Tahir mahmood lecturer department of statistics
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Sampling Theory and Methods. Tahir Mahmood Lecturer Department of Statistics. Outlines:. 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

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Tahir Mahmood Lecturer Department of Statistics

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Tahir mahmood lecturer department of statistics

Sampling Theory and Methods

Tahir Mahmood

Lecturer

Department of Statistics


Outlines

Outlines:

  • 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


What is sampling

What is Sampling?

  • 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


Tahir mahmood lecturer department of statistics

  • 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

  • Can you sample the entire population?


  • Why sampling

    Why sampling?

    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


    Important factors in selecting a sample design

    Important Factors in selecting a Sample Design

    Research objectives

    Degree of accuracy

    Time frame

    Resources

    Research scope

    Knowledge of

    target population

    Statistical analysis needs


    Common methods for determining sample size

    Common Methods for Determining Sample Size

    • Common Methods:

      • Budget/time available

      • Executive decision

      • Statistical methods

      • Historical data/guidelines


    Determining sample size

    Determining Sample Size

    • 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.


    Important statistical terms

    IMPORTANT STATISTICAL TERMS

    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


    Sampling frame

    Sampling Frame

    • 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


    Sampling methods

    Sampling Methods

    probability

    sampling

    Nonprobability

    sampling


    Probability sampling

    Probability 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

    Non-Probability Sampling

    • 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.


    Types of sampling methods

    Types of Sampling Methods

    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

    Simple Random Sampling

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


    Simple random sampling1

    Simple random sampling


    Systematic random sampling

    Systematic Random Sampling

    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


    Steps in drawing a systematic random sample

    Steps in Drawing a Systematic Random Sample

    • 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


    Tahir mahmood lecturer department of statistics

    Systematic sampling


    Stratified random sampling

    Stratified Random 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.


    Steps in drawing a stratified random sample

    Steps in Drawing a Stratified Random Sample

    • 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


    Example

    Example:


    Cluster sampling

    Cluster sampling

    • 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.


    Cluster sampling1

    Cluster sampling

    Section 1

    Section 2

    Section 3

    Section 5

    Section 4


    Tahir mahmood lecturer department of statistics

    • 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.


    Tahir mahmood lecturer department of statistics

    • 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.


    Errors in sample

    Errors in sample

    • 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


    Type i error

    Type-I Error

    • 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)


    Type ii error

    Type-II Error

    • 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%


    Factors affecting sample size for probability designs

    Factors Affecting Sample Size for Probability Designs

    • Variability of the population characteristic under investigation

    • Level of confidence desired in the estimate

    • Degree of precision desired in estimating the population characteristic


    Comparison b w probability and nonprobability sampling

    Comparison b/w Probability and Nonprobability Sampling

    • 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.


    Tahir mahmood lecturer department of statistics

    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)


    Probability sampling advantages

    Probability Sampling Advantages

    • Less prone to bias

    • Allows estimation of magnitude of

      sampling error, from which you can

      determine the statistical significance

      of changes/differences in indicators


    Probability sampling disadvantages

    Probability Sampling Disadvantages

    • 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


    Non probability sampling advantages

    Non Probability Sampling Advantages

    • More flexible

    • Less costly

    • Less time-consuming

    • Judgmentally representative

      samples may be preferred when

      small numbers of elements are to be

      chosen.


    Non probability sampling disadvantages

    Non Probability Sampling Disadvantages

    • 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


    Tahir mahmood lecturer department of statistics

    Thank you


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