STATISTICS FROM A TO Z<br />-- CONFUSING CONCEPTS CLARIFIED
  • Home
    • Why This Book Is Needed
    • Articles List, Additional Concepts
    • Examples: 1-Page Summaries
    • Examples: Concept Flow Diagram
    • Examples: Compare and Contrast Tables
    • Examples: Cartoons
    • Example: Which to Use When Article
  • Buy
  • Blog
  • Sample Articles
  • Videos
  • Author
  • Communicate
  • Files
  • Errata

Statistics Tip of the Week: Formulas for Degrees of Freedom vary by the Statistic and the test they are used in.

5/11/2017

1 Comment

 
A Statistic is a numerical property of a Sample, for example, the Sample Mean or Sample Variance. A Statistic is an estimate of the corresponding property (“Parameter”) in the Population or Process from which the Sample was drawn. Being an estimate, it will likely not have the exact same value as its corresponding population Parameter. The difference is the error in the estimation.

So, if we calculate a Statistic entirely from data values, there is a certain amount of error. For example, the Sample Mean is calculated entirely from the values of the Sample data. It is the sum of all the data values in the Sample divided by the number, n, of items in the Sample. There is one source of error in its formula – the fact that it is an estimate because it does not use all the data in the Population or Process.
Picture
If we then use that Statistic to calculate another Statistic, it brings its own estimation error into the calculation of the second Statistic. This error is in addition to the second Statistic’s estimation error. This happens in the case of the Sample Variance. 
​The numerator of the formula for Sample Variance includes the Sample Mean. It takes each data value (the x’s) in the Sample and subtracts from it the Sample Mean, squares it. Then it sums all those subtracted values. 

So, the Sample Variance has two sources of error: 
  • the estimation error from the Sample Mean ​​
  • its own estimation error
Picture
That is why the Degrees of Freedom for the Chi Square Test for the Variance is n - 1. Subtracting 1 from the n in the denominator results in a larger value for the Variance. This addresses the two sources of error.

Here are the formulas for Degrees of Freedom for some Statistics and tests:
Picture
1 Comment
Indrajeet DILIPSINH
7/17/2018 09:57:18 am

Nice knowledge

Reply



Leave a Reply.

    Author

    Andrew A. (Andy) Jawlik is the author of the book, Statistics from A to Z -- Confusing Concepts Clarified, published by Wiley.

    Archives

    March 2021
    December 2020
    November 2020
    October 2020
    September 2020
    August 2020
    May 2020
    March 2020
    February 2020
    January 2020
    December 2019
    November 2019
    October 2019
    September 2019
    July 2019
    June 2019
    May 2019
    April 2019
    March 2019
    February 2019
    January 2019
    December 2018
    November 2018
    October 2018
    September 2018
    August 2018
    July 2018
    June 2018
    May 2018
    April 2018
    March 2018
    February 2018
    January 2018
    December 2017
    November 2017
    October 2017
    September 2017
    August 2017
    July 2017
    June 2017
    May 2017
    April 2017
    March 2017
    February 2017
    January 2017
    December 2016
    November 2016
    October 2016
    September 2016
    August 2016

    Categories

    All
    New Video
    Stats Tip Of The Week
    You Are Not Alone

    RSS Feed

  • Home
    • Why This Book Is Needed
    • Articles List, Additional Concepts
    • Examples: 1-Page Summaries
    • Examples: Concept Flow Diagram
    • Examples: Compare and Contrast Tables
    • Examples: Cartoons
    • Example: Which to Use When Article
  • Buy
  • Blog
  • Sample Articles
  • Videos
  • Author
  • Communicate
  • Files
  • Errata