Question 3.37

3.37 Systematic random samples versus simple random samples.

The previous exercise introduces systematic random samples. Explain carefully why a systematic random sample does give every case the same chance to be chosen but is not a simple random sample.

3.37

Call the initial number chosen the “leading” number. All numbers form groups based off their leading number. Certainly, each leading number has an equal chance of being selected. Then, for each subsequent number, it is automatically chosen if its leading number is chosen. Which means all numbers (a.k.a. all groups) have an equal chance to be chosen. It is not a simple random sample because certain numbers can’t be chosen together, so all possible samples are not possible, only the pre-formed groups based off leading numbers.