When to use a chi-square
Not clear about when you should use a chi-square vs. when to use a t test?
First, you should check out my free, downloadable PDF, A Practical Guide to Psych Stats.
Now that that's out of the way—if you're still not sure, how about a tasty example?
Let's say that we want to know whether a bag of Original Skittles has a truly
random distribution of colors. If so, we’d expect to find roughly
equal numbers of red, green, purple, yellow, and orange Skittles, right?
A chi-square goodness-of-fit test [that is, a one-variable chi-square] can help us evaluate this. If there are 18 red, 13 green, 18 purple, 19 yellow, and 17 orange, the chi-square goodness-of-fit test tells us whether this distribution is different enough from an even distribution of 17 apiece (85 Skittles / 5 colors) that we can reject the notion that the colors are evenly distributed.
If you're really curious about my made-up numbers, by the way, here's a straightforward, easy-to-use online calculator to help you: http://www.socscistatistics.com/tests/goodnessoffit/Default2.aspx
A chi-square goodness-of-fit test [that is, a one-variable chi-square] can help us evaluate this. If there are 18 red, 13 green, 18 purple, 19 yellow, and 17 orange, the chi-square goodness-of-fit test tells us whether this distribution is different enough from an even distribution of 17 apiece (85 Skittles / 5 colors) that we can reject the notion that the colors are evenly distributed.
If you're really curious about my made-up numbers, by the way, here's a straightforward, easy-to-use online calculator to help you: http://www.socscistatistics.com/tests/goodnessoffit/Default2.aspx
***
Now, let's say
we’re looking for differences in the proportion of red Skittles to
the other colors in a bag of Original vs. a bag of Tropical Skittles.
In this case, we have two categorical variables [Original vs. Tropical Skittles, and unequal distribution of colors], so we would need a chi-square test for independence. The additional category makes the calculation a little more complex (but not if you use statistical software to handle the dirty work! 😊), but ultimately, we're looking at the same thing as before: are there roughly equal numbers of each type Skittles in each bag?
In this case, we have two categorical variables [Original vs. Tropical Skittles, and unequal distribution of colors], so we would need a chi-square test for independence. The additional category makes the calculation a little more complex (but not if you use statistical software to handle the dirty work! 😊), but ultimately, we're looking at the same thing as before: are there roughly equal numbers of each type Skittles in each bag?
In case you missed it, there are some fantastic, easy-to-use, and FREE stats programs available now! I review them here.
For more help explaining statistical concepts and when to use them,
please download my freely available PDF guide here!
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