The question you submitted, “How Do I Select The Sample Method And Statistical Distribution For Statistical Analysis?” is really a multi-part question:
- Recommended sample method (random or systematic with or without stratification)
- Likely data distribution the sample came from (normal or non-normal)
- Best method to analyze the sample data (which depends on the answers to both of the above)
The Sample Method: The standard method for capturing data is Random Sample. Identify your “population of interest,” assign each element in the population a unique number, then use a random number table (or computer generated list) to select the specific elements to include in the sample.
The Statistical Distribution: This will be the first part of the story your sample data needs to expose. After you collect your sample data, utilize a normality test in a statistical software package (or produce a histogram of the sample data) to determine the probability that your data came from a population with a normal distribution (the ‘p’ value in software and a visual assessment with a histogram).
The Statistical Analysis: If your data comes from a population with a normal distribution you will likely use the T-test to judge either:
- Does the average value of our population fail to meet a standard/goal? – One Sample T-Test
- Does our population average from group #1 exceed our population average from group #2? – Two Sample T-Test
If your data does not come from a population with a normal distribution then you can use the One Sample Sign Test in place of the One Sample T-Test, and you can use the Mann-Whitney Test in place of the Two Sample T-Test.
As always, we will be more than happy to expand on or clarify any parts of the above answer.