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I'll admit right off the bat that degrees of freedom is not a concept I understand very well in general. That being said, I was reading a study that reported the following results:

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I struck me that the df for most of these factors is way, way higher than I'm used to seeing in other contexts (when I actually pay attention to the df). Is it normal to have dfs as high as 2,125? Why would only one variable end up being a tiny fraction of that (the last with a df of 25.69)?

joshisanonymous
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  • As you may know, the DF is an increasing function of the sample size. Unless you are concerned that the authors pseudoreplicated, or lied, I would not be concerned about high degrees of freedom as long as they seem to have a large sample size. – Galen Apr 21 '22 at 18:30
  • Read this thread on DF to get you started. DF can in some scenarios be a little ad hoc, but it is useful to learn the well-established cases first. – Galen Apr 21 '22 at 18:33
  • @AgnesianOperator No, I have no doubt that the authors were being honest, and the sample size was 2,131, so I guess this makes sense. Mostly, I just didn't realize you could have a df that large in a good model. – joshisanonymous Apr 21 '22 at 18:41
  • What is that study? Got interested – taciturno Apr 21 '22 at 22:27
  • @taciturno Gudmestad, A., & Carmichael, K. (2022). A variationist analysis of first-person-singular subject expression in Louisiana French. Language Variation and Change, 1–25. https://doi.org/10.1017/S0954394521000235 – joshisanonymous Apr 23 '22 at 20:44

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The discrepancy between DF for different estimates likely means that these are the results of a mixed model. There were probably a bit more than 25.69 participants in the study (leading to 25.69 DF for fluency), but these people probably had over 100 measurements each, or over 2125 total (leading to 2125 DF on other coefficients). Because there were only around 30ish measurements of whether individuals were fluent or not (one for each person in the study), and there were over 2125 measurements of features of speech (one for each speech sample collected), more DF can be used for the features of speech.

clementzach
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    I see; that makes sense. And your estimates are quite correct, 29 participants and 2,131 tokens of the feature being analyzed in total. – joshisanonymous Apr 21 '22 at 18:43