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Tahir Mahmood Lecturer Department of Statistics

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Sampling Theory and Methods

Tahir Mahmood

Lecturer

Department of Statistics

- Explain the role of sampling in the research process
- Distinguish between probability and non probability sampling
- Understand the factors to consider when determining sample size
- Understand the steps in developing a sampling plan

- Sampling is the procedure a researcher uses to gather people, places, or things to study.
- Samples are always subsets or small parts of the total number that could be studied.
- Sampling is the process of selecting a small number of elements from a larger defined target group of elements such that the information gathered from the small group will allow judgments to be made about the larger groups

- What is your population of interest?
- To whom do you want to generalize your results?
- All doctors
- School children
- Indians
- Women aged 15-45 years
- Other

- To whom do you want to generalize your results?

Get information about large populations

- Less costs
- Less field time
- More accuracy i.e. Can Do A Better Job of Data Collection
- When it’s impossible to study the whole population

Research objectives

Degree of accuracy

Time frame

Resources

Research scope

Knowledge of

target population

Statistical analysis needs

- Common Methods:
- Budget/time available
- Executive decision
- Statistical methods
- Historical data/guidelines

- How many completed questionnaires do we need to have a representative sample?
- Generally the larger the better, but that takes more time and money.
- Answer depends on:
- How different or dispersed the population is.
- Desired level of confidence.
- Desired degree of accuracy.

Population:

a set which includes all measurements of interest

to the researcher

(The collection of all responses, measurements, or counts that are of interest)

Sample:

A subset of the population

- A list of population elements (people, companies, houses, cities, etc.) from which units to be sampled can be selected.
- Difficult to get an accurate list.
- Sample frame error occurs when certain elements of the population are accidentally omitted or not included on the list.
- See Survey Sampling like HIES PDHS, PSLM, MICS

probability

sampling

Nonprobability

sampling

- A probability sampling scheme is one in which every unit in the population has a chance (greater than zero) of being selected in the sample, and this probability can be accurately determined.

- Non probability sampling is any sampling method where some elements of the population have no chance of selection (these are sometimes referred to as 'out of coverage‘ / 'under covered'), or where the probability of selection can't be accurately determined.
- It involves the selection of elements based on assumptions regarding the population of interest, which forms the criteria for selection.

Probability

- Simple random sampling
- Systematic random sampling
- Stratified random sampling
- Cluster sampling

Non probability

- Convenience sampling
- Judgment sampling
- Quota sampling
- Snowball sampling

Simple random sampling is a method of probability sampling in which every unit has an equal non zero chance of being selected

Systematic random sampling is a method of probability sampling in which the defined target population is ordered and the sample is selected according to position using a skip interval

- 1: Obtain a list of units that contains an acceptable frame of the target population
- 2: Determine the number of units in the list and the desired sample size
- 3: Compute the skip interval
- 4: Determine a random start point
- 5: Beginning at the start point, select the units by choosing each unit that corresponds to the skip interval

Systematic sampling

Stratified random sampling is a method of probability sampling in which the population is divided into different subgroups and samples are selected from each.

- 1: Divide the target population into homogeneous subgroups or strata
- 2: Draw random samples from each stratum
- 3: Combine the samples from each stratum into a single sample of the target 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.

Section 1

Section 2

Section 3

Section 5

Section 4

- Accidental, Haphazard or convenience sampling
members of the population are chosen based on their relative ease of access. To sample friends, co-workers, or shoppers at a single mall, any one on the street

- Snowball method
The first respondent refers to next and then a chain starts Example: Addicts, HIV etc.

- Judgmental sampling or Purposive sampling
The researcher chooses the sample based on who they think would be appropriate for the study. This is used primarily when there is a limited number of people that have expertise in the area being researched.

- Quota sampling:
- There are two types of quota sampling: proportional. In proportional quota sampling you want to represent the major characteristics of the population by sampling a proportional amount of each.
Non proportional:

Non proportional quota sampling is a bit less restrictive. the minimum number of sampled units is specified in each category. not concerned with having numbers that match the proportions in the population

- Ad hoc quotas:
- A quota is established (say 65% women) and researchers are free to choose any respondent they wish as long as the quota is met.
- Expert Sampling
- Expert sampling :involves the assembling of a sample of persons with known or demonstrable experience and expertise in some area.
- Often, we convene such a sample under the auspices of a "panel of experts." There are actually two reasons you might do expert sampling. First, because it would be the best way to elicit the views of persons who have specific expertise.

- Systematic error (or bias)
Inaccurate response (information bias)

- Selection bias

- Sampling error (random error)
Sampling error is any type of bias

that is attributable to mistakes

in either drawing a sample or

determining the sample size

- The probability of finding a difference with our sample compared to population, and there really isn’t one….
- Known as the α (or “type 1 error”)
- Usually set at 5% (or 0.05)

- The probability of not finding a difference that actually exists between our sample compared to the population…
- Known as the β (or “type 2 error”)
- Power is (1- β) and is usually 80%

- Variability of the population characteristic under investigation
- Level of confidence desired in the estimate
- Degree of precision desired in estimating the population characteristic

- The difference between nonprobabilityand probability sampling is that nonprobability sampling does not involve random selection and probability sampling does.
- Nonprobability sampling techniques cannot be used to infer from the sample to the general population.
- Any generalizations obtained from a nonprobability sample must be filtered through one's knowledge of the topic being studied.
- Performing nonprobability sampling is considerably less expensive than doing probability sampling, but the results are of limited value.

Probability Sampling and Sample Sizes

- When estimating a population mean
n = (Z2B,CL)(σ2/e2)

- n estimates of a population proportion are of concern
n = (Z2B,CL)([P x Q]/e2)

- Less prone to bias
- Allows estimation of magnitude of
sampling error, from which you can

determine the statistical significance

of changes/differences in indicators

- Requires that you have a list of all
sample elements

- More time-consuming
- More costly
- No advantage when small numbers
of elements are to be chosen

- More flexible
- Less costly
- Less time-consuming
- Judgmentally representative
samples may be preferred when

small numbers of elements are to be

chosen.

- Greater risk of bias
- May not be possible to generalize
to program target population

- Subjectivity can make it difficult to
measure changes in indicators overtime

- No way to assess precision or
reliability of data

Thank you