To use parametric test like as t test, Z test ,ANOVA test it is necessary for data are random or sampling technique should probability sampling?
It is necessary for probability sampling for parametric test?
In sampling and experimental design I tend to prefer maximally dispersed over random. So the outcome hinges on this problem. Say that I have 2 factors each at two levels to give 1a, 1b, 2a, 2b as possible treatments. I have three reps. So I have 1a1, 1a2, 1a3, etc... In a linear series. One possible randomization would be 1a1, 1a2, 1a3, 2a1, 2a2, 2a3, 1b1, 1b2, 2b3, 2b1, 1b3, 2b2. Would you accept this? Most researchers would not. So the next question is this: is the statistical requirement for a randomized order satisfied if we restrict the randomization to only those patterns that we like? Another alternative is to randomly pick the treatment applied to the first replicate and then maximally disperse all remaining treatments.
The issue with randomization is that there may be factors that you are not aware of (cannot see, cannot measure, haven't thought about) that could influence the outcome of the experiment. So I want to know the effect of dosage on the outcome of a new drug. I could test the drug at dose 1 on the first fifty mice, at dose 2 on the second set of 50 mice, and dose 3 on the final 50 mice. The problem is that my hand gets tired, and my concentration wanes as the day progresses. My accuracy in the first 10 mice is therefore different than the last ten mice. If the effect is large enough I could get significant treatment differences that occur because I am tired at the end of the day. Randomization helps reduce the effect of "I am tired" on the experimental outcome. Maybe the effect is that people that enter the hospital at 7am are mostly from the area within 1 km of the hospital, while at noon the hospital sees people from 100 km distant, and by 7pm the draw is back down to 5 km area. In the morning people have not had a chance to travel long distances to get to the hospital. In the evening people are reluctant to travel alone at night. If I treat the people in the experiment like I suggested treating the mice, then there could be problems.
Did this help?
Sir Ronald Fisher, the inventor of modern Design of Experiments, once said that there is no experimentation without randomization. Unfortunately there is confusion between randomized experiments and random sampling. I suggest looking at the 5 links below
https://en.wikipedia.org/wiki/Randomized_experiment
https://en.wikipedia.org/wiki/Design_of_experiments
https://en.wikipedia.org/wiki/Survey_sampling
https://en.wikipedia.org/wiki/Simple_random_sample
https://en.wikipedia.org/wiki/Statistical_inference
as a start in clarifying things.
Best wishes, David Booth
PS Statistical inference is based on probability models. Thus there is no statistical inference without a probability sample. A statistical inference is an inference with an associated probability that it is true.
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