What is a degree of freedom?
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- Опубликовано: 11 фев 2025
- In this video I explain what is a degree of freedom. I jump into how data is free to move, this freedom becomes more limited after you apply a statistical model. We explore the relationship of model complexity and the degrees of freedom of the data. I explain how the more complex the statistical model is the less truly free the data is to vary. This lack of degrees of freedom undermines the predictive utility of model and that is disappointing to Karl Popper. Finally, we discuss the balance of explained variation, degrees of freedom and statistical power.
Learning objectives
Understand the concept of degrees of freedom
Explain what happens to degrees of freedom when statistical models are applied to the data
Discuss the relationship between degrees of freedom, model complexity, explained variation and statistical power
Wow. The best explanation I've ever heard. Thank you so much for your great video.
Everything makes sense after listening to your lecture.. salute to you sir
Best explanation I’ve come across, thanks
How did I missed this channel!!! Excellent explanation !👏👏 Thank you!!
Thanks, Jack! Your video was super entertaining and informative and I finally understand how all these terms come together. Thank you thank you thank you soooooo much!
Thank you very much, great explanation!!!:)
This video is so helpful!
Extremely gud and clear explanation
This makes me love statistics even more.
Awesome🥰
I am studying the chi-squared goodness of fit hypothesis test to compare a histogram of a set of samples to the normal distribution with some mean and standard deviation.
Some literature says that to calculate the amount of degrees of freedom we must use the expression:
n_of_bars_of_histogram -1 - n_of_parameters.
If I understand your explanation well, in the expression of the literature the parameters will take out 2 degrees of freedom and there is a number which cannot vary given some mean and standard deviation.
Is this correct?
excellent
8:21 This is technically not true. If I measure 1 bear, and then measure 1 ant, on almost all metrics I can create an estimation that can classify future instances of bears or ants into their corresponding classes. The bottom-line is that the less true variance there exists between the classifications in your data, the more data you will need to establish a significant difference. But after a certain point, 1 instance of two classes is enough to establish the scale of the expected effect size given we got a larger sample. One datapoint estimates the true mean, just worse than a sample with any amount of variance.
Only because you have a prior model of what a bear is and what an ant is.
If you gave one patient a drug and it cured them and one patient a placebo and they died, you would not be sure about any future efficacy of the drug.
The ONLY reason you know that you could classify ants and bears with an N=1 is because you've seen images of hundreds of bears and ants. So your N is actually hundreds.
And of course what about the amazing water bear lol.
@@dr.jackauty4415 "If you gave one patient a drug and it cured them and one patient a placebo and they died, you would not be sure about any future efficacy of the drug."
Not "sure", but I would have knowledge. Given that you observe your fellow tribesman die after eating a suspicious plant, would you eat the plant even though N = 1? It's just not AS reliable a sample as observing more people eat that plant, but here we stumble to philosophical territory where the importance of the outcome changes how we should conduct inference.
My point is that a datapoint that represents a population is more likely to be empirically similar to other instances of that population than not, and thus even one datapoint tells us something. We just lack variance, which means we can't do fancy sample statistics (because we can't measure error).
I don’t understand. I wonder if I’m genuinely stupid. Why is the mean free to vary? It seems like Only the points we observe are free to vary and the sample mean is fixed given these points
The point is not that you could have gone out and collected a measurement for the mean and then figured out the last data point from the mean. Tha would be silly. The point is that the mathamatics doesn't care which came first. The statement "1+2 = 3" has 3 numbers but only 2 of them (any 2) are free to vary. (And if we use the sum "3" in our statisitcal model, there is only one left that was free to vary).
There is no explanation here. You just mechanically transposed the same formulaic approach you criticized in the opening part of your video and translated it to "cells." You never really explained what dof is (hint: it is the amount of non-redundant information in a sample) and what this concept is used for (hint: It's used squarely in the inferential statistics world to obtain unbiased estimates of population parameters). A full explanation would require explaining what inferential statistics is, what unbiased estimators are, and how to obtain them from sample data.
kc3t4
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