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17.10: Phi Correlation is Not a Correlation

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    As we we’ve seen throughout this textbook, if your data are purely quantitative (ratio or interval scales of measurement), then Pearson’s is perfect. If your data happens to be rankings or ordinal scale of measurement, then Spearman’s is the way to go. And if your data is purely qualitative, then Chi-Square is the way to go. But there’s one more cool variation of data that we haven’t talked about until now, and that’s called binary or dichotomous.

    Note

    Look up “binary” or “dichotomous” to see what they mean.

    The root of both words (bi- or di-) mean “two” but the Phi (sounds like “fee,” rhymes with “reality”) correlation actually uses two variables that only have two levels. You might be thinking, “That sounds like a 2x2 factorial design!” but the difference is that a 2x2 factorial design has two IVs, each with two levels, but also has a DV (the outcome variable that you measure and want to improve). The Phi correlation has one of the two variables as the DV and the DV only has two options, and one of the two variables in the IV and that IV only has two levels. Let’s see some example variables:

    • Pass or Fail
    • Pregnant or Not pregnant
    • Urban or rural
    • Yes or No
    • On or Off
    • Conservative or Progressive

    How does this work into IVs and DVs?

    • Does tutor (tutored or not-tutored) affect passing (pass or fail)?
    • Does caffeine (coffee or no-coffee) affect energy (sleepy or not-sleepy)?
    • Does exercise (exercise or no-exercise) affect weight loss (lose 10+ pounds or do not lose 10+ pounds)?

    We are not going to get into the formula for this one, but the formula is built off of the foundation of Chi-Square analyses. The Phi correlation is a unique statistical analysis that is designed for very specific variables. So when you have two binary variables, the Phi correlation is exactly what you should be using!

    At this point, you've learned about all introductory statistical analyses, and some that are a little more advanced. The next section helps you to think about which analysis you would use with the different types of variables (and their relationships).

    Contributors

    This page titled 17.10: Phi Correlation is Not a Correlation was last modified on Fri, 24 Jul 2026 02:08:35 GMT and is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Michelle Oja.