sampling and statiscal inference

Presented by:-
Dr.Shruti Mishra

S/N Learning
objectives
Domain Level Criteria
1 Parameter and
statistic
Cognitive Must know All
2 Sampling and Non
sampling error
Cognitive Must know All
3 Sampling
distribution
Cognitive Desired to know All
4 Standard error Cognitive Desired to know All
5 Sampling methods Cognitive Must to know All
6 Bias Cognitive Must to know All

 Parameter and statistic
 Sampling and Non sampling error
 Standard Error
 Sampling methods
 Bias
 Ethical considerations

 Sampling : defined as the selection of some part of an aggregate or totality on the
basis of which a judgement or inference about the aggregate or totality is made.
 The researcher quite often selects only a few items from the universe for his study
purposes. All this is done on the assumption that the sample data will enable him to
estimate the population parameters. The items so selected constitute what is
technically called a sample, their selection process or technique is called sample
design and the survey conducted on the basis of sample is described as sample
survey.

 Sampling :-
 can save time and money. A sample study is usually less expensive than a census
study and produces results at a relatively faster speed.
 may enable more accurate measurements for a sample study is generally
conducted by trained and experienced investigators.
 remains the only way when population contains infinitely many members.
 remains the only choice when a test involves the destruction of the item under
study.
 usually enables to estimate the sampling errors and, thus, assists in obtaining
information concerning some characteristics of the population.

 The collection of all the items about which the information is desired, is called as
population.
 Population can be :-
1. Infinite
2. Finite

 Any characteristic or measure of population units is known as a “parameter”.
 Population mean, population standard deviation, population proportion are
commonly studied parameters.
 These parameters are denoted by µ,π,σ respectively.
 Parameters are usually unknown as we do not always study the whole population.
 Unknown parameter are estimated by studying a subpart of the whole population
which is known as a sample.

 Sample surveys do imply the study of a small portion of the population and as such
there would naturally be a certain amount of inaccuracy in the information
collected.
 This inaccuracy may be termed as sampling error or error variance.
 In other words, sampling errors are those errors which arise on account of sampling
and they generally happen to be random variations in the sample estimates around
the true population values.

ResponseResponse
Response
error
Chance
error
Frame
error
Population
Sampling frame
Sample
Sampling error=
frame error+ chance
error+ response error

 Sampling errors occur randomly and are equally likely to be in either direction.
 The magnitude of the sampling error depends upon the nature of the universe: the
more homogenous the universe, smaller the sampling error.
 Sampling error is inversely related to the size of the sample;, sampling error
decreases as the sample size increases and vice versa.
 A measure of the random sampling error can be calculated for a given sample design
and size and this measure is often called the precision of the sampling plan.
 Sampling error is usually worked out as the product of the critical value at a certain
level of significance and the standard error.

 As opposed to sampling errors, we may have non sampling errors which may creep in
during the process of collecting actual information and such errors occurs in all
surveys whether census or sample.
 There is no way to measure non sampling errors.

 A statistical population is a collection of items or individuals about which we wish to
draw some conclusion.
 Whenever we do not study the whole population to make conclusions about some
characteristics of that population, we study a sample and using the sample we make
conclusions about the unknown characteristics of that population.
 Statistics is helpful in studying the sample and drawing meaningful inferences from
the sample.
 This requires probabilistic sample as stastiscal results are based on probability
theory.

 Drawing inference from the probabilistic sample about unknown population
parameters is called as statistical inference.
 It is concerned mainly with two things : hypothesis testing and estimation.
 Hypothesis testing – testing of the claims made about unknown population
parameters using sample.
 Estimation – estimating unknown population parameters using a sample.

1. Probablity sampling methods. (random)
2. Non probability sampling methods. (non random)

 Simple random sampling
 Systematic sampling
 Stratified sampling
 Cluster sampling
 Multi stage sampling
 Multi phase sampling

 Convenience sampling
 Purpose sampling
1. Extreme case sampling
2. Quota sampling
3. Homogenous sampling
4. Typical case sampling
5. Critical case sampling
6. Snowball or chain sampling

 This type of sampling is useful to measure variables distributed in a population.e.g.
diseases, disability, etc. or to test hypotheses, where factors are contributing
significantly to a certain problem and we want to generalize the findings obtained
from a sample to the total study population.
 Involves using random selection procedures to ensure that each unit of the sample is
chosen on the basis of chance.

 This is the simplest form of sampling.
 Procedure :-
a) Prepare or search for an existing numbered list of all the units in the population
from which sample is to be drawn.
b) Decide the size of the sample
c) Select the required number of sampling units, using a ‘lottery’ method or tables
of random numbers.

 A simple random sample of 50 students is to be selected from a school of 250 students. Using
a list of 250 students, each student is a given a number from 1 to 250, and these numbers are
written on small pieces of paper. The population is divided into two or more groups called
strata, according to some criterion, such as geographic location, grade level, age, or income,
and subsamples are randomly selected from each strata
 All the 250 papers are put in a box , after which the box is shaken vigorously, to ensure
randomization.
 Then , 50 papers are taken from the box and the numbers are recorded.
 The students belonging to those numbers will constitute the sample size.

 In this sampling, individuals are chosen at regular intervals. E.g. every 5th, from the
sampling frame.
 Procedure :
a) Number the units in the population (N)
b) Decide the sample size (n) that you need or want
c) k= N/n = the interval size
d) Then take every kth unit.

 Example :- a systematic sample is to selected from 1200 students of a school. The
sample size selected is 100.
 N=1200, n=100
 K=N/n=1200/100=12
 The sampling interval is, therefore 12.
 The number of first student to be included in the sample is chosen randomly , for
e.g. If number 6 is picked, then every twelfth student will be included in the
sample, starting from 6,18,30, 42…

 This sampling is usually less time consuming and easier to perform.
 But there is a risk of bias, as the sample interval may coincide with the systematic
variation in the sampling frame.

The population is divided into two or more
groups called strata, according to some
criterion, such as geographic location,
grade level, age, or income, and
subsamples are randomly selected from
each strata.

Advantage :
 Enhancement of representativeness to each sample
 Higher statistical efficiency
 Easy to carry out
Disadvantage:
 Classification error
 Time consuming and expensive
 Prior knowledge of composition and of distribution of population

 Cluster sampling is an example of 'two-stage sampling' .
 First stage a sample of areas is chosen;
 Second stage a sample of respondents within those areas is selected.
 Population divided into clusters of homogeneous units, usually based on
geographical contiguity.

 Sampling units are groups rather than individuals.
 A sample of such clusters is then selected.
 All units from the selected clusters are studied.
 The population is divided into subgroups (clusters) like families. A simple random
sample is taken of the subgroups and then all members of the cluster selected are
surveyed.
 Often used to evaluate vaccination coverage in epidemics.

sampling and statiscal inference

 Advantages :
Cuts down on the cost of preparing a sampling frame. This can reduce travel and
other administrative costs.
 Disadvantages:
Sampling error is higher for a simple random sample of same size.

 For a very large and diverse population, sampling may be done in two or more
stages.
 This is often the case in community based studies.
 E.g. in a study of utilization of electricity in a district, a total of 150 households are
to be visited for interviews with family members. The district is composed of 6
wards and each ward has between 6 to 9 villages.

 The following procedure has to be performed:-
a) Go to the center of the village
b) Choose a direction in a random way: spin a bottle on the ground and choose the
direction the bottleneck indicates
c) Walk in the chosen direction and select every household until you have the 10 you
need.

 This is an adaptation of the method developed by the EPI division in WHO Geneva to
measure EPI coverage in districts.
 Advantages :
a) A sampling frame of individual units is not required for the whole population.
Existing sample frames of clusters are sufficient.
b) Sample is easier to select than a random sample of similar size, because the
individual units in the sample are physically together in groups, instead of
scattered all over the study population.

 Disadvantage :
a) Compared to simple random
sampling, there is a larger
probability that the final sample
will not be representative of the
total study population.

 In this method, part of the information is collected from the whole sample and part
from the sub sample. Example –tuberculosis survey.
 Phase I : mantoux test was performed on all cases of sample
 Phase II: all persons positive for mantoux test were subjected to X-ray chest.
 Phase III: all those who were having clinical symptoms and X ray positive were
subjected to sputum examination for confirmation and diagnosis categorization.

 It is a method in which for convenience sake the study units that happen to be
available at the time of data collection are selected in the sample.
 This may happen at the beginning of a study when researchers are merely orienting
themselves, or , when there are many similar informants and the researchers do not
have a preference for specific categories.
 When there seems no other choice researchers may also sample conveniently.

 Qualitative research methods are typically used when focusing on a limited number
of informants, whom we select strategically so that their in depth information will
give optimal insight into an issue about which little is known. This is called
purposive sampling.
 In purposive sampling, we sample with a purpose in mind.

Purposive
sampling
Extreme case
sampling
Quota
sampling
Homogenous
sampling
Typical case
sampling
Critical case
sampling
Snowball or
chain
sampling

 Selection of extreme cases, such as good or very poor compliers to treatment, is a
powerful and rapid strategy to identify contributing factors to poor compliance.
 In the same way, selection of well nourished children of the same age will help to
identify contributing factors for malnutrition.

 In this sampling, we select randomly according to some fixed quota.
There are two types of quota sampling :-
a) Proportional quota
b) Non proportional quota

 In proportional quota sampling, we want to represent the major characteristics of
the population by sampling a proportional amount of each.
 For instance, if we know the population has 40% women and 60% men, and the total
sample size of 100, we will continue until we get these percentages and then we
will stop.

 Non proportional quota sampling is a bit less restrictive.
 In this method, we specify the minimum number of sampled units we want in this
category.
 Here , we are not concerned with having numbers that match the proportions in the
population; instead we want to have enough to assure that we will be able to talk
about even small groups in the population.

 E.g. the stigma of leprosy, TB,HIV, epilepsy, is considered a complicating factor in
the control of these diseases. In order to obtain insight in how stigma manifests
itself in different cultures in males and females, in rural and urban areas, in well to
do and poor patients, or in educated and illiterate ones, an investigator has to take
care that all these groups are included in the sample.

 If someone likes to have specific information about one particular group only, such
as, a group which, for unclear reasons, is more at risk than others: for e.g. , in a
country, death registers indicate that suicide among adolescents is on the increase
at an alarming rate and within that group twice as many boys as girls commit
suicide. Researchers may, therefore, want to concentrate on the boys to identify
what factors may be contributing to these suicides.

 It is sometimes illustrative to describe in depth some cases which are ‘typical 'for
the group one is interested in.
 For e.g., one may describe a ‘typical’ family in a rural area in a country A, or a
‘typical’ young school leaver who migrates from the rural area to town in search of
work, or ‘typical’ health problems of miners or malnourished children.

 Critical cases are those who ‘can make the difference’ with respect to an
intervention you want to introduce or to evaluate.
 E.g. an investigator has developed a local weaning food that is considered to be
affordable to all mothers. Before propagating it at a larger scale through MCH
clinics, it is better to first interview and observe some low income mothers as ‘test
cases’. If they manage to produce and use it, this will indicate that it is affordable
to whole group.

 This approach is particularly suitable for locating key informants or critical cases.
 We start with one or two information –rich key informants and ask them if they
know persons who know a lot about the topic of interest.

 E.g. in an exploratory study on coping behavior among AIDS orphans, it seemed that
child –headed households managed by girls survived better than those managed by
boys. The researcher then interviewed more adolescent boys and girls heading
households, to see whether this gender difference in ability to cope was real, and
how it could be explained. Patton labelled this kind of additional sampling during
the study as opportunistic sampling.

 It is a systematic error in sampling procedures, which leads to a distortion in the
results of the study.
 It can also be introduced as a consequence of improper sampling procedures, which
result in the sample not being representative of the study population.
 E.g. a study was conducted to determine the health needs of a rural population in
order to plan primary health care activities . However, a nomadic tribe, which
represented one third of the total population, was left out of the study.
 As a result, the study did not give an accurate picture of the health needs of the
total population.

 The most well known source is non response.
 Non response can occur on any interview situation, but it is mostly encountered in
large scale surveys with self administered questionnaires. Respondents may refuse
or forget to fill in the questionnaire. The problem lies in the fact that non –
respondents in a sample exhibit characteristics that differ systematically from the
characteristics of respondents.

 Other sources of bias in sampling may be less obvious, but may be serious :
- Studying volunteers only : the fact that volunteers are motivated to participate in
the study may mean that they are also different from the study population on the
factors being studied. Therefore, it is better to avoid using non random selection
procedures that introduce such an element of choice.

 Sampling of registered patients only : patients reporting to a clinic are likely to
differ systematically from people seeking alternative treatments.
 Missing cases of short duration : in studies of the prevalence of disease , cases of
short duration are more likely to be missed. This may mean missing fatal cases,
cases with short illness episodes and mild cases.

 Seasonal bias : it may be that the problem under study, for e.g., malnutrition may
exhibit different characteristics in different seasons of the year. For this reason,
data should be collected on the prevalence and distribution of malnutrition in a
community during all seasons rather than just at one point in time.

 Tarmac bias : study area are often selected because they are easily accessible by
car. However these areas are likely to be systematically different from more
inaccessible areas.

 If the recommendations from a study will be implemented in the entire study
population, one has the ethical obligation to draw a sample from this population in
a representative way.
 If during the research new evidence suggests that the sample was not representative
,this should be mentioned in any publication concerning the study, and care must be
taken not to draw conclusions or make recommendations that are not justified.

 Research methodology for health professionals by RC Goyal.
 Research methodology : methods and techniques 3rd edition. CR Kothari, Gaurav
Garg.
 Essentials of Preventive and Community Dentistry. 4th edition. Soben Peters.

sampling and statiscal inference

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