STATISTICS FROM A TO Z<br />-- CONFUSING CONCEPTS CLARIFIED
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Statistics Tip: In 2-Factor (2-Way) ANOVA, separated lines show that Factor A has an effect

10/24/2019

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​In this example, we are testing 2 Factors for their effect on the y Variable, Cleanliness. 
  • Factor A is the Detergent type.  There are 2 "levels": Detergent #1 and Detergent #2. 
  • Factor B is the Water Temperature. There are 3 levels: Cold, Warm, and Hot.
 
We see from the graph that -- for all three levels of Factor B, Detergent #1 cleans better than Detergent #2. The lines are substantially separated, indicating that the difference is Statistically Significant. (The ANOVA numbers will tell us for sure.) 
 
If Factor B did have an effect, the lines would be slanted. Again, separated lines tell us that Factor A has an effect. 
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​If the lines were not separated, as below, then Factor A does not have an effect. 
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Statistics Tip: Analysis of Residuals is required for a Regression Model

10/3/2019

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The purpose of Regression analysis is to develop a cause and effect "Model" in the form of an equation. To keep things simple, let's talk about Simple Linear Regression, in which the equation is

                                                                           y = bx + a
 
The Regression analysis comes up with the values for b and a.
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​Residuals represent the Error in the Regression Model. They represent the Variation in the y variable which is not explainedby the Regression Model. 
 
So, Residuals must be Random.  If not -- if Residuals form a pattern -- that is evidence that one or more additional factors (x's) influence y.
 
A Scatterplot of Residuals against y-values should illustrate Randomness: 
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​Being Random means that the Residuals 
  • are Normally distributed
  • have constant Variance
  • show no patterns when graphed 
  • have no unexplained Outliers
 
Here are some patterns which indicate the Regression Model is incomplete. 
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    Author

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

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  • 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