**Sampling**

__What is a sample?__When dealing with people, it can be defined as a set of respondents (people) selected from a larger population for the purpose of a survey.

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__population__is a group of individuals’ persons, objects, or items from which samples are taken for measurement for example a population of presidents or professors, books etc__Sampling Rationale__

• Explain the reasoning behind proposed sample locations, number of samples, types of analyses,

• Sampling is the process of selecting units (e.g., people, organizations) from a population of interest so that by studying the sample we may fairly generalize our results back to the population from which they were chosen.

• When an organizations require data they either use data collected by somebody else (secondary data), or collect it themselves (primary data).This is usually done by SAMPLING that is collecting data from a representative SAMPLE of the population they are interested in.

__Types of sampling__

Probability and Non-probability sampling

__Probability__

The term

__probability__samplings used when the selection of the__sample__is purely based on chance.__The human mind__has no control on the selection or non- selection of the units for the sample. Every unit of the population has known nonzero probability of being selected for the sample.• The probability of selection may be equal or unequal but it should be non-zero and should be known

*.*The probability samplings also called the random sampling (not simple random sampling).__Probability Sampling Methods__

__Simple Random Sample__

Every subset of a specified size n from the population has an equal chance of being selected

• Simple Random sample is obtained by choosing elementary units in such a way that each unit in the population has an equal chance of being selected from a very large Population. Random sample is free from sampling bias. However, using a random number table to choose the elementary units can be cumbersome. If the sample is to be collected by a person untrained in statistics, then instructions may be misinterpreted and selections may be made improperly. Instead of using a list of random numbers, data collection can be simplified by selecting say every 10th or 100th unit after the first unit has been chosen randomly as discussed below. Such a procedure is called systematic random sampling.

2.

*SystematicRandom Sample*•

*Systematic*Random sample is obtained by choosing elementary units in such a way that each unit in the population has an equal chance of being selected.Every kth member ( for example: every 10th person) is selected from a list of all population members.3) A stratified sample:-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.

A stratified sample is obtained by independently selecting a separate simple random sample from each population stratum.A population can be divided into different groups may be based on some characteristic or variable like income of education. Like any body with ten years of education will be in group A, between 10 and 20 group B and between 20 and 30 group C. These groups are referred to as strata. You can then randomly select from each stratum a given number of units which may be based on proportion like if group A has 100 persons while group B has 50, and C has 30 you may decide you will take 10% of each. So you end up with 10 from group A, 5 from group B and 3 from group C.

4) A cluster sample:-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.

A cluster sample is obtained by selecting clusters from the population on the basis of simple random sampling.The sample comprises a census of each random cluster selected. For example, a cluster may be something like a village or a school, a state.So you decide all the elementary schools in Peshawar are clusters. You want 20 schools selected. You can use simple or systematic random sampling to select the schools, and then every school selected becomes a cluster.

__Non Probability Sampling Methods__

In non-probability sampling, the sample is not based on chance. It is rather determined by some person. We cannot assign an element of population the probability of its being selected in the sample.

__1) Convenience Sampling:-__Where the researcher questions anyone who is available. This method is quick and cheap. However we do not know how representative the sample is and how reliable the result.A convenience sample is a matter of taking what you can get. It is an accidental sample. Although selection may be unguided, it probably is not random, using the correct definition of everyone in the population having an equal chance of being selected. Volunteers would constitute a convenience sample.

• Convenience Sample

• Selection of whichever individuals are easiest to reach

• It is done at the “convenience” of the researcher

__2) Quota Sampling:-__Using this method the sample audience is made up of potential purchasers of your product. For example if you feel that your typical customers will be male between 18-23, female between 26-30, then some of the respondents you interview should be made up of this group, i.e. a quota is given.

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__3) The judgment sample:-__A judgment sample is obtained according to the discretion of someone who is familiar with the relevant characteristics of the population.

**4.**

__purposive sample__

• A purposive sample is a non-representative subset of some larger population, and is constructed to serve a very specific need or purpose. A researcher may have a specific group in mind, such as high level business executives. It may not be possible to specify the population - they would not all be known, and access will be difficult. The researcher will attempt to zero in on the target group, interviewing whomever is available.

**5)**

__snowball sample__

• A subset of a purposive sample is a snowball sample -- so named because one picks up the sample along the way, A snowball sample is achieved by asking a participant to suggest someone else who might be willing or appropriate for the study. Snowball samples are particularly useful in hard-to-track populations, such as truants, drug users, etc.

__In statistics, sampling error__is incurred when statistical characteristics of a population are estimated from a subset, or sample, of the population. Since the sample does not include all members of the population, statistics on the sample, such as means, generally differ from statistics on the entire population. For example, if one measures the height of a thousand individuals from a country of one million, the average height of the thousand is typically not the same as the average height of all one million people in the country.

• Since sampling is typically done to determine the characteristics of a whole population, the difference between the sample and population values is considered a

*sampling error*• Exact measurement of sampling error is generally infeasible since the true population values are unknown; however, sampling error can often be estimated by probabilistic modeling of the sample

• Errors in Sampling

• Non-Observation Errors

– Sampling error: naturally occurs

– Coverage error: people sampled do not match the population of interest

– Underrepresentation

– Non-response: won’t or can’t participate

• Errors of Observation

• Interview error- interaction between interviewer and person being surveyed

• Respondent error: respondents have difficult time answering the question

• Measurement error: inaccurate responses when person doesn’t understand question or poorly worded question

• Errors in data collection

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