.0001
conc*seed contr
ol
mustar
d
contr
ol
wheat 0.2575 0.3565 16
5
0.72 0.4712
Tests of Effect Slices
Effect conc seed
Num
DF
Den
DF F Value Pr > F
conc*seed 100 3 165 3.62 0.0144
conc*seed 25 3 165 60.20 <.0001
conc*seed 5 3 165 85.79 <.0001
conc*seed 50 3 165 32.65 <.0001
conc*seed contr
ol
3 165 47.25 <.0001
conc*seed alfalfa 4 165 12.68 <.0001
STAT 370: Homework 4 Fall 2017
Page 17 of 17
Tests of Effect Slices
Effect conc seed
Num
DF
Den
DF F Value Pr > F
conc*seed lettuce 4 165 0.21 0.9350
conc*seed mustar
d
4 165 19.02 <.0001
conc*seed wheat 4 165 44.62 <.0001
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