Chi-Square Test Explained: Is There an Association?

Product passed or failed, a customer subscribed or did not, a patient recovered or did not. These are categories, not measurements to average. A chi square test of independence asks whether two categorical variables are associated. Let’s build a two by two table from a fictional study. Learn with a fictional teaching example. Fictional observational table [[40,10],[20,30]]; row totals50,50; column totals60,40; N100. Expected [[30,20],[30,20]]. Pearson uncorrected chi²=100/30+100/20+100/30+100/20=16.6666667, df1, p=erfc(sqrt(chi²/2))≈0.00004456. Recovery proportions .8 and .4, difference40 percentage points. Counts are independent/mutually exclusive by stipulation; expected counts20/30. No continuity correction, causal efficacy, or real clinical claim. Discusses exact methods for sparse data and different methods for paired/clustered observations. Explore https://datastatpro.com Like, subscribe, and share. Further reading: https://openstax.org/books/introducto... CHAPTERS 00:00 When the outcome is a category 00:20 Our fictional study 00:41 Compare proportions too 01:01 What is the null? 01:21 Expected counts under H₀ 01:40 The expected table 02:00 Build the statistic 02:22 Turn it into evidence 02:43 Check the assumptions 03:05 Report more than a p-value 03:28 The takeaway 03:50 Statistics made simple #Statistics #DataStatPro #StatisticsExplained