Inverse Sampling to Estimate Rare Events
In number of studies inverse
sampling for the estimation of a rare population parameter has been used. The
use is due to saving as the sample size requirement is less for the same
precision as in conventional sampling.
Even this can be adopted for the large scale survey at national level.
In addition, when
conventional sampling is used to detect rare events there is likelihood of not
getting even a single event even after covering a large sample. In such
situations, sampling techniques for rare event are more appropriate to be used
for estimation. Inverse sampling is one of such techniques that detect predetermined
cases in the study population. It is said to be appropriate for the survey of
rare events wherein the number of rare events are fixed in advance or
predetermined and the sampling is continued till the predetermined number of
rare event is obtained in the population.
Under inverse sampling the
number of rare event is fixed in advance say ‘m’ (new cases of maternal death)
and sampling is continued till the desired numbers of such rare events appear
in the population. Apparently the required sample size ‘n’ is a random
variable. It is contrary to the conventional cluster sampling where sample size
‘n’ is fixed in advance and the rare event is counted after attaining the
sample size ‘n’, then the rare event ‘P’ is estimated as m/n where m is the
number of events in the study population.
Under inverse sampling if
‘n’ is the sample size (random variable), at which the mth rare event occures,
an unbiased estimate of P is given by p = (m-1)/(n-1). The unbiased variance
estimator of p is given by (N-n+1)*p*(1-p)/[N*(n-2)], where, N is the total population
of the study area.
Hence, the coefficient of
variation (CV) is given by √[(N-n+1)*(1-p)/{N*p*(n-2)}] * 100.
A sample of m new cases of
rare event is assumed. The total sample size to be covered at this stage is
unknown (random variable). Hence, sampling is to be continued until m new cases
of rare events were found. It is
observed that the inverse sampling can yield better precision at very low
sample size requirement.
Snowball Sampling
Some populations that we
may be interested in studying can be hard-to-frame. These include populations
such as of AIDS/HIV positive individuals, individuals/ institutions involved in
some illegal activities like theft, burglary, prostitution, use of banned
drugs, abortions for sex determination etc. and so forth. Snowball sampling is
a non-probability based sampling technique that can be used to gain access to
such populations partially up to certain number and then say the findings based
on the group selected about such group of individuals.
To have such a sample
from the hard-to-frame population, there are two steps namely, i) try and
identify one or more sample units in the desired population or render access to
such individuals/units; and ii) use these individuals/units to find further
similar individuals/units and so on until the required sample size is obtained.
Supposing, the population
we are interested in are the students of a university that take banned drugs.
Each student may be referred to as a sample unit. Collectively, all students of
the university who are such drug users make up our population. However, we are
only interested in examining the sample of these drug users who are the students
of the university.
Firstly, we need to try
and find one or more such students from the university we are concerned.
Finding just a small number of individuals willing to identify themselves and
take part in the research study on banned drug users may be quite difficult, so
the aim is to start with just one or two students.
Due to the sensitivity of
the study, the researcher should ask the initial students who agreed to take
part in the study to help also in identifying some more students that are also
the banned drug users. The process continues until sufficient students of the
university have been identified to meet the desired sample size. We need not
consider the individuals who are not part of the University at that point of
Time.
Snowball sampling is a
useful choice of sampling strategy when the population is hard-to-frame
because:
• It is difficult to
identifying individuals/units to include in your sample, perhaps because there
is no obvious list/frame of the population you are interested in.
• There may be no other
way of accessing/getting your sample, making snowball sampling the only viable
choice of sampling strategy.
• The sensitivity of
coming forward to take part in a survey is more adverse in such contexts.
However, since snowball sampling involve like individuals who know each other
and may take part in such a survey as there may be some common characteristics
and other social factors between these individuals that help to break down some
of the barriers that prevent them from taking part outside their association.
• The unknown nature of
some groups may also make it difficult to identify various parts of the
population that warrant investigation. In the case of banned drug users, it may
be obvious to identify strata such as gender, type of banned drugs used,
frequency of the drugs used and so forth. One need to find the characteristics
of the population you want to examine at the start of the survey and the same
may not be known in its entirety. The snowball sampling may also be helpful in
finding the unknown characteristics that could be of interest before settling
on your sampling criteria.
Snowball sampling is a
not very useful choice of sampling strategy when the population is
hard-to-frame if we need to determine the possible sampling error and make
generalizations from the sample to the population, since snowball sampling does
not select sample units randomly as in case of probability sampling techniques.
As such, snowball samples should not be considered to be true representative of
the population being studied.
Quota Sampling
Quota sampling technique
is a method for selecting survey respondents from a population. In quota
sampling, a population is first segmented into mutually exclusive sub-groups
(or two or more strata). Then judgment is used to select the units from each
segment based on a specified proportion. For example, a surveyor may be asked
to sample x males and y females between the certain age groups. This means that
individuals can set a demand on who they want to sample.
This second step of
selection makes the technique non-probability sampling. In quota sampling, the
selection of the sample is non-random sample and thus can be unreliable for
making inferences. It is just possible that interviewers might be tempted to
interview only those people who look to be most helpful, or may choose to use
accidental sampling to question those closest to them, for time-saving sake.
The problem is that such samples may be biased because not everyone gets a
chance of selection. This non-random element is a source of biasness in the
actual sample. Quota is normally confused and is advocated to give some
probability of selection of units/individuals in the sample.
Quota sampling is useful
when time is limited, a sampling frame is not available, the research budget is
very tight or when detailed accuracy is not important. Subsets are chosen and
then either convenience or judgment sampling is used to choose people from each
subset. The researcher decides how many of each category is selected.
Quota sampling is clearly
the non probability version of stratified sampling. In stratified sampling,
subsets of the population are formulated so that each subset has a common
characteristic, such as gender, age. Random sampling chooses a number of subjects
from each subset with, unlike a quota sample, each potential subject having a
known probability (normally equal probability) of being selected. Fixing of
quota or sample size of each strata (or group) on the basis of reliability of
estimates one wish to have is fine. But the second stage selection should then
be on basis of some random selection as otherwise we are assuming every one is
same (homogeneous) within the various groups and this can’t be true. One can’t
have convenience sampling at the second stage of sampling.
The Indian corporate
sector is divided into two segments namely, Public Limited Companies and
Private Limited Companies and some quota of companies to be selected from each
segment is fixed. But as the full sampling frame for both the segments is not
available even with the Department of Company Affairs, Government of India as
there are large many number of respective companies who do not file their
annual reports with the Ministry of Corporate Affairs. Many a times it has been
noted that even Top Indian Companies do not bother of filing their annual
reports with the Ministry regularly. Many companies get themselves registered
with the Ministry at the time of its constitution, but quite a few Private
Limited Companies close their operations and do not report this important event
to the Ministry. In the absence of correct sampling frames, random selection
can’t be done. Thus, the estimates generated by using Quota Sampling are under
question on account of their reliability. Many such examples are exiting and
are crippling the Indian Official System.
Accidental Sampling / Grab Sampling / convenience sampling or opportunity sampling
Supposing one is interested in knowing the incidence of pest
infestation for a particular crop in a size able area. Getting interior to the
crop is difficult. Investigators may decide to move around the area on the road
and inspect the road side plots for pest infestation for the crop. Can they
make a correct idea about the percentage of effected crop area? The answer
should be ‘No’ as he has not inspected the random portion of the crop area to
be inspected. The sampling method adopted is “Accidental Sampling”. It is a
type of non probability sampling which involves the sample being drawn from
that part of the population which is close to hand. That is, a sample selected
from the population is biased one, because it is that part which is convenient
to choose. The researcher using such a sample cannot scientifically make
generalizations about the total population from this sample as it would not be
representative enough. This accidental sampling can be adopted at best for some
pilot testing or can be used to frame certain hypothesis to be tested
scientifically. If some questionnaires need to be field tested, there may not
be a big requirement of selecting a rigorous random sample using a population
frame. Thus, for such type of work, accidental sampling can be adopted. If one
has to just get a feel of public opinion on some happening around in the
community at large, well framed questions can be put on even on some social
site and may get the answer to the same from the public whosoever wants to give
some reaction. But caution is that one should not generalize the same for the
entire community.
Accidental Sampling is also called Grab Sampling or Convenience Sampling or Opportunity Sampling.
