 |
Analysis of Data from Designed Experiments |
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|
Cross-Over Design |
Analysis Using SAS
To answer the question whether there is any difference between treatment and residual effects. Rearrange the data in the following order: animal numbers as units; periods (code 1 to 3).
|
ANIMAL
NUMBERS
|
UNITS
|
|
53
|
1
|
|
54
|
2
|
|
58
|
3
|
|
75
|
4
|
|
81
|
5
|
|
97
|
6
|
|
72
|
7
|
|
79
|
8
|
|
106
|
9
|
|
84
|
10
|
|
89
|
11
|
|
70
|
12
|
alphabetical numbers as treatments
|
ALPHABETICAL
CODE
|
TREATMENT
NUMBER
|
|
A
|
1
|
|
B
|
2
|
|
C
|
3
|
and
residual effect as residual (coding could be done as
follows: for every first period the number one has assigned
(fixed) and for other periods
code 1 to 3 are given according to the treatment
received by the unit in the previous period).
Note: A carry-over or residual term has the special
property as a factor, or class variate, of having no level
in the first period because the treatment in the first
period is not affected by any residual or carry over effect
of any treatment. When we consider the residual or carryover
effect in practice the fact that carry-over or residual
effects will be adjusted for period effects (by default all
effects are adjusted for all others in these analysis). As a
consequence, any level can be assigned to the residual
variate in the first period, provided the same level is
always used. An adjustment for periods then removes this
part of the residual term. (For details a reference may made
to Jones, B. and Kenward,M.G. 2003. Design and Analysis of Cross Over Trials. Chapman and Hall/CRC.
Data
Input:
For
performing analysis, input the data in the following format.
{Here we call animal
numbers as units, periods as periods, treatment number as
treat and residual effect as residual. It may, however, be
noted that one can retain the same name or can code in any
other fashion}.
Prepare
a SAS data file using
data cod;
input units periods treat residual yield;
cards;
1
1
1
1
72
1
2
2
1
73
1
3
3
2
77
2
1
2
1
75
2
2
3
2
78
2
3
1
3
70
3
1
3
1
75
3
2
1
3
77
3
3
2
1
73
4
1
1
1
64
4
2
3
1
68
4
3
2
3
71
5
1
2
1
80
5
2
1
2
72
5
3
3
1
80
6
1
3
1
74
6
2
2
3
76
6
3
1
2
70
7
1
1
1
58
7
2
3
1
62
7
3
2
3
67
8
1
2
1
64
8
2
1
2
56
8
3
3
1
60
9
1
3
1
72
9
2
2
3
69
9
3
1
2
66
10
1
2
1
76
10
2
3
2
79
10
3
1
3
65
11
1
1
1
61
11
2
2
1
50
11
3
3
2
60
12
1
3
1
71
12
2
1
3
72
12
3
2
1
75
;
*Analysis
can be performed by using the following SAS statements;
proc glm data=cod;
class units periods treat residual;
model yield = units periods treat residual/ss3;
lsmeans treat/pdiff adjust =tukey;
lsmeans residual/pdiff adjust =tukey;
run;
/*Note: Type III sum of squares provide adjustment against all the effects appearing in the model. If the user is interested in getting separate ANOVA for the two cases viz. (i) adjusted treatment effects and unadjusted residual effect and (ii) unadjusted treatment effects and adjusted residual effects, then the above code may be written twice with type I sum of squares as respectively:*/
proc glm data=cod;
class units periods treat residual;
model yield = units periods residual treat /ss1;
LSmeans treat/pdiff adjust =tukey;
run;
proc glm data=cod;
class units periods treat residual;
model yield = units periods treat residual /ss1;
LSmeans residual/pdiff adjust =tukey;
run;
/*Note: If any one is interested on random effect of units, can use Proc
mixed instead of proc glm.*/
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For
exposure on SAS, SPSS,
MINITAB, SYSTAT and
MS-EXCEL
for analysis of data from designed experiments:
Please see Module I of Electronic Book II: Advances in Data Analytical Techniques
available at Design Resource Server (www.iasri.res.in/design)