What is meant by Degrees of Freedom?
I didn't comprehend the "degrees of freedom" terminology used in the lectures of Student's T and Chi squared distributions. Can you please explain its meaning? What actually degree of freedom is?
Thank you for your question!
The degrees of freedom give you the number of independent pieces of information i.e., independent observations.
Let us try to explain this in simple mathematical terms. Imagine two variables a and b which are related through the following equation:
b = 2*a
In this problem, we only need to be given a value for a in order to estimate b. Knowing a and b simultaneously prior to solving the task would mean we are given redundant information.
In statistics, you can take a look at the sample variance formula. The denominator corresponds to the number of observations minus one rather than just the number of observations. The reason for that is, the following. Knowing the mean of all observations, denoted usually by x bar, together with the values of all (n-1) observations, we can always calculate that last observation. Therefore, the number of degrees of freedom becomes n-1.
Unfortunately, this topic is quite big and I am not able to cover it in one answer. I suggest you perform a small research and try to grasp this idea. Keep up the good work! :)