Explain a chi-squared test like I'm 5.
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Okay, let's say you have a pizza and you want to know if it has the right ingredients. To find out, you take a bite and count how many pieces of each ingredient you taste, like cheese, pepperoni, mushrooms, and so on.

Then you compare that to the recipe that says how much of each ingredient should be on the pizza. If the ingredients on your pizza match the recipe, then you have the right ingredients. If not, then you have the wrong ingredients.

This is like a game of finding differences. You compare the ingredients on your pizza to the recipe and see if they match. If they don't match, then there is a difference.

This is called a chi-squared test. It helps you figure out if things are the same or different. Just like finding differences with the ingredients on a pizza!
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Show me the equation for it, along with dummy data.
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The formula for a chi-squared test is:

χ² = Σ [(O - E)² / E]

where:
χ² is the test statistic, which measures the difference between the observed and expected values.
O is the observed frequency, or the actual count of an event.
E is the expected frequency, or the count of an event that we would expect based on the hypothesis being tested.
Σ is the symbol for "sum," so the formula is adding up all the differences between observed and expected values, squared and divided by the expected value, for all categories being tested.

For example, let's say we want to test if the proportion of toppings on a pizza is equal to the recipe. The recipe calls for 50% cheese, 25% pepperoni, and 25% mushrooms. We take a sample of 100 bites of the pizza and count the following toppings:

Observed: cheese (50), pepperoni (30), mushrooms (20)
Expected: cheese (50), pepperoni (25), mushrooms (25)

We can use the formula like this:

χ² = [(50 - 50)² / 50] + [(30 - 25)² / 25] + [(20 - 25)² / 25] = 0 + 2.4 + 1 = 3.4

The resulting χ² value of 3.4 tells us that there is a significant difference between the observed and expected proportions of toppings on the pizza, indicating that the proportions do not match the recipe.
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#ChatGPT #teaches #statistics #ChiSquared

Feel free to argue with our #RobotOverlords in the replies.

Today's cultural learnings for make great nation of Statistics:

* Chi Squared distribution is useful
* Likert data is hard work
* I have a lot of survey data that needs re-doing... :)

#rstats #chisquared #likert