Completely Randomized Design
        Completely Randomized Design
      1. Experimental Units (Subjects) Are 
      1. Experimental Units (Subjects) Are 
           Assigned Randomly to Treatments
           Assigned Randomly to Treatments
            •Subjects are Assumed Homogeneous
              Subjects are Assumed Homogeneous
      2. One Factor or Independent Variable
      2. One Factor or Independent Variable
            •2 or More Treatment Levels or 
              2 or More Treatment Levels or 
              Classifications
              Classifications
      3. Analyzed by One-Way ANOVA
      3. Analyzed by One-Way ANOVA
      
                                     
                                     
           Randomized Design Example
           Randomized Design Example
                                 Factor (Training Method)
                                 Factor (Training Method)
                                                                       
      Factor levels          Level 1          Level 2         Level 3
                                                                       
       Factor levels          Level 1          Level 2         Level 3
       (Treatments)
       (Treatments)
      Experimental
       Experimental                     
                                                                
            units             
            units
                              21 hrs.          17 hrs.         31 hrs.
        Dependent             21 hrs.          17 hrs.         31 hrs.
        Dependent
          variable
          variable            27 hrs.          25 hrs.         28 hrs.
                              27 hrs.          25 hrs.         28 hrs.
       (Response)
        (Response)            29 hrs.          20 hrs.         22 hrs.
                              29 hrs.          20 hrs.         22 hrs.
      
                                         
                                         
                     The Linier Model 
                     The Linier Model 
                     y  
                       ij          i     ij
    i = 1,2,…, t j = 1,2,…, r
    y  = the observation in ith treatment and the jth 
     ij
           replication
      = overall 
   mean                           th
    i = the effect of the i  
    treatment
    ij = random error
      
                                     
                                     
           One-Way ANOVA F-
           One-Way ANOVA F-
                               Test
                               Test
      
                                     
                                     
           One-Way ANOVA F-Test
           One-Way ANOVA F-Test
      1. Tests the Equality of 2 or More (p) 
      1. Tests the Equality of 2 or More (p) 
          Population Means
          Population Means
      2. Variables
      2. Variables
           • One Nominal Scaled Independent Variable
             One Nominal Scaled Independent Variable
               2 or More (p) Treatment Levels or 
                2 or More (p) Treatment Levels or 
                Classifications
                Classifications
           • One Interval or Ratio Scaled Dependent Variable
             One Interval or Ratio Scaled Dependent Variable
      3. Used to Analyze Completely Randomized 
      3. Used to Analyze Completely Randomized 
          Experimental Designs 
          Experimental Designs