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The Practice of Statistics Third Edition Chapter  (13.1) 14.1: Chi-square Test for Goodness of Fit Copyright © 2008 by W. H. Freeman & Company Daniel S. Yates
When to use the Chi Square,  χ 2 , Procedure ,[object Object],[object Object]
This Chapter will Cover Three Tests based on the Chi-square Distributions. ,[object Object],[object Object],[object Object]
Required Conditions For Goodness of Fit Procedure ,[object Object],[object Object],[object Object],[object Object],[object Object]
 
Hypothesizes for Goodness of Fit Test ,[object Object],[object Object]
Chi-square Test Statistic Degree of freedom = k – 1, where k is the number of categories. Use the appropriate chi-square distribution based on degree of freedom, to find the critical value of  χ 2  at an  α  level.
 
 
 
Properties of Chi-square Distributions ,[object Object],[object Object],[object Object]
Example 1 ,[object Object],From the Motor Vehicle Bureau records, we select a random sample of 1,000 of new car purchases for one of these four types of foreign cars in the current year.  The information is displayed below: Frequency Is the current year’s sales distribution the same as last year’s sales ? 37% Honda 35% Toyota 10% Mazda 18% Nissan 400 Honda 385 Toyota 65 Mazda 150 Nissan
Example 1 Continued ,[object Object],[object Object],[object Object],[object Object],[object Object]
Example 1 Continued ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Example 1 Continued ,[object Object],Observed  Expected Count  (O)  Count  (E) Sum =  23.18 From Table D using df = 3 and  α  = 0.05, the critical  χ 2  * = 7.81. 2.43 370 400 Honda 3.50 350 385 Toyota 12.25 100 65 Mazda 5 180 150 Nissan
Example 1 Continued ,[object Object],[object Object],[object Object]
Example 2 ,[object Object],[object Object],[object Object],[object Object]
Example 2 Continued ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Example 2 continued ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Example 2 Continued ,[object Object],Use calculator. L1 = Observed counts L2 = Expected counts L3 – (O –E) 2 /E = (L1 – L2) 2 / L2 Sum (L3) Sum =  χ 2 2 nd  Distr  χ 2 cdf( Lower bound, Upper bound, df)
Example 2 Continued ,[object Object],[object Object],[object Object]

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131 141 Chi Square Goodness Of Fit

  • 1. The Practice of Statistics Third Edition Chapter (13.1) 14.1: Chi-square Test for Goodness of Fit Copyright © 2008 by W. H. Freeman & Company Daniel S. Yates
  • 2.
  • 3.
  • 4.
  • 5.  
  • 6.
  • 7. Chi-square Test Statistic Degree of freedom = k – 1, where k is the number of categories. Use the appropriate chi-square distribution based on degree of freedom, to find the critical value of χ 2 at an α level.
  • 8.  
  • 9.  
  • 10.  
  • 11.
  • 12.
  • 13.
  • 14.
  • 15.
  • 16.
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