Which hypothesis test should I use?

Question

I'm doing a personal project and would like to see if High Caloric Food has a statistical significance on Weight Level.

I've tried Chi Squared Contingency test as suggested by chatgpt but it gives a p-value of 1 which fails to reject null hypothesis that there is no association between High Caloric Food and Weight Level. Visually I can see that High Caloric Food does increase the Obesity Count.

What test should I use in this scenario?

Code:

weight_order = ['Normal_Weight', 'Overweight_Level_II', 'Insufficient_Weight', 'Overweight_Level_I', 'Obesity_Type_I', 'Obesity_Type_II', 'Obesity_Type_III']

df[['High Caloric Food Freq', 'Weight Level']].groupby('High Caloric Food Freq').value_counts(normalize=True).reindex(weight_order, level=1).unstack()

I've normalized the data since the 'yes' to High Caloric Food count is almost 3x greater than 'no'.

Here is what the table looks like:

Edit: sorry for the confusion. The numbers represent the proportion of each weight level that answered 'no' or 'yes' to frequent High Calorie food consumption. For example, 32.24% who have answered 'no' to frequent high calorie consumption have a normal weight.

Answer 1

As Peter Flom points out in comments, a chi-square test requires to use counts, not proportions (that is, in your code, you should set the normalize parameter to False, not True). The fact that you have much larger counts of "yes" than "no" does not change that.

The sample size has a direct impact on the p-value. If you feed the chi-square test a table where you removed information about the sample size (like you did), you can't trust the results the test gives you. That's why you need to provide the actual counts, not the percentages.

On a side note, if you're in the specific case of some complex survey sampling design, you may want to use the survey weights associated to the observations along with the Rao-Scott chi-square test (instead of the "vanilla" chi-squared test). But even in this case you have to provide the counts as input, not proportions.

Note that if you have a very large number of observations, a test may be not necessary to judge if there is a difference between the two groups in the population, given the differences of percentages in your table.

Besides a chi-squared test, an interesting method when the outcome is ordinal, is ordinal regression. You can find several online resources about it, including questions and answers on this website; having a look at Frank Harrell's website should be informative too.

In any case, you should also focus your attention on a better visualization of your data if you intend to present the data to other people. You could for example consider using bar plots, instead of a table that uses an order that is quite confusing. For instance, why did you voluntarily put "Insufficient_Weight" between "Overweight_Level_II" and "Overweight_Level_I"? This is confusing, if one wants to see how the percentages change in the two groups, as we move from the weight level "Insufficient weight" to "Obesity type III".