Some of the common assumptions for the parametric tests include Normality, Randomness, Absence of Outliers, Homogeneity of Variances, Independence of Observations, and Linearity.
whether Random sampling (data collection method) is included this list or not?
Reply with references .
When data was collected by nonprobability selection, then the sample results cannot be generalized to the population. Therefore use of parametric tests can be redundent in this case.
Hello Shahul,
as random sampling only exists in an ideal work and every actual sample more or less differs from a random sample, the question is how far the sampling deviates from random sampling and whether this deviations actually changes the theoretical distribution distribution that underlies the estimation of Standard errors (and thus, p values). Nobody knows that. Therefore, a practical solution is to apply parametric tests when its defendable and even than being a bit modest in one's conclusions. Otherwise, we have to stop to apply them at al.
My thoughts (being a person with only moderate statistical background ;)
Best,
--Holger
In behavioral and psychological research, wherein respondents' perceptions are measured, data are collected on continous/interval scales and lots of studies have been published that employed convenience sampling (non-random) technique. Random/probability sampling cannot be applied in most of the situations.
To clarify the issue, the relevant article is available on my ResearchGate Site.
Ayhan, Öztas (2011) Non-probability Sampling Survey Methods. In: Lovric M. (eds.) International Encyclopedia of Statistical Science. Springer, Berlin & Heidelberg. Part 14, pp. 979–982.
The convenience of not utilising probability based sampling methods to collect data fades away by the introduction of parametric statistics since it would be useless to appropriate the data to a population.
In cases where probability sampling cannot be used, nonprobability selection (like convenience sampling) can be used. In this case, Statistical tests still should not be used. The survey results can be evaluated with available measures, and can represent within the selected sample only. Again this cannot be generalized to the population, because the population is undefined in this case.
As others have noted, neither parametric nor non-parametric methods give inferential statistics (significance, confidence intervals) that are strictly valid unless the sample was drawn from an identifiable population using probability (or at least, quasi-random) sampling.
Unfortunately, journal editors and referees, grant panel reviewers, and others in your target audience may expect to see such statistics reported regardless. If you choose to report inferential statistics from a non-probability sample, a disclaimer is in order to acknowledge that the results indicate whether the effects observed in this particular data set would have reached statistical significance if obtained in a random sample of the same size.
If you're willing to make that big leap, it might be only a small additional step to use parametric methods for doing so.
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