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I know what degrees of freedom are, the definition that is and it's application. I know it's intuition as well. However as far as t-distributions go, can anyone explain what was the need of including degrees of freedom in the t-table? Can anyone explain the actual intuition of degrees of freedom in inference statistics with any example or something? Like how does degrees of freedom fit in our hypothesis?

  • Welcome to this site. What is the intution that you have about the concept of degree of freedom ? –  Aug 13 '17 at 12:57
  • One thing I believe is not observed in most of our posts about [t distributions and degrees of freedom](https://stats.stackexchange.com/search?tab=votes&q=degrees%20freedom%20t%20) is that there is not just one Student t distribution: there are infinitely many of them, conventionally parameterized by a number $\nu \gt 0$. Since no two of these are alike, *that fact alone* mandates breaking down tables of $t$ distributions by values of $\nu$. $\nu$ is, of course, the "degrees of freedom" of the distribution. – whuber Aug 13 '17 at 13:31
  • @subhashc.davar Thanks. What I understand about degrees of freedom is that it is the number of variables that you can assign any number of values given a certain condition. In simple words if you want to find 10 variables that add up to 100 you can assign any value to 9 variables but the tenth variable would depend on the other 9. But how does this relate to our sample size when we select random samples from a population with unknown standard deviation? How does this play a role in finding out the t-score using the t-table? –  Aug 13 '17 at 13:50
  • @whuber I am aware of the multiple t-distribution for different sample sizes. However my question is what is the significance of the degrees of freedom when we try to find out a particular t-score? How does that play a role in the t-table? Could you give me an example where the idea of degrees of freedom arises when we do hypothesis testing? –  Aug 13 '17 at 13:57
  • Why do we even need the concept of degrees of freedom? The person who built the t-table could have randomly assigned the the column name as sample size - 1. But why introduce the concept of degrees of freedom as it exists today? –  Aug 13 '17 at 14:00
  • Your comments seem not to appreciate the fact that the t distribution with $\nu$ df and the t distribution with $\nu^\prime$ df, $\nu^\prime\ne \nu$, are *different* (and are not even the same up to any change of location or scale, either). This mathematical fact has nothing to do with sampling except insofar as probability assumptions made about the sampling procedure and the population or process being sampled often determine the appropriate value of $\nu$ to use in a hypothesis test. Those are the issues discussed in the duplicate question. – whuber Aug 13 '17 at 19:55

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