California Department of Resources Recycling and Recovery (CalRecycle) 

Diversion Study Guide, Appendix J

Determining the Number of Samples to Take or Surveys to Conduct

A universally accepted or legally mandated statistical formula to determine the number of solid waste diversion audits or surveys needed for a statistically representative study does not exist.  The following standard formulas (designed for determining sample sizes for proportions) have been used to fill that void. A very large jurisdiction such as Los Angeles could take more samples and set up stratified sampling within business groups.

While other methods may exist or may be developed later, this method should provide a base (minimum number of samples needed) to which additional samples may be added as the specific conditions in a jurisdiction dictate. If you are only interested in diversion in a single business group, it is suggested that the jurisdiction take a minimum of 40 samples within that single business group to get reliable, useful results. Note: When using cluster and stratified sampling in medium or large jurisdictions, groupings should be made using either the four- or six-digit SIC code. This level may not be useful in smaller communities. Jurisdictions should work with a statistician to determine groupings.

If you are only interested in diversion in the overall business sector, then you need to determine the number of random samples needed for a 90 percent confidence interval, with a plus or minus 5 percent precision level. Because the participation level for any given diversion program or activity is unknown prior to sampling, the initial estimated participation level is assumed to be 50 percent (thus maximizing the number of samples required).

*In the table, if the number of entities in a jurisdiction fall between the values given, use the value that results in the smaller number of samples needed (the entity number represents the bottom of the range of values).

Step 1.  Number of samples for an infinitely large population

Where:
z = 1.645 (value for 90 percent confidence interval)
p = 0.5 (estimate for unknown participation level of 50 percent)
r = 0.05 (5 percent precision level)


Step 2. Corrected number of samples for a finite population

Where:
N = Number of entities (businesses or households) in population to be sampled.
no = 270.6025 
n = Number of samples needed

Tables: Number of samples based on the number of entities in the population:

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Last updated: March 19, 2000
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Local Assistance & Market Development: LAMD@calrecycle.ca.gov (916) 341-6199