What are degrees of freedom?
"the number of variables that can be varied independently"
I'm sorry, but this means nothing to me. Which variables are those? So, I'm getting a sample of 36 elements and I want the standard deviation, so the degress of freedom are 36 minus one. Why 35 of these elements can be varied freely and one not? And if I take two samples for a regression, it's two elements that cannot be varied freely! Can someone gimme a clue about all that degrees of freedom thing?
I have tried using google , but it always syas the same thing! Number of variables that can be varied independently! Or, in some cases, return some results that explain degrees of freedom in physics.
My question is: How can I know how many degrees of freedom I'm gonna use?
Degrees of Freedom (DF) are calculated by taking the dimensions of your matrix and use formual (R-1) x (C-1) = DF
So of your sample looks like this, for observed values to see if Gender is independant of Smoking.
Male 105 867
Female 98 456
The dimensions of the matrix are 2 x 2 = DF > (R-1)(C-1) > (2-1)(2-1) = 1 DF
The DF value is then used with the significance value/confidence level to obtain the crtical value from
the chi-squared distribution table and compared against your statistical chi-squared value.
But why there is one degree of freedom? I know, it's what the formula says, but I would be grateful if someone could give me an explanation of the origin of this formula
Plus, is this matrix somehow related to the t-student table? Because it has degrees of freedom as well. Why cannot all the variables vary freely?