Sth 232
March 20 2013
1
Example of multi-stage cluster sampling
Random Sample of Canadian Adult Population:
Randomly select clusters, e.g. five provinces or territories from a list of all
provinces and territories.
Randomly select a number of subunits from each cluster (province/territory) e.g.
census districts.
From each census district selected, randomly select census subdivisions.
Randomly select a certain number of residential blocks from each census
subdivision selected.
Randomly select a number of households from each block selected.
Randomly select a person to be included in the study from each selected
household.
Cluster samples are usually stratified as well, i.e. divided into strata or subgroups
before the clusters or subunits are selected .
In our example, to ensure regional representation, the provinces and territories
might be categorized into regions: BC, Prairies, Ontario, Quebec, Atlantic
provinces, and the northern territories.
A certain number of provinces or territories could be randomly selected from each
region that contains more than one province or territory.
Then the next steps would be taken.
Qualities of a probability sample
representative - allows for generalization from sample to population.
inferential statistical tests.
sample means can be used to estimate population means.
standard error (SE): estimate of discrepancy between sample mean and
population mean.
95% of sample means fall between +/- 1.96 SE from population mean.
Sampling Error
Probability samples with sufficient sample sizes minimize the amount of sampling
error, but some sampling error is bound to occur.
e.g. there is usually some difference between a sample mean and the
population mean (μ) that it is designed to represent.
About 95 per cent of all sample means lie within 1.96 standard errors of the mean.
Hence this range is called a confidence interval, a 95% confidence interval.
Sample Size
The absolute size of the sample matters.
(not the proportion of the population that it comprises.) Sth 232
March 20 2013
2
As sample size increases, sampling error tends to decrease.
Common sample sizes:100, 400, 900, 1600, 2500.
Each size increase cuts the sampling error by 1/2, then 1/3, then 1/4, and then 1/5
respectively.
The biggest change occurs between 100 and 400.
Is an increased sample size worth the time and effort?
Often sample size is dictated by financial concerns.
Non-response
The response rate is the percentage of the sample that participates in the study.
Is there some particular issue common to the non-responders that brings them to
differ in some important way from those who participate?
Heterogeneity of the Population
Generally, the greater the heterogeneity of the population on the characteristics
of interest, the larger the sample size should be.
Kind of Analysis
The sample size needed may vary depending on what sort of analysis will be
done.
Types

More
Less