What is a sample?

A sample is a finite part of a statistical population whose properties are studied to gain information about the whole(Webster, 1985).
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.

A 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

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 knownThe 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

       SystematicRandom 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.
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
              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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