OBS ROWBLOCK COLBLOCK TRMT GRKBLOCK RESPONSE
1 1 1 A a 24
2 1 2 B c 20
3 1 3 C e 19
4 1 4 D b 24
5 1 5 E d 24
6 2 1 B b 17
7 2 2 C d 24
8 2 3 D a 30
9 2 4 E c 27
10 2 5 A e 36
11 3 1 C c 18
12 3 2 D e 38
13 3 3 E b 26
14 3 4 A d 27
15 3 5 B a 21
16 4 1 D d 26
17 4 2 E a 31
18 4 3 A c 26
19 4 4 B e 23
20 4 5 C b 22
21 5 1 E e 22
22 5 2 A b 30
23 5 3 B d 20
24 5 4 C a 29
25 5 5 D c 31
note: This is just a listing of the data. This is how you should
enter the data into your .dat file. The upper case letters correspond
to the treatment levels and the lower case letters correspond to the
Greek letters in the text book.
General Linear Models Procedure
Dependent Variable: RESPONSE
Source DF Sum of Squares F Value Pr > F
Model 16 610.00000000 4.62 0.0171
Error 8 66.00000000
Corrected Total 24 676.00000000
R-Square C.V. RESPONSE Mean
0.902367 11.30819 25.4000000
note: For the above F Value, the "full" model contains the overall
mean, treatment effect, row block effect, column block effect, and
Greek letter block effect. The "reduced" model contains just the
overall mean.
Source DF Type III SS F Value Pr > F
ROWBLOCK 4 68.00000000 2.06 0.1783
COLBLOCK 4 150.00000000 4.55 0.0329
GRKBLOCK 4 62.00000000 1.88 0.2076
TRMT 4 330.00000000 10.00 0.0033
note: Use the Type III F Values to test for significant treatment and
blocking effects. Here, we see that blocking was helpful for the
colblock (i.e. operator) while it appears that blocking on batch of
raw material (rowblock) and test assemblies (grkblock) was not
necessary. Furthermore, note that there is a significant treatment
effect (p-value = 0.0033). Thus, we will proceed to the stage II
analysis.
T tests (LSD) for variable: RESPONSE
NOTE: This test controls the type I comparisonwise error rate
not the experimentwise error rate.
Alpha= 0.05 df= 8 MSE= 8.25
Critical Value of T= 2.31
Least Significant Difference= 4.1891
Means with the same letter are not significantly different.
T Grouping Mean N TRMT
A 29.800 5 D
A
A 28.600 5 A
A
B A 26.000 5 E
B
B C 22.400 5 C
C
C 20.200 5 B
mote: Using the Protected LSD method, we see that treatment
(formulation) B gives a statistically "better" burning rate than the
other formulations, except treatment C. However, since treatment C is
not different from treatment E I would be inclined to choose treatment
B as the "best" formulation.
Plot of RESPONSE*TRMT='*'. Plot of EXPECTED*RESID='*'.
---+--+--+--+--+--- -+--------+--------+-
RESPONSE | | 2 + +
40 + + | * |
| * | | * |
| * | EXPECTED | * |
| | | * |
32 + * * + | * |
| * * * | | *** |
| * * | 0 + * +
| * * * | | ** |
24 + * * * * * + | * |
| * * * | | * |
| * * | | * |
| * * | | * |
16 + + | * |
| | -2 + +
---+--+--+--+--+--- -+--------+--------+-
A B C D E -5 0 5
TRMT RESID
NOTE: 1 obs hidden. NOTE: 9 obs hidden.
W:Normal 0.978978
Pr<W 0.8594
Plot of STDRESID*FIT='*'. Plot of STDRESID*TRMT='*'.
-+-----+-----+-----+- ---+--+--+--+--+---
2 +---------*---------+ 2 +--------*--------+
| | | |
| * ** | | * * * |
STDRESID | | STDRESID | |
| * * | | * * |
| * * * | | * * * |
| | | |
0 + * * * * + 0 + * * * * +
| * * | | * * |
| | | |
| * * * * | | * * * |
| * | | * |
| | | |
| * | | * |
-2 +---------*---------+ -2 +--------------*--+
-+-----+-----+-----+- ---+--+--+--+--+---
10 20 30 40 A B C D E
FIT TRMT
NOTE: 3 obs hidden. NOTE: 4 obs hidden.
Plot of STDRESID*ROWBLOCK='*'. Plot of STDRESID*COLBLOCK='*'.
--+---+---+---+---+-- --+---+---+---+---+--
2 +-----------------*-+ 2 +-------------*-----+
| | | |
| * * | | * * * |
STDRESID | | STDRESID | |
| * * | | * * |
| * * | | * * * |
| | | |
0 + * * * * + 0 + * * * * +
| * | | * * |
| | | |
| * * * * | | * * * |
| * | | * |
| | | |
| * | | * |
-2 +-----------------*-+ -2 +-*-----------------+
--+---+---+---+---+-- --+---+---+---+---+--
1 2 3 4 5 1 2 3 4 5
ROWBLOCK COLBLOCK
NOTE: 6 obs hidden. NOTE: 4 obs hidden.
Plot of STDRESID*GRKBLOCK='*'. Variable=RESID
---+--+--+--+--+--- Stem Leaf # Boxplot
2 +--*--------------+ 3 4 1 |
| | 2 224 3 |
| * * | 1 00022 5 +-----+
STDRESID | | 0 0008 4 *--+--*
| * | -0 6422 4 | |
| * * * * | -1 866622 6 +-----+
| | -2 8 1 |
0 + * * * + -3 2 1 |
| * * | ----+----+----+----+
| |
| * * * * |
| * |
| |
| * |
-2 +--------------*--+
---+--+--+--+--+---
a b c d e
GRKBLOCK