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.

## Why Is Random  Sampling Important?

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