Ok, I'm going to preface my question with letting you know that it's more of a weird thought experiment.
I’m trying to understand the independence assumption of a Chi Square Test for Independence by purposefully misapplying it, specifically by thinking about how that assumption is violated in an application of the Chi Square test on a data set that came entirely from my own behavior.
I was trying to analyze my own junk food eating habits from my bank statements, and collected some data that looks like this:
| M | T | W | Th | F | |
|---|---|---|---|---|---|
| Filiberto's | 33 | 22 | 8 | 18 | 16 |
| Jack In The Box | 23 | 16 | 9 | 7 | 12 |
I had other restaurants, ten total, that I collected Weekday data for, over a span of 12 months, but these were the two I went to most frequently. The data is a convenience sample, so I know it’s not generalizable to my regular junk food eating habits, but the assumption I’m primarily wondering about is that of the independence of the data.
From my conscious perspective, I’m not aware of any patterns regarding what day of the week I eat Jack or Filiberto’s or anywhere else for that matter, I’m pretty random about where and what I eat each night, often it’s a struggle choosing, but it’s possible that there is some hidden unconscious pattern in my behavior that would be uncovered by a significant finding between the two variables. This is the wacky application that I'm after. It's like the independence assumption is being held constant, to focus on the randomness in my own behavior, and my ability to detect whether there may be unconscious patterns within. This is not empirical, me telling you that I'm random about where I eat, but from my subjective perspective it really is!
Can I interpret the data as being independent despite it having all come from me?
Are there any examples or studies of the Chi Square Independence test being applied intra-personally in this or a similar way? Or any other tests for non-independent data like this?
edited: 1/27/2024