One-Way ANOVA
                One-Way ANOVA
     The one-way analysis of variance is used 
      The one-way analysis of variance is used 
      to test the claim that three or more 
      to test the claim that three or more 
      population means are equal
      population means are equal
     This is an extension of the two 
      This is an extension of the two 
      independent samples t-test
      independent samples t-test
                               
                  One-Way ANOVA
                  One-Way ANOVA
      The response variable is the variable 
       The response variable is the variable 
       you’re comparing
       you’re comparing
      The factor variable is the categorical 
       The factor variable is the categorical 
       variable being used to define the groups
       variable being used to define the groups
         We will assume k samples (groups)
          We will assume k samples (groups)
      The one-way is because each value is 
       The one-way is because each value is 
       classified in exactly one way
       classified in exactly one way
         Examples include comparisons by gender, 
          Examples include comparisons by gender, 
          race, political party, color, etc.
          race, political party, color, etc.
                                   
                One-Way ANOVA
                One-Way ANOVA
     Conditions or Assumptions
      Conditions or Assumptions
        The data are randomly sampled
         The data are randomly sampled
        The variances of each sample are assumed 
         The variances of each sample are assumed 
         equal
         equal
        The residuals are normally distributed
         The residuals are normally distributed
                               
                    One-Way ANOVA
                    One-Way ANOVA
      The null hypothesis is that the means are all 
        The null hypothesis is that the means are all 
        equal
        equal         H :   
                        0    1     2     3           k
      The alternative hypothesis is that at least one 
        The alternative hypothesis is that at least one 
        of the means is different
        of the means is different
                                             ®
                                              ®
           Think about the Sesame Street  game where 
           Think about the Sesame Street  game where 
           three of these things are kind of the same, but one 
           three of these things are kind of the same, but one 
           of these things is not like the other.  They don’t all 
           of these things is not like the other.  They don’t all 
           have to be different, just one of them.
           have to be different, just one of them.
                                       
                One-Way ANOVA
                One-Way ANOVA
     The statistics classroom is divided into 
      The statistics classroom is divided into 
      three rows: front, middle, and back
      three rows: front, middle, and back
     The instructor noticed that the further the 
      The instructor noticed that the further the 
      students were from him, the more likely 
      students were from him, the more likely 
      they were to miss class or use an instant 
      they were to miss class or use an instant 
      messenger during class
      messenger during class
     He wanted to see if the students further 
      He wanted to see if the students further 
      away did worse on the exams
      away did worse on the exams