Statistics: theory about the degrees of freedom

Self-tutoring about statistics: the tutor mentions some intriguing ideas (and resources they came from) about degrees of freedom.

Degrees of freedom (df) is a concern in calculating statistics, eg., the t or Chi-squared, since the higher the df, the more precisely the data can describe its corresponding population. One gets more df from more data points; hence, the reason more data is generally seen as better.

Yet, explaining degrees of freedom and its importance may sometimes get less priority than it deserves. Academia to the rescue: today I watched a video by Quant Psych on YouTube which gives a refreshing way to understand degrees of freedom. The source paper, by Joseph Lee Rodgers, is here.

Put simply, the idea is that every parameter used to model the data, but calculated from the data itself, “costs” a degree of freedom. Therefore, a two-parameter model, such as a regression line (y=a +bx), costs two degrees of freedom, and so on. Yet, it seems a parameter that is wholly calculated from already-calculated parameters won’t cost any df, since it doesn’t derive further information from the data.