Hi. I had done a non probability survey to collect information on retirment planning among workers about to retire and those who had already retired. I now want to compare the two populations planning strategies. My variables are categorical include aspects of financial planning, housing, living arrangement, health and so on. Please suggest a suitable method to do this.
First, the use of non-probability sample means that any statistical analyses you do will be limited to your own sample and not generalizable to a larger population. So, you might characterize your results as "suggestive" or "exploratory."
With regard to statistics, the fact that you have a two-category comparison means that you do t-Tests whenever you are dealing with an interval variable or a another two-category variable (which would be a t-Test of proportions).
Alternatively, if all your other variables are categorical, then you can represent the data as cross-tabulations and use chi-square.
In this situation, chi-square test is suitable to compare categorical variable(s) between two groups.
First, use the appropriate type of hypothesis test, given the assumptions of the test models. The Kolmogorov-Smirnov test of uniformity and normality is definitive as to what kind of tests to use: parametric (t-test, ANOVA, General Linear Models: (multivariate multiple linear regression, correlation, etc.) OR non-parametric equivalents to t-test (Mann-Whitney U, Wilcoxon Signed Rank), ANOVA (Kruskal-Wallis with multi-way post hoc).
A very powerful non-parametric method that I highly recommend for both exploring data and predictive model development is Chi-Square-Automatic-Interaction-Detection (CHAID), also known as "decision trees". When used collaboratively with Binary Logistic Regression (BLR). The c-statistic (model probability) of both methods can be compared directly in a sensitivity-specificity AUROC plot (area under the operating characteristic plot of the curve). And this comparison can provide internal cross-validation of findings using two different modeling methods. This is useful in trimming (discarding insignificant predictors) the model. If your sample is large enough, BLR provides a very convenient method for comparing a dichotomous outcome variable (Dependent Variable) Retired = 1 (Yes) Not Retired = 0 (No), using all of the factors described as the Independent (predictor) Variables in the model. What are the Odds that a person is retired (Yes) vs not (No), given the factor (financial planning, health, housing, living arrangement, etc.). Unfortunately, BLR usually requires much larger data sets (500 to 1,200 rows), but CHAID does not. It will still work (using chi-square Likelihood Ratio) with as few as 20-30 rows (observations) of data for a minimal explorative model.
I hope this helps. For non-randomized convenience samples, the non-parametric inferential hypothesis testing methods are almost always the only mathematically appropriate statistical analysis methods that are available to use to report research findings that will be published in professional peer-reviewed scientific journals.
Richard E. Gilder, RN MS
Bioinformatics Scientist
The Gilder Company
TTUHSC Adjunct Faculty
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