Definition of a Sample
The sample normally comes from a larger group of individuals or objects, called the target population.
Choice of Sampling Frame
To obtain a working definition of the population to be studied, which constitutes the sampling frame.
The Electoral register, the ‘Yellow Pages’ telephone directory, or companies listed on the New York stock exchange.
Types of Sample
Sampling techniques fall into two broad categories, namely non-probability samples, which are the domain of the phenomenologist, and probability samples, which are used by the positivistic researcher. Examples of nonprobability samples include convenience samples, judgment samples, quota samples and snowball samples.
In probability sampling the assumption is that each individual or element of the population has a known, not necessarily equal, probability of being selected. Examples of probability sampling include simple random sampling. systematic sampling, stratified sampling, cluster sampling, and multi-stage sampling. Probability samples can be rigorously analysed by means of statistical techniques.
Non-Probability Samples
From the point of view of phenomenologist, the selection of a random sample is seldom if ever relevant.
Non-probability samples are particularly relevant in exploratory research. The more popular non-probability sampling methods are described below.
Convenience Samples
Convenience samples comprise those individuals or organisations that are most readily available to participate in the study.
Judgment Samples
Judgment samples, also called purposive samples, are samples where individuals are selected with a specific purpose in mind, such as their likelihood of representing best practice in a particular issue. The composition of such a sample is not made with the aim of it being statistically representative of the population. This approach is extensively used in the exploratory research stage.
Snowball Samples
A snowball sample is one where the researcher uses an informant to help him or her find the next informant. Sometimes this is the only way in which a researcher will obtain access to appropriate informants.
Probability Samples
In obtaining a probability sample, use is made of some random procedure for the selection of the individuals or organisations. This is done in an attempt to remove the possibility of selection bias.
Simple Random Sampling
In simple random sampling each member of the population should have an equal chance of being selected. This can be achieved by numbering the individuals in the sampling frame, and then selecting from these using some random procedure produced manually or on a computer.
Should there be some pattern present in the sampling frame, then such samples will be biased. For example, a systematic sample from the daily sales of a supermarket could result in picking out sales figures for Saturdays only.
Stratified Sampling
In stratified sampling the population is subdivided into homogeneous groups, called strata, prior to sampling. Random samples are then drawn from each of the strata and the aggregate forms the stratified sample. This can be done in one of two ways:
The overall sample size n can comprise items such that
the number of items from each stratum will be in
proportion to the size of the stratum.
The overall sample size can comprise items from each
stratum where the number of items from each of the
strata are determined according to the relative
variability of the items within each of the strata.
Cluster Sampling
In cluster sampling, the population is considered to be made up of groups, called clusters, where the clusters are naturally formed groups such as companies, or locational units.
A cluster sample from a large organisation could be achieved by treating the various departments of a company as the clusters. A random sample of departments could then be chosen and all individuals in the departments sampled. In other words a census of the selected departments (clusters) is performed.
Multi-Stage Sampling
An extension of cluster sampling is multi-stage sampling. The simplest multi-stage sample involves random selection of the clusters in the first stage, followed by a random selection of items from each of the selected clusters. This is called two-stage sampling. More complex designs involve more than two stages.
Size of Sample
Type of sample, variability in the population, time, costs, accuracy of estimates required, and confidence with which generalisations to the population are made.
Statistical Determination of Sample Size
The first situation concerns how to determine the sample size for estimating a population mean to a specified margin of error, or accuracy, with a specified level of confidence
.
The second situation shows how to determine the sample size needed to estimate a population proportion (or percentage) to a specified margin of error, or accuracy, within a specified level of confidence.
Sample size to Estimate the Mean
The question is now what size of sample is needed to be 95 per cent confident that the sample mean will be within E units of the true mean, where the unit of measurement of E can be in, say, seconds or minutes? E is therefore the accuracy required from the estimate. Under the assumption that the population from which the sample is being made is very large, the sample size is given by:
n = 4σ ²
E ² (1)
Where σ is the population standard deviation of response times. In practice σ is inevitably unknown and will have to be estimated. This can be done by using response times for a pilot sample of size nр’ say, in the sample standard deviation formula:
S= Σ(χ¡ - m) ²
n p – 1
S R = max(χ¡ ) - min(χ¡ ) = range(χ¡ )
4 4
Some texts suggest division by 6. Of course a purely subjective estimate of σ is also possible. Level of 99 per cent, then the sample size is given by:
N = 9 σ ²
E ²
Where σ can be estimated as described above.
Sample Size to estimate a Percentage
Suppose a firm wished to estimate the actual percentage, p, say, of its customers who purchase software from a competing company.
n = 4p(100 – p )
E ²
Where p can be estimated as described above.
The caveat in this case is that p is not known, as it is the parameter being estimated. In practice the value of p used in the above formula can be estimated in a number of ways. It can be estimated subjectively, i.e. guessed or it can be taken from a pilot sample or taken to be 50 per cent. The latter results in the most conservative sample size estimate.
For a 99 per cent confidence level.
n = 9p(100-p)
E²
Where p can be estimated as described above.
The sample normally comes from a larger group of individuals or objects, called the target population.
Choice of Sampling Frame
To obtain a working definition of the population to be studied, which constitutes the sampling frame.
The Electoral register, the ‘Yellow Pages’ telephone directory, or companies listed on the New York stock exchange.
Types of Sample
Sampling techniques fall into two broad categories, namely non-probability samples, which are the domain of the phenomenologist, and probability samples, which are used by the positivistic researcher. Examples of nonprobability samples include convenience samples, judgment samples, quota samples and snowball samples.
In probability sampling the assumption is that each individual or element of the population has a known, not necessarily equal, probability of being selected. Examples of probability sampling include simple random sampling. systematic sampling, stratified sampling, cluster sampling, and multi-stage sampling. Probability samples can be rigorously analysed by means of statistical techniques.
Non-Probability Samples
From the point of view of phenomenologist, the selection of a random sample is seldom if ever relevant.
Non-probability samples are particularly relevant in exploratory research. The more popular non-probability sampling methods are described below.
Convenience Samples
Convenience samples comprise those individuals or organisations that are most readily available to participate in the study.
Judgment Samples
Judgment samples, also called purposive samples, are samples where individuals are selected with a specific purpose in mind, such as their likelihood of representing best practice in a particular issue. The composition of such a sample is not made with the aim of it being statistically representative of the population. This approach is extensively used in the exploratory research stage.
Snowball Samples
A snowball sample is one where the researcher uses an informant to help him or her find the next informant. Sometimes this is the only way in which a researcher will obtain access to appropriate informants.
Probability Samples
In obtaining a probability sample, use is made of some random procedure for the selection of the individuals or organisations. This is done in an attempt to remove the possibility of selection bias.
Simple Random Sampling
In simple random sampling each member of the population should have an equal chance of being selected. This can be achieved by numbering the individuals in the sampling frame, and then selecting from these using some random procedure produced manually or on a computer.
Should there be some pattern present in the sampling frame, then such samples will be biased. For example, a systematic sample from the daily sales of a supermarket could result in picking out sales figures for Saturdays only.
Stratified Sampling
In stratified sampling the population is subdivided into homogeneous groups, called strata, prior to sampling. Random samples are then drawn from each of the strata and the aggregate forms the stratified sample. This can be done in one of two ways:
The overall sample size n can comprise items such that
the number of items from each stratum will be in
proportion to the size of the stratum.
The overall sample size can comprise items from each
stratum where the number of items from each of the
strata are determined according to the relative
variability of the items within each of the strata.
Cluster Sampling
In cluster sampling, the population is considered to be made up of groups, called clusters, where the clusters are naturally formed groups such as companies, or locational units.
A cluster sample from a large organisation could be achieved by treating the various departments of a company as the clusters. A random sample of departments could then be chosen and all individuals in the departments sampled. In other words a census of the selected departments (clusters) is performed.
Multi-Stage Sampling
An extension of cluster sampling is multi-stage sampling. The simplest multi-stage sample involves random selection of the clusters in the first stage, followed by a random selection of items from each of the selected clusters. This is called two-stage sampling. More complex designs involve more than two stages.
Size of Sample
Type of sample, variability in the population, time, costs, accuracy of estimates required, and confidence with which generalisations to the population are made.
Statistical Determination of Sample Size
The first situation concerns how to determine the sample size for estimating a population mean to a specified margin of error, or accuracy, with a specified level of confidence
.
The second situation shows how to determine the sample size needed to estimate a population proportion (or percentage) to a specified margin of error, or accuracy, within a specified level of confidence.
Sample size to Estimate the Mean
The question is now what size of sample is needed to be 95 per cent confident that the sample mean will be within E units of the true mean, where the unit of measurement of E can be in, say, seconds or minutes? E is therefore the accuracy required from the estimate. Under the assumption that the population from which the sample is being made is very large, the sample size is given by:
n = 4σ ²
E ² (1)
Where σ is the population standard deviation of response times. In practice σ is inevitably unknown and will have to be estimated. This can be done by using response times for a pilot sample of size nр’ say, in the sample standard deviation formula:
S= Σ(χ¡ - m) ²
n p – 1
S R = max(χ¡ ) - min(χ¡ ) = range(χ¡ )
4 4
Some texts suggest division by 6. Of course a purely subjective estimate of σ is also possible. Level of 99 per cent, then the sample size is given by:
N = 9 σ ²
E ²
Where σ can be estimated as described above.
Sample Size to estimate a Percentage
Suppose a firm wished to estimate the actual percentage, p, say, of its customers who purchase software from a competing company.
n = 4p(100 – p )
E ²
Where p can be estimated as described above.
The caveat in this case is that p is not known, as it is the parameter being estimated. In practice the value of p used in the above formula can be estimated in a number of ways. It can be estimated subjectively, i.e. guessed or it can be taken from a pilot sample or taken to be 50 per cent. The latter results in the most conservative sample size estimate.
For a 99 per cent confidence level.
n = 9p(100-p)
E²
Where p can be estimated as described above.
No comments:
Post a Comment