When to use a chi-square

 
 
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? 

https://68.media.tumblr.com/df823e9a5429bc683f0d56b95b8d8d80/tumblr_oi945q8yMm1tsozubo1_1280.gif

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

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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. 

https://upload.wikimedia.org/wikipedia/en/7/7b/Skittles-Tropical-Small.jpg

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!

A practical guide to Psych Stats

I've previously found the document "Reporting Statistics in Psychology" highly useful, and so I made a presentation for a stats course that I think is worth sharing! My own guide, a supplement of sorts, goes into a slightly broader variety of topics than the previous link, and mine also lists a 'bottom-line' approach that I think will be helpful to the people who just want to know what they should do!


Mine is called "A practical guide to Psych Stats," and I've made a freely available, freely downloadable PDF of that presentation here.

This is probably going to be useful to you if any of the following are true:

Early-career/inexperienced students:

• You've been unsure which test is appropriate for a certain dataset
• You've struggled to understand psych stats from a conceptual perspective
• You've struggled to write up statistical results in APA style
• You've wished there was an easier-to-use stats program
• You've wished there was a free stats program that you can run on your own computer

 More experienced/advanced students:

• You've thought that null hypothesis significance testing (NHST) procedures didn't make sense
• You think that the APA's reporting standards for statistical tests aren't stringent enough
• You're not sure how to interpret standardized measures of effect size
• You want to know a little bit more about Bayesian statistics
• You're not sure how to interpret your Bayesian statistics
• You're looking for a free/better/more user-friendly/more widely-compatible stats program to run on your own computer

Instructors:

• You're looking for a quick, easy, free, relatively brief resource to guide your students through the morass that is psych stats
• Bonus: links are embedded! :D
  However, for best effect, you must download the PDF, as the online preview version may randomly insert characters that will break the links :(

 Enjoy, and I hope you find this helpful!