The sample size for my study is 350. I have used Quota sampling.
Which is the most appropriate statistics to find out the relationships between two variables with this sample selcted with non-random sampling.
Hello Pradeep,
The answer depends not on the sampling method, but on the nature of the two scores you are trying to correlate. If interval strength (and, if you're willing to presume a bivariate normal distribution), the good old Pearson product-moment correlation may be computed and evaluated for difference from zero (or whatever constant makes sense for your study).
If ordinal strength (or the normality assumption is questionable), the Spearman rank-order correlation may be used.
If nominal strength (e.g., correlating a respondent's sex with disease status, such as infected vs. uninfected), chi-square test of independence (or the related correlation coefficient, the phi coefficient or Cramer's V) may be used.
Good luck with your work.
You may have read in your statistics reference that statistical analyses require random sampling only. Anything else is inappropriate because the data may be biased. And that is generally true if you're sampling production units in a factory. (That's where many statistical techniques were developed.) But in social research it's impossible to have a truly random sample of a given population of interest. The Bureau of Statistics often attempts it and it's mighty expensive and involved.
Instead, social researchers have to use non-random-sampling methods and try to ensure that their samples are representative of the population of interest as much as they can. That's why the APA, for example, puts so much emphasis on explaining the sampling procedure in it's guidebook: The researcher and the reader of research have to make a judgement on whether the sample is sufficiently representative of the population, and make a judgement on whether any sources of bias are great enough to make a difference to your results.
In the case of a quota sample, you are using prior information about the nature of the population to ensure proportionately similar numbers of particular groups. Marketing researchers typically use sex and age-group as quota groups. Here, it's not so much the quota, but the selection of respondents in each quota, which is usually a combination of judgement sampling and convenience sampling, that may cause bias.
If you conclude that your sample is sufficiently representative of the population, then, as explained by David Morse, your analysis is driven by the nature of your data, not by the sampling method.
Like what was said, you need to apply an ordinal type of correlation like Spearman's if non-random or stratified sampling occurred. Before doing so, you need to assess normality in your dataset. If normality was indeed violated, you should be seeing a non-convergence of the mean and median.
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