sampling (1)
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Chapter 7
Salam Abdallah, PhD
MGT524
Sampling
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Survey elements
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Basic terms and concepts: 1
Population: the universe of units from which the sample is to be selected
Sample: the segment of population that is selected for investigation
Sampling frame: list of all units e.g. If all the workers in a factory make a population, a single worker is a unit of the population. If all the factories in a country are being studied for some purpose, a single factory is a unit of the population of factories. The sampling frame contains all the units of the population. It is to be defined clearly as to which units are to be included in the frame.
The frame provides a base for the selection of the sample.
The sampling frame operationally defines the target population from which the sample is drawn and to which the sample data will be generalized.
Representative sample: a sample that reflects the population accurately
Sample bias: distortion in the representativeness of the sample
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Basic terms and concepts: 2
Probability sample: sample selected using random selection
Non-probability sample: sample selected not using random selection method
Sampling error: difference between sample and population
Non-sampling error: are the unpredictable errors resulting from poor estimation or Non-response: when members of sample are unable or refuse to take part
Systematic errorsare those errors that tend to accumulate over the entire sample. For example, if there is an error in the questionnaire design, this could cause problems with the respondent's answers, which in turn, can create processing errors, etc. These types of errors often lead to a bias in the final results.
Census: data collected from entire population
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SAMPLING BREAKDOWN
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Picture of sampling breakdown
Sampling error
Difference between sample and population
Biased sample does not represent population
some groups are over-represented; others are under-represented
sources of bias
non-probability sampling, inadequate sample frame, non-response
Probability sampling reduces sampling error and allows for inferential statistics
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Probability sampling
The four stage process
Identify sampling frame from research objectives
Decide on a suitable sample size
Select the appropriate technique and the sample
Check that the sample is representative
4 types of probability sample
Simple random sample
Systematic sample
Stratified random sample
Multi-stage cluster sample
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Sample size
Choice of sample size is influenced by
Confidence needed in the data
Margin of error that can be tolerated
Types of analyses to be undertaken
Size of the sample population and distribution
Simple random sampleing
Each unit has an equal probability of selection
Sampling fraction: n/N
where n = sample size and N = population size
List all units and number them consecutively
Use random numbers table to select units
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Simple random sampleing
Example we want to conduct a survey to measure the levels training, skill development and learning among employees. And we selected a company that has 9000 employees. Surveying the whole population may not be feasible.
Decide your sample size e.g. 450
Number all the employees from 1 to 9000
450/9000 i.e 1 in 20
Generate 450 random numbers using random number generators, the numbers generated will the numbers given to represent the employees to be surveyed: http://www.psychicscience.org/random.aspx
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Systematic sampleing
Select units directly from sampling frame
From a random starting point, choose every nth unit (e.g. every 4th name)
a starting point is chosen at random , choose every nth unit , and choices thereafter are at regular intervals. For example, suppose you want to sample 450 employees from 9000. 9000/450=20, so every 20 employee is chosen after a random starting point between 1 and 20. If the random starting point is 16, then the employees selected are 16, 36, 56, 76, 96, 116, etc.
Make sure sampling frame has no inherent ordering if it has, rearrange it to remove bias
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Starting point is to categorise population into strata (relevant divisions, or departments of companies for example) i.e. stratifying the population by criterion,
Five departments, will result in 5 strata
So the sample can be proportionately representative of each stratum
Then, randomly select within each category as for a simple random sample
This approach will ensure the resulting sample will be distributed in the same as the population
We can also stratify by several criteria, i.e. by both department and gender and whether or not employees are above or below a certain salary level or occupational grade.
Note we can only stratify the sample if we have the relevant information accessible.
Stratified random sampling
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Stratified sampling an example
Using sampling fraction of of 1 in 20, we would expect to have 90 employees in our sample from this department of the company. However, because of sampling error, it is unlikely that this we will occur and that there will be a difference, so that there my be, say 85 or 93 from this department.
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Sample size required from a population 5,000 given a 95% confidence level for 2.5 margin of error you need a sample size of 1176
STATISTICAL SAMPLING
Multi-stage cluster sampleing
Useful for widely dispersed populations
First, divide population into groups (clusters) of units, like geographic areas, or industries, for example
Sub-clusters (sub-groups) can then be sampled from these clusters, if appropriate
Now randomly select units from each (sub)cluster
Collect data from each cluster of units, consecutively
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Multi-stage cluster sampleing
Example: We want a nationally representative sample of 5,000 employees who are working for the 100 largest companies in the UK.
Problem: Using simple random or systematic sampling would yield a widely dispersed sample, which would result in a great deal of travel for interviewers.
One solution to sample companies and then employees from each company. We randomly sample ten companies from the entire population of 100 largest companies in the UK, resulting in ten clusters, and we would then interview 500 randomly selected employees at each of the at of the ten companies i.e. 5,000 employees.
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Qualities of a probability sample
Good Representative Sample- allows for generalization from sample to population
Use inferential statistical tests to generalize
Sample means can be used to estimate population means
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Sample size
Absolute size matters more than relative size
The larger the sample, the more precise and representative it is likely to be
As sample size increases, sampling error decreases
Important to be honest about the limitations of your sample
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Factors affecting sample size: 1
Time and cost
after a certain point (n=1000), increasing sample size produces less noticeable gains in precision
very large samples are not cost-efficient
Non-response
response rate = % of sample who agree to participate (or % who provide usable data)
responders and non-responders may differ on a crucial variable
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Factors affecting sample size: 2
Heterogeneity of the population
the more varied the population is, the larger the sample will have to be
Kind of analysis to be carried out
some techniques require large sample (e.g. inferential statistics)
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Types of non-probability sampling: 1
1. Convenience sampling
the most easily accessible individuals
useful when piloting a research instrument
may be a chance to collect data that is too good to miss
2. Snowball sampling
researcher makes initial contact with a small group
these respondents introduce others in their network
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Types of non-probability sampling: 2
3. Quota sampling
often used in market research and opinion polls
relatively cheap, quick and easy to manage
proportionately representative of a populations social categories (strata)
but non-random sampling of each stratums units
interviewers select people to fit their quota for each category, so the sample may be biased towards those who appear friendly and accessible (e.g. in the street), leading to under-representation of less accessible groups
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Limits to generalization
findings can only be generalized to the population from which the sample was selected
be wary of over-generalizing in terms of locality
time, historical events and cohort effects
results may no longer be relevant and so require updating (replication)
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Error in survey research
Sampling error
unavoidable difference between sample and population
Sampling-related error
inadequate sampling frame; non-response
makes it difficult to generalize findings
Data collection error
implementation of research instruments
e.g. poor question wording in surveys
Data processing error
faulty management of data, e.g. coding errors
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Primary
Clusters
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Secondary
Clusters
Simple Random Sampling within Secondary Clusters
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