Question: Does PTSD have any effects on returning veterans?
For data points to be analyzed using a Z-test the data points (PTSD and veterans) should be independent from each other. Z-test will be preferred when the sample size n is greater than 30. If n<30 then the distribution should be normal but IF n>30 the distribution on the data must not be normal. The variation in the samples should be equal. The selection should be random meaning that all individual elements ought to have equal chances of being included in the sample. Though some differences are allowed, the sample sizes should be really equal.
For data sets to be analyzed using students t-test they should be independent from one another unless they are paired. It is also used when the sample size is less than 30 (n<30). Distributions are supposed to normal for both equal and unequal variances tests. The samples should have the same variance and their selection should be done at random. If the data is large enough random number tables are used whereby the population is allocated numbers and then selection is done from the random numbers.
Question posted: Does PSTD and retuning veterans relate?
In this case one uses simple random sampling which is a probability sampling procedure. This method is preferable because it gives equal chance for the individuals of interest to be incorporated in the samples. This is a requirement for use of z-tests and t-test in the analysis.
Question posted: Is returning of veterans located in different places affected by PTSD?
Here we use clustered sampling which is also a probability sampling procedure. It will give equal chances of selection of individuals. This method was necessary because the veterans were in different location and therefore have to be grouped into sections from where the samples are picked from, with each given an equal chance of selection to avoid biasness.
Cochran, W.G. (1999). Sampling techniques, 3rd Ed. New York: Wiley Publishers