ch12 ANOVA Extra - Chapter12 ANALYSISOFVARIANCE...

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Chapter 12 ANALYSIS OF VARIANCE
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2 THE  F  DISTRIBUTION Definition  1. The  F  distribution  is continuous and  skewed to the right. 2. The  F  distribution  has two numbers of  degrees of freedom: df for the numerator  and df for the denominator. 3. The units of an  F  distribution , denoted F,  are nonnegative.
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3 THE F DISTRIBUTION cont. df  = (8, 14) First number denotes the  df  for the numerator Second number denotes  the  df  for the denominator
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4 Figure 12.1  Three F distribution curves. df  = (1 , 3) df  = (7 , 6) df  = (12 , 40) F
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5 Example 12-1 Find the F value for 8 degrees of freedom  for the numerator, 14 degrees of freedom  for the denominator, and .05 area in the  right tail of the F distribution curve.
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6 Solution 12-1 Degrees of Freedom for the Numerator 1 2 . . . 8 . . . 100 1 2 . 14 . 100 161.5 18.51 . . .  4.60 . . .  3.94 199.5 19.00 . . .  3.74 . . .  3.09 . . . . . . . . . . . . . . . . . . 238.9 19.37 . . .  2.70 . . . 2.03 . . . . . .  . . . . . . . . . . . . 253.0 19.49 . . . 2.19 . . . 1.39 Degrees of Freedom for the  Denominator  Table 12.1 The F value for 8 df for the numerator, 14 df for the  denominator, and .05 area in the right tail 
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7 Figure 12.2  The critical value of F for 8 df for the      numerator, 14 df for the denominator,                  and .05 area in the right tail.   df   = (8, 14) .05    2.70 F  0             The required  F  value
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8 ONE-WAY ANALYSIS OF  VARIANCE Calculating the Value of the Test Statistic One-Way ANOVA Test
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9 ONE-WAY ANALYSIS OF  VARIANCE cont. Definition ANOVA  is a procedure used to test the null  hypothesis that the means of three or more  populations are equal.
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10 Assumptions of One-Way  ANOVA The following assumptions must hold true to  use  one-way ANOVA . 1. The populations from which the samples are  drawn are (approximately) normally distributed. 2. The populations from which the samples are  drawn have the same variance (or standard  deviation). 3. The samples drawn from different populations  are random and independent.
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11 Calculating the Value of the  Test Statistic Test Statistic F for a One-Way ANOVA  Test The value of the  test statistic  F  for an  ANOVA test is calculated as MSW MSB or samples within Variance samples between Variance = F
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12 Example 12-2 Fifteen fourth-grade students were  randomly assigned to three groups to  experiment with three different methods of  teaching arithmetic. At the end of the 
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This note was uploaded on 09/25/2010 for the course OMIS OMIS 1000 taught by Professor Alexandershoumarov during the Fall '09 term at York University.

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ch12 ANOVA Extra - Chapter12 ANALYSISOFVARIANCE...

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