Should degrees of freedom be explained?

[checolt]

I've always been dissatisfied with the "explanations" of degrees of freedom presented in statistics courses. These explanations either rely on mystery ("the number of scores that are free to vary") or magic (N-dimensional geometry). It turns out there is an explanation that non-math majors can comprehend, but it is very time consuming. So should statistics courses take the time to explain degrees of freedom?

 

[Dason]

I've always been dissatisfied with the "explanations" of degrees of freedom presented in statistics courses. These explanations either rely on mystery ("the number of scores that are free to vary") or magic (N-dimensional geometry). It turns out there is an explanation that non-math majors can comprehend, but it is very time consuming. So should statistics courses take the time to explain degrees of freedom?

Which explanation are you referring to?

 

[checolt]

There's one version on my homepage but there's bound to be others. It's very long.

 

[spunky]

or magic (N-dimensional geometry)

how on earth is this multi-dimensional geometry "magic"? it actually makes perfect sense, especially for linear models if you know from which space to which space you're projecting onto....

 

[Dason]

There's one version on my homepage but there's bound to be others. It's very long.

I'm sorry but your page told me to download Internet Explorer so I'm not sure I can trust you anymore.

 

[checolt]

For most people who study statistics as an applied science (I was a psych major) N-dimensional geometry seems like magic. But so does matrix algebra, tensor calculus and quantum mechanics. We know that some brilliant people understand it but for us it's a bridge too far. I admire you but always wished someone would explain degrees of freedom in a manner I could understand without having to conquer another exotic mathematical discipline.

 

[checolt]

I apologize. I wrote the explanation on MSWord and saved as a MIME HTML file because the equations didn't translate when I saved in other formats. I then uploaded and could open it successfully with IE so I thought it was ok. If there's some better way I'm open to suggestion.

 

[Dason]

You could just upload the word document itself.

But the best alternative is to learn and use LaTeX for anything that needs math!

 

[spunky]

But the best alternative is to learn and use LaTeX for anything that needs math!

i second that !!!

(but i HATE LaTeX when it comes to creating tables...)

 

[Dason]

i second that !!!

(but i HATE LaTeX when it comes to creating tables...)

Meh - most times when I'm making a table in LaTeX the bulk of it is coming from something in R. So for me at least I just use xtable to get the main part of the table and then it's just small alterations from there.

 

[spunky]

uhm... i never really thought about that before... let R work on building the base and just take it from there... that's a GREAT idea.. thanks Dason!

 

[Itai]

I've always been dissatisfied with the "explanations" of degrees of freedom presented in statistics courses. These explanations either rely on mystery ("the number of scores that are free to vary") or magic (N-dimensional geometry). It turns out there is an explanation that non-math majors can comprehend, but it is very time consuming. So should statistics courses take the time to explain degrees of freedom?

@checolt - I am not sure if that helps, but generally in math, "degrees of freedom" refers to the number of variables that you can "control" given the solution to your problem. The first time that I learned about it in high school, I was given this very simple example: x + y = 5, which has has degree of freedom - once you pick x, y is immediately defined, so here you have the freedom of choosing one variable as you wish.

Not sure if that helps, but thats the most primitive example that I can think of for explaining DOF. Same idea applies in stats. Good luck.

 

[noetsi]

I think of degrees of freedom as the ability of the data to vary once you have estimated required parameters and (more practically) if you have enough data to estimate various models.

But I am sure there will be a collective gasp of horror from the true statistical types here when I say that

 

[checolt]

I must turn to the wisdom of others when dealing with the interwebs. (LaTeX sounds intriguing.) I was advised (more than once) to never, ever post a word doc because (a) some people refuse to acknowledge the existence of Microsoft and (b) someone smarter than I might insert a computer disease known as a rickroll(?) into the file and others would be infected and blame me. However I have translated the file into pdf and posted on my homepage.

 

[Dason]

\begin{MostImportantMessageOnTalkStats}
A rickroll is not a computer virus (but it did go viral). It's an internet meme consisting of linking somebody to Rick Astley's song "Never gonna give you up" typically the link is disguised through some means. You can learn more at know your meme. \end{MostImportantMessageOnTalkStats}

PDFs are definitely preferable to .docs but I'd prefer a doc to a web page I can't read - at least I can open the doc in a virtual machine.

LaTeX is definitely great but there is a learning curve associated with it.