# How to deal with very large degrees of freedom? [closed]

I am using a dataset from an online database and the df seems to be huge. I do understand that higher degrees of freedom generally mean larger sample sizes. But can it be so big? If yes how can I report it?

• Why not and what is the problem with reporting it? – Tim Oct 24 at 18:21

It is rather rare to find tabular results in a scientific journal that do not report the study's total sample size $$N$$. A reviewer may raise an eyebrow if the reporting of your $$N$$ is entirely absent. A journal's editorial board might even require it in the presentation of tabular figures. In your case, a 'data scrape' of approximately 17.5 million observations from on online source is rather large and worth reporting. I'm assuming you scraped it but it could be any form of data extraction.

But can it be so big?

Sure. But the real question you should be asking is did you intend to pull this much data? Did this online resource provide any documentation on the dimensions of your dataset? If your original data frame was much smaller, then you need to investigate why your degrees of freedom have changed so much. Often times during the 'data cleaning' phase people might transform their data frame to 'long format' so they can visualize a relationship, only to forget to convert it back when fitting a model. This is just something to think about as you navigate your results. If you intended to acquire this much data, then leave it as is.

If yes how can I report it?

A study's $$N$$ is customarily listed near the bottom of a table, usually after the reporting of a model's coefficients. For example, if you're running a series of regressions with different specifications then you might see each model's $$N$$ reported beneath each column of coefficients. Other times a research includes the sample size in a "notes section" beneath the table. In my opinion, your ANOVA output is sufficient if you're sharing it with a colleague. However, if this is something you want to publish, then I would be guided by previous scientific reporting in the relevant journal.

Aside: I shouldn't use "sample size" and "degrees of freedom" interchangeably, but I think you get the idea. Typically, your degrees of freedom equal your sample size. In general, when you calculate your degrees of freedom, you decrement the number of parameters you need to estimate from the sample size.

Textual reporting of degrees of freedom may also be necessary if you conducted certain ad hoc tests in support of your study, such as a chi-square (i.e., $$\chi^2$$) or $$F$$-test. That being said, reporting your degrees of freedom in scientific text is often test-dependent. Again, I would guided by the previous work in your particular discipline. To offer a simple example, some ANOVA tests often report the degrees of freedom associated with the test statistic, such as $$F(1, 120) = 1.50$$, $$p = .25$$. The values expressed inside of the parenthetical denote the between- and within-group degrees of freedom, respectively.

In sum, I wouldn't invoke 'researcher degrees of freedom' in the reporting of your degrees of freedom (pun intended). In my opinion, you should report it. And, if you choose not to, I stand by @Tim and ask: why not?

I hope this helps!

• Thank you very much for the elaborated answer, Thomas. This is the sample size N = 17460166 used for the above-mentioned analysis. Your question about pulling this much data is indeed valid and I was also thinking about it. Just another very simple question, using your example for the ANOVA test how would you report the F? F (1, 175) = 314789.769? – Delia Oct 26 at 10:06
• @Delia If you’re conducting the appropriate test, then yes, you can report the $F$-statistic in this manner. Please note my toy example was completely fictitious so you should also include the degrees of freedom. If you have further questions, you should update your post as it is already too broad. Otherwise, you can accept my answer. – Thomas Bilach Oct 27 at 0:01
• Thanks once again, Thomas! All clear now :) – Delia Oct 27 at 14:18