Dear Experts,
Can we use the chi-square test (which is non-parametric) on normally distributed data? A follow-up to this is.. can both parametric and non-parametric tests be performed on the same data? and If we have to see the relationship between categorical variables, what type of statistic can be used from parametric tests?
Another out-of-context question...
Apart from skewness and kurtosis values, Kolmogorov-Smirnov and Shapiro wilk test, and Histograms, are there any other ways to determine the normality of the data?
Honestly, there are way too many questions in this post, without much context.
For your first question, what context are you thinking about where you have normally distributed data and would be inclined to use a chi-square test ?
Sal Mangiafico I am trying to check the relationship between 2 categorical variables (V1, V2 below). My data is also normally distributed. However, since chi-square is non-parametric, can I use it on my data? If not, which statistic can I use to check the relationship between my categorical variables?
V1: Have you taken counseling (yes/no)
V2: Education (No education, High School, Undergraduate, Postgraduate, Doctoral)
Hello Maneela Sirisety. One of your variables is dichotomous, and the other consists of a set of 4 ordered categories. Neither of those variables can be normally distributed.
What is your sample size? Are you thinking of one variable as explanatory and the other as an outcome? If so, which is the outcome variable? Can you show us a cross-tabulation of the two variables?
Hello Bruce Weaver
My sample size is 363. I have performed chi-square on 3 combinations. Kindly ignore the previous combination and consider the below. I would like to know whether it is valid.
Regarding normal distribution, I have read that normality cannot be checked for categorical variables. Given my scale variables are normally distributed, I mentioned that my data is normally distributed.
So, can we perform both parametric and non-parametric statistics on this data?
Thank you for providing those contingency tables, Maneela Sirisety.
- The first one shows a 2x2 table where the minimum expected count = 20.79.
- The second shows a 2x3 table where the minimum expected count = 28.51.
- The third shows another 2x3 table where the minimum expected count = 12.27.
Those minimum expected count values do not set off any alarm bells for me, as they are well above the cutoffs that are discussed in typical rules of thumb:
- https://sites.google.com/a/lakeheadu.ca/bweaver/Home/statistics/notes/chisqr_assumptions
So no one should have any serious complaints about your Chi2 tests.
Also, for both 2x3 tables, the variable with 3 levels appears to be nominal, not ordinal. I mention this, because it rules out the use of the test of linear-by-linear association shown in your SPSS output.
Looking at your tables, I imagine that Type of Marriage may be explanatory for the first table with Occurrence of Counseling as an outcome. And I can imagine that the dichotomous Separation by variable is the outcome for the two 2x3 tables. If I am imagining things correctly, then you could estimate binary logistic regression models rather than Chi2 tests. If you did that, the overall test of model fit would be equivalent to the likelihood ratio Chi2 values you are getting from CROSSTABS. But you would be able to report odds ratios (ORs) with confidence intervals as a nice effect size measure. Here is a nice resource on binary logistic regression you might find helpful.
- https://www.restore.ac.uk/srme/www/fac/soc/wie/research-new/srme/modules/mod4/index.html
I hope this helps.
Thank you for the explanation and suggestions, Bruce. It makes more sense to me now.
You're welcome, Maneela Sirisety.
By the way, given that you initially asked about normally distributed data, I recommend that you view the responses by Jochen Wilhelm and Ronán Michael Conroy in this discussion:
https://www.researchgate.net/post/Mathematical_Statistics_What_factors_affect_the_normal_distribution
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