The Chi Square is a statistic that is used to test sample statistics against a population parameter. As such, the size of the sample is not a determiner of its appropriateness. If you use the Chi Square (or an other statistical test) and achieve significance, all that means is that the sample statistic that estimates the parameter you are testing is different from the population. Once you achieve statistical significance, you determine the meaningfulness of that difference by computing an effect size.

Dear Adetayo Adeniran,

You may note that for all numeric data (Ratio data) or quantitative data like height, weight, income, sales, expenditure, heart rate we can use parametric tests like t-test, Z-test. Each numeric data may represent some distribution or the other. Essentially for such data, we test whether it follows normal distribution or not? As t-test, Z -test, ANOVA, Regression, Correlation , all these requires the assumption that the data follows normal distribution.However, when we are dealing with qualitative data like Nationality, Music preference, Marital status, Socio-economic status, we essentially deal with numbers (frequency) and not with any measurement. In such a case, Chi-square test is suitable to test whether the frequency as seen in different categories are according to some theory or some hypothesis. As there are no assumptions involved about any parameter (mean, SD) of the data, we call the test as Non-parametric. The Chi-square is also known as a distribution free statistics as it makes no assumptions about the sample distribution

Your justification mentioned above are not correct.

The Chi Square is a statistic that is used to test sample statistics against a population parameter. As such, the size of the sample is not a determiner of its appropriateness. If you use the Chi Square (or an other statistical test) and achieve significance, all that means is that the sample statistic that estimates the parameter you are testing is different from the population. Once you achieve statistical significance, you determine the meaningfulness of that difference by computing an effect size.

Reinforcing James McLean's comment above, Sample Size does not preclude using one method or another. Yes, with very large sample sizes, *everything* becomes "statistically significant", but that does not make it unreliable. The term "statistical significance" does not mean very much - it is simply a statement that we think that a value is not zero (in a t-test, that the difference between two means is not zero; in a cross-tabulation, that the joint distributions of frequencies are not different). A p-value says little about how strong is a relationship or a difference. In your case you would include Cramer's V as the Effect Size measure. So, with a large sample size, you may conclude that a Chi-square statistic is "statistically significant" but the effect size is quite low.

Look at your data. Draw a set of bar charts showing frequencies (or proportions) and ask yourself if values for different groups really look different. (see Anscombe's Quartet or, more recently, the Datasaurus Dozen.) https://www.autodeskresearch.com/publications/samestats

Re: Probability Sampling

If you are doing social research, then it is impossible to have a truly random sample. People are fickle and answer questions differently depending on mood or how a question is asked; there may be something different about those who do agree to answer your questions compared with those who do not. Your sampling frame always requires some sort of judgement about where and how to recruit, and this also creates another form of potential bias. This is why, in social research, we have to make a big deal of reporting on our sampling procedures, so that our readers can judge for themselves whether our samples are sufficiently representative of the population of interest for the purposes of the research.

Note: recruiting people you don't know as they enter the campus library is NOT random sampling. That's a convenience sample.

Chi square is a non parametric test to infer the association between the two variables which are obtained from nominal or ordinal measurement

@ Thenmozhi P, you hit it. Thank you.

Thank you

Seems two contradictory views. James E. McLean says a Chi-sq estimates (or is testing a hypothesis involving) a parameter (consider a 2x2 table , phi [ie, sqrt(chi-sq/n) ] ) while Thenmozhi P saying that the procedure is not estimating this parameter. Thenmozhi P are you saying the Chi-sq test does not do this?