Agriculture Reference
In-Depth Information
In the following section we will discuss pair
comparison.
The LSD/CD test is most appropriate for
comparing planned pair; in fact it is not advisable
to use LSD for comparing all possible pairs of
means. When the number of treatment is large,
the number of possible pair of treatment means
increases rapidly, and thereby, increasing the prob-
ability of significance of at least one pair of means
will have the difference exceeding the LSD value.
As a result LSD test is used only when the
10.6.1 Pair Comparison
Quite a good number of test procedures are
available for the purpose of comprising pair of
treatment means. Among the methods
F
-test
for treatment effects is significant and the number
of treatments is not too many, preferably less than
six. LSD test is best used in comparing the control
treatment with that of the other treatments.
the least
significant difference test (LSD), also known as
critical difference (CD) test; student Newman-
Keuls test, Duncan multiple range test (DMRT),
and Tukey's honestly significant difference test
are commonly used. Again, among the four test
procedures, the CD and the DMRT are mostly
used.
10.6.1.2 Duncan Multiple Range Test
In the experiment, very large numbers of treat-
ment means are compared in number, as has been
mentioned already, and thus, the LSD test is
not suitable. The fact
10.6.1.1 CD/LSD Test
The essence of LSD test is to provide a single
value at specified level of significance which
serves as the limiting value of significant or non-
significant difference between two treatment
means. Thus, two treatment means are declared
significantly different at the specified level of
significance if the difference between the treat-
ment means exceeds the LSD/CD value; other-
wise they are not.
that LSD can be used
only when the
-test is significant in the analysis
of variance has prompted the use of Duncan
multiple range test.
F
Duncan multiple range test
can be used irrespective of the significance or
nonsignificance of the F-test in the analysis of
variance
. The essence of Duncan multiple range
test calculation is that instead of using standard
error of difference between the two means, we
use standard error of mean in this case. The
standard error of mean is multiplied by
r
p
values
Calculation of LSD Values
LSD
for different values of
(the number of treatment
means involved in the comparison) from the sta-
tistical tables for significant studentized ranges at
p ¼
p
standard error of difference between two
treatment means under comparison multiplied by
the table value of
¼
distribution at error degrees of
freedom with specific level of significance.
Thus,
t
...
t
treatments with different error
degrees of freedom.
Thus, if SE
m
¼
2, 3,
,
for both-sided tests LSD
α
=
CD
α
¼
q
, then
ErMS
r
SE
ð
Þt
2
;
error d
:
f
.
The standard error of difference is calculated as
difference
r
p
SE
m
gives
us
R
p
is subtracted from the largest
mean arranged in either ascending or descend-
ing order. All the means less than the above
subtracted values are declared as significantly
different from the largest mean. Other treatments
whose values are larger than the above differ-
ence, these are compared with appropriate
R
p
value. This
s
1
r
i
þ
1
r
i
0
SE
d
¼
ErMS
;
where
r
i
0
are the replications/number of
observations for the
r
i
and
i
0
th treatment
i
th and the
R
p
values depending upon the number of treatment
means to be compared. That means for three
means to be compared with
under comparison. For
r
i
¼ r
i
0
(in case of designs
like RBD LSD), the CD values are calculated as
R
3
,
two means
r
2ErMS
r
remain to be compared with
R
2
and so on. Let
us demonstrate the procedure with the help of
the following example.
CD
d
¼
t
2
;
error d
:
f
:
