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a guest Jun 19th, 2017 45 Never
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  1. Which way do I calculate the F statistic in this problem:
  2. DATA:
  3.             northside   southside   eastside    westside    average
  4. small properties    12      12      10      6       10
  5. large properties    13      10      7       8       9.5
  6. average         12.5        11      8.5     7       9.75 (GRAND MEAN)
  7.  
  8. QUESTION:
  9. Want to find out if location of a property affects the number of properties sold by size.
  10.  
  11. Null H: Location does not affect.
  12. Alt. H: Location does affect.
  13.  
  14. Grand mean: (12+12+10+6+13+10+7+8)/8 = 9.75
  15. Between treatment sum of squares: 2(12.5-9.75)^2 + 2(11-9.75)^2 + 2(8.5-9.75)^2 + 2(7-9.75)^2 = 36.5
  16. Within treatment: (12.5-12)^2+(13-12.5)^2+(12-11)^2+(10-11)^2+(10-8.5)^2+(7-8.5)^2+(6-7)^2+(8-7)^2 = 9
  17.  
  18. F = [36.5/(4-1)] / [9/(8-4)] ~ 5.41
  19.  
  20. OR
  21.  
  22. Grand mean: 9.75
  23. Between treatment sum of squares: 4(10-9.75)^2+4(9.5-9.75)^2 = .5
  24. Within treatment: (12-10)^2+(12-10)^2+(10-10)^2+(6-10)^2+(13-9.5)^2+(10-9.5)^2+(7-9.5)^2+(8-9.5)^2 = 45
  25.  
  26. F = [.5/(2-1)] / [45/(8-2)] ~ 0.7
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