How can you explain the concept of chi-square tests to a non-statistician?

The chi-square test is a statistical method used to compare what we observe in the real world with what we would expect to see by chance. In essence, the chi-square test helps us determine if there’s a significant difference between what we actually see and what we would expect to see if everything was distributed based on chance alone.

A chi-square test helps determine if there's a significant association between two categorical variables. Imagine you want to know if people’s favorite ice cream flavors are linked to their age groups. By comparing the observed counts to the expected counts, the chi-square test tells us if the differences are due to chance or if they suggest a real relationship.

In my experience , the concept of frequency is mostly related to winning a lottery ticket in a event where you are just one of the very few who purchased the lottery ticket for a certain event considering either you are the only purchaser of it.

The Chi-Square test is one of the non-parametric tests that can help you to determine if there is an independence or dependency between two categorical variables (Nominal or ordinal) if you were testing the relationship which we called the Chi-Square test for independence; while the Chi-Square test for goodness-of-fit uses frequency data from a sample to test hypotheses about the shape or proportions of a population.

Chi-square tests come in two flavors: independence and goodness-of-fit. Independence tests check if two things are related, like hair color and ice cream preference. Goodness-of-fit tests see if data fits a certain pattern, like store visits throughout the week. So, one checks if variables dance together, while the other sees if the data grooves to a particular beat.

Chi-square tests help us see if what we observe in data matches what we'd expect by chance. Imagine you're expecting certain outcomes in categories like colors of candies in a bag. You count the actual numbers and compare them with what you anticipated. The chi-square score tells you how much these differ: low scores mean close matches, high scores signal surprises. It's like checking if reality aligns with your predictions, helping spot when something unexpected is going on.

The Chi-Square statistic is computed to measure the amount of discrepancy between the ideal sample (expected frequencies from H0) and the actual sample data (The observed frequencies), a large discrepancy results in a large value for chi-square indicating that the data do not fit the null hypothesis and the hypothesis should be rejected, Note the Chi-square statistic can be calculated automatically when you use any statistical software such Excel, SPSS, STATA, R or python if you prefer coding

When you want to interpret the results from a Chi-Square, report the chi-square statistic with the p-value or sig which will give you the decision to reject or accept the null hypothesis, you can also report the effect size for the Chi-Square for independence when both variables in the test consist of exactly 2*2 variables, so in this case, you can provide the Phi coefficient which the value range between 0 & 1, it measures the strength of relationship, value of 0.9 means that there is a strong relationship.