![]() ![]() You're welcome to pull nine of them out of your ass, but the tenth will be determined by the first nine (or that pesky mean will not be what we wanted it to be). In fact you have 9 "degrees of freedom" when picking ten values who have a mean of 5. It may look like you can just pick any ten values you like (like a combination of 4s and 6s or 3s and 7s), but consider that we will do things one at a time, and that when once we get to the 10th choice, we really have no choices left if we started out with the knowledge (or intention) of having the average of all ten values be 5. I don't have ten degrees of freedom for my ten values, because we are not free to have the mean be any other number than 5. Ignoring the variance for a moment, I could have calculated a mean of 5 from 10 values in an infinite number of ways.įive "4s" and five "6s" have a mean of 10. The number of "degrees of freedom" I have in this circumstance is a count of the opportunities I have to change my N values, while maintaining the same mean and variance that I calculated before. I can take a vector of N values and calculate for them a mean and a variance. I can specify a normal distribution exactly with just one mean and just one variance. My intuitive understanding of degrees of freedom is that there's something about capturing how generalisable our results are: That’s what’s meant by degrees of freedom That’s exactly like degrees of freedom - if you’re calculating a mean of a sample, every person in the analysis can be any score, but if you know the mean, the last person MUST be a specific score to make it true that the mean is what you observed (i.e., if you give me the first 19/20 scores on a variable and the mean of the variable, i can mathematically know with certainty what the 20th score on the variable was). But she doesn’t ask “who has the AmEx card?” - why? Because if the other three cards went to your three friends, the last one MUST be yours. The waitress comes back and asks “who has the Visa card?” and then hands it out. The best analogy I’ve ever heard about it - imagine you’re at a restaurant with 3 friends, and it’s time to pay the bill. I saw this in a recent post and thought it was one of the best ways I have seen df explained.ĭegrees of freedom refer to what “can” vary with respect to a given analysis. ![]()
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