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: F is a Test Statistic  which is the ratio of two Variances.

1/28/2018

0 Comments

 
In the book's article on F, the first Key to Understanding is:
Picture
​A Test Statistic is one whose Distribution has known Probabilities. So, for any value of F (on the horizontal axis below), there is a known Probability of that value occurring. That Probability is the height of the curve above that point. 
Picture

More importantly, we can calculate the area under the curve beyond any value of F. This gives us a Cumulative Probability (such as p, the p-value) which we can use to compare to the Significance Level, 𝛼 (also a Cumulative Probability), in various types of analyses in Inferential Statistics. A Cumulative Probability is usually depicted as a shaded area under the curve.

F is Continuous Distribution. Its curve has a smooth shape, unlike the histogram-like shape of Discrete Data Distributions. However, it can work with Samples of Discrete data. The ratio of the Variances of two sets of Discrete Data is Continuous.
​
F is the ratio of Two Variances. To keep things simple, the larger Variance is entered as the numerator, and the smaller is the denominator, except for ANOVA, where the numerator and denominator are specified.
Picture
​where s1 and s2 are the symbols for the Standard Deviations of a Samples 1 and 2, respectively. The square of any Standard Deviation is a Variance. 
Picture
​In ANOVA: F = MSB/MSW,
where MSB is the Mean Sum of Squares Between and MSW is the Mean Sum of Squares Within. Both are special types of Variances. My previous blog post talks about SSW, which is used to calculate MSW.

For more on F, see my video: F Distribution. There is also a video on Test Statistics. There is also a playlist with several videos on ANOVA and related concepts . You can always get the latest status of my videos on the "Videos" page of this website.
0 Comments



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