COMMON MISTEAKS MISTAKES IN
USING STATISTICS: Spotting and Avoiding Them
Other Types of Random
Samples
There are other types of random samples (sometimes called probability samples)
besides simple random samples. These may be
appropriate in some studies. but when they are used, the correct method of statistical analysis
will differ from the method for a simple random sample. 1
Examples:
1. In a stratified
random sample, the population is first classified into groups
(called strata) with similar
characteristics. Then a simple random sample is chosen from each strata
separately. These simple random samples are combined to form the
overall sample.
Examples of characteristics
on which strata might be based include: gender, state, school district,
county, age.
Reasons to use a stratified rather than simple
random sample include:
- The researchers may be interested
in studying results
by strata as well as overall. Stratified sampling can help ensure that
there are enough observations within each strata to be able to make
meaningful inferences by strata.
- Statistical techniques can be
chosen taking the
strata into account to allow stronger conclusions to be drawn.
- Practical considerations may make
it impossible to take
a simple random sample.
2. In one-stage
cluster sampling, the population is also divided into groups,
called clusters. But instead
of sampling within each cluster, a simple random sample of clusters is selected, and the
overall sample consists of all individuals in the clusters that
constitute this simple random sample of clusters. For example, if the
purpose of the study is to find the average hourly wage of convenience
store employees in a city, the researcher might randomly select a
sample of convenience stores in the city and find the hourly wages of
all employees in each of the stores in the sample.
The results from cluster
samples are not as reliable as the results of simple random samples or
stratified samples, so it should only be used if practical
considerations do not allow a better sample scheme. For example, in the
convenience store example, it may be practically speaking impossible to
draw up a list of all convenience store employees in the city, but it
would be much less difficult to draw up a list of all the convenience
stores in the city.
3. There are also many adaptive sampling designs2,
in which the sampling pattern is updated (by a method depending on the
particular design) depending on the data already collected.
1. See, for example, M. Davern et
al (2007) Drawing Statistical Inferences from Historical Census Data,
Minnesota Population Center; download from
http://www.pop.umn.edu/research/mpc-working-papers-series/2007-working-papers-1/
2. See http://web.eecs.umich.edu/~qstout/AdaptSample.html
for a brief discussion of adaptive sampling designs, focusing on
clinical trials and computer applications.
See Seber, George A. F. and Mohammad M. Salehi (2013), Adaptive Sampling Designs: Inference for
Sparse and Clustered Populations for discussion of several types
of adaptive sampling designs, together with appropriate methods of
analysis. (This book focuses mainly on biological applications. It
requires some background in mathematical statistics. )
Last updated June 4, 2013