REPORT - Search CIMMYT repository

Optimum Sample Size for Determining
Stem Borer Incidence
An arbitrary sample, which may be inaccurate
and inefficient, is used frequently in
chemical studies to estimate stem borer Infestations.
In the experiments reported here,
attempts ~ were made to estimate optimum
sampl$ size, utilizing the data secured from
three tests conducted at Paza Rica, Veracruz.
There were a total of 68 plants in each
plot. Experiment 1 obtained estimates on
the effectiveness of several granular insecticide.
Experiment 2 obtained estimates for
timing applications of granular insecticides;
While experiment 3 obtained estimates of the
number of granular applications needed
for effective control of borers, as well as fall
armyworm. Damage records (number of Injured
internodes per plant) were obtained
from all plants within each plot. For the statistical
analysis, random samples of four plants
were combined in a stepwise manner to form
the plot sizes. studied.
Table 27 summarizes the results of the
analyses. The data show that the experimental
error mean square increased as the sample
size increased. Also, the sampling error mean
square (except in experiment 2) Increased
slightly as the sample size increased.
The stability of the sampling error indicates
the homogeniety of the samples taken in each
experimental plot. The reduction of the estimated
variance of the mean permits estimation
of the optimum sample size for experiments of
this kind.
It can be observed (Table 27), that the
variance of the mean is considerably larger
for a sample of 4 plants than for a sample
of 48 plants. However, it also becomes obvious
from the three tests, that the variance of
the mean becomes stabilized for samples of
24 plants or more. Thus, it may be considered
that any increment of a sample size above 24
plants will not result in a substantial reduction
in the variance of the mean. The variance of
the mean is important because it generates
the standard error of mean.
The estimation of treatment means is one
of the basic objectives of the experiments,
hence as the standard error of the mean becomes
smaller, a greater precision is obtained
in the comparisons of treatments. Finally, this
information suggests that for experiments such
as those mentioned above, 24 plants per plot
(taken at random) is the most efficient sample
size.
TABLE 27. Statistics for estlmatlnS! optimum sample size for stem borer incidence in chemical control
field trials. Poza Rica, Veracruz, Mexico, 1970.
No." "ant.
lnlpaCted
Experiment No. 1 Experlmant No. 2 Experiment No.3
EMS. EMS. 5·-
X
EMS. EMS.
SI_
Sz_
EMS" EMS.
X X
41 7.49 3.70 0.031 9.17 2.99 0.031 3.16 2.59 0.016
44 7.51 3.71 0.034 10.23 2.94 0.046 4.03 2.58 0.018
40 7.35 3.69 0.037 9.06 2.93 0.045 3.48 2.57 0.022
36 5.67 3.59 0.031 8.14 2.99 0.045 2.87 2.61 0.016
32 4.30 .65 0.027 8.04 3.00 0.050 2.98 2.55 0.019
2. 4.59 3.45 0.033 5.77 2.96 0.041 2.79 2.51 0.020
24 4.24 3.47 0.035 6.29 3.00 0.052 2.19 2.53 0.018
20 4.36 3.44 0.044 6.57 3.05 0.066 2.56 2.49 0.026
16 5.33 3.59 0.067 5.12 3.18 0.064 2.48 2.64 0.031
12 3.55 3.33 0.059 4.19 3.02 0.070 1.54 2.35 0.026
•
2.59 3.25 0.065 3.60' 2.66 0.090 1.17 2.16 0.029
4 3.15 3.36 0.157 2.11 3.00 0.106 1.34 2.05 0.067
EMS. = Experimental error mean square.
_5. = Sampling error meen square. E.periment No. I: 6 tr.atment., 5 replication•.
Experiment No.2: 5 treatment., 5 replication•.
5·- = Varlanca of the meen.
X
Experiment No.3: 6 treetment., 5 replication•.
NOTE:
The number of In/urec:l Internod.. per plant wa. the criterium usec:l In determ'nlng the aHici.ncy of the dlffer.nt .ample .i•••.
42