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When samples from different sized subgroups are used and sampling is taken with the same probability, the chances of selecting a member from a large group are less than selecting a member from a smaller group. This is known as probability proportional to size (PPS). For example, if one sample had 20,000 members, the probability of a member being selected would be 1/20000 or .005 percent. If another sample had 10,000 members, the chance of a member being selected would be 1/10000 or .01 percent.

Sampling methods are classified as either probability or nonprobability. Nonprobability samples are selected in some nonrandom manner, but with an unknown probability of a particular member of the population being selected. Probability samples have a known non-zero probability of being selected.

There can be a difference between the results obtained using the sample and the target population. This difference is known as sampling error. Sampling cannot be measured in nonprobability sampling. It can be measured in probability sampling. When the results of a study are reported, they include the plus or minus range of sampling error.

If the sample size cannot be equalized, a factor or weight can be used to equalize the relative importance of a member in the study. If the example of samples with 10,000 members and 20,000 members were used, a member from the sample of 10,000 can be multiplied by a factor of 1X, while a member from the sample of 20,000 can be multiplied by 2X. This would result in an equal value or weight for each member despite a different probability of the members being selected.rnrnSampling bias is the result of a subgroup being underrepresented in a study due to its smaller size. Weighting can be used to reduce sample bias. PPS is self-weighting thanks to the difference in sample size.

Even when PPS is used, there needs to be a method for dividing a target population into subgroups. Members of the subgroups can be selected by preexisting conditions such as their membership in a group. This is known as cluster sampling.

PPS can be combined with other methods of selecting samples. For example, clustering could be used where members of the subgroups were already assigned to a subgroup such as a military unit. Then stratification could be used so that demographics such as rank were equally distributed. Finally, simple random sampling (SRS) could be used to avoid sample bias. PPS can then be used for the study.

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Harvey Sells is a freelance writer specializing in manufacturing, technology, organization and science. He has been writing short mysteries for several years with a number of stories published on various mystery websites. Sells has won an international mystery writing competition and has published one mystery novel. He holds a Master of Education from the University of Georgia.