A manual of rice seed health testing - IRRI books - International Rice ...

Example. In a two-stage random
sampling, let the population be the
collection of all ricefields in a town.
The attribute of interest is the average
number of nematodes per hectare.
The primary sampling unit is a
field and the secondary sampling
unit is a 200-ml soil sample. A sample
of n fields is first selected and
from each of these selectcd fields, a
sample of m soil samples are taken.
Stratified random sampling. The
population of N units is divided into
strata of N 1 , N 2 , . . . . . . N k units and
from each stratum N i , sample size n i
is taken. Stratification is done to
bring about a gain in precision in the
estimates of attributes of a heterogeneous
population. The heterogeneous
population is divided into
strata, each of which is internally homogeneous.
The estimates of samples
of each homogeneous stratum
when combined give a more precise
estimate of the population value.
Example. A field where discase
intensities vary from one part of the
field to another. The whole field is
divided into k sub-areas, each subarea
representing a different level of
disease intensity. All plants of each
sub-area will be harvested separately.
From the bulk seeds of each
sub-area, n sample seeds will be
taken for seed testing.
Sampling from binomial population
(Steel and Torrie 1960, Snedecor
and Cochran 1967)
There are sampling situations which
allow only two possible outcomes.
An example is the number of individuals
showing the presence or absence
of a qualitative characteristic.
In assessing seed quality, it could be
the number of seeds infected or not,
diseased or not, discolored or not,
viable or not, and so on. An estimate
of a population proportion of a particular
trait is often required. The parameter
to be estimated by a confidence
interval is the proportion of,
say, infected seeds in the population.
The parameter is generally denoted
by p and its estimate, the observed
Table 4.1. Estimated sampling variation ( x 10 -4 ) at varying sample sizes for different proportions
of infected seeds.
Sample
True percentage of infected seeds in population
size
(n) 50 40 30 20 10
10
25
50
100
200
300
400
500
250.0
100.0
50.0
25.0
12.5
8.3
6.2
5.0
240.0
96.0
48.0
24.0
12.0
8.0
6.0
4.8
210.0
84.0
42.0
21.0
10.5
7.0
5.2
4.2
160.0
64.0
32.0
16.0
8.0
5.3
4.0
3.2
90.0
36.0
18.0
9.0
4.5
3.0
2.2
1.8
Table 4.2. Probability of not detecting infected seeds for different sample sizes and different true
proportions of infected seeds.
Sample
True percentage of infected seeds a
size
(n) 1 2 5 10
10
25
50
100
200
300
400
500
1000
0.90
0.78
0.61
0.37
0.13
0.05
0.02
0.01
0.00
0.82
0.60
0.36
0.13
0.02
0.00
0.00
0.00
0.00
a 0.00 is given in table if actual probability is less than 0.005.
0.60
0.28
0.08
0.01
0.00
0.00
0.00
0.00
0.00
0.35
0.07
0.01
0.00
0.00
0.00
0.00
0.00
0.00
Table 4.3. The values of 2SD for varying values of sample size and true proportion of infected
seeds. a
Sample
True percentage of infected seeds in population
size
(n) 10 15 20 25 30 35 40 45 50
10
25
50
100
200
300
400
500
1000
0.19
0.12
0.08
0.06
0.04
0.03
0.03
0.03
0.02
0.23
0.14
0.10
0.07
0.05
0.04
0.04
0.03
0.02
0.25
0.16
0.11
0.08
0.06
0.05
0.04
0.04
0.03
0.27
0.17
0.12
0.09
0.06
0.05
0.04
0.04
0.03
a Applicable when estimating the proportion p of infected seeds.
0.29
0.18
0.13
0.09
0.06
0.05
0.04
0.04
0.03
0.30
0.19
0.13
0.10
0.07
0.06
0.05
0.04
0.03
0.31
0.20
0.14
0.10
0.07
0.06
0.05
0.04
0.03
0.31
0.20
0.14
0.10
0.07
0.06
0.05
0.04
0.03
0.32
0.20
0.14
0.10
0.07
0.05
0.05
0.04
0.03
18 Rice seed health testing manual