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F Test Examples xlsx (Excel) by ajizai

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									    Examples of F-Test for Equality of Population Variances

                                                                Group 1                   Group 2    Group 1
  Note: You can set m and s.                   Pop. Mean (m )       50                       50         50
  All samples are from normal               Pop. Std. Dev. (s )     10                       10         10
  populations with the stated               Pop. Variance (s )
                                                             2
                                                                   100                         100      100
  mean and standard deviation.
  Samples are generated using
                                                                                 Random samples        Random samples
  Excel's function
                                                                               Group 1 Group 2       Group 1
  =NORMINV(RAND(),m,s) .
                                                                                 52.49    61.73        34.73
                                                                                 56.61    42.83        31.74
                                                                                 76.11    50.85        63.03
                                                                                 34.84    63.57        69.09
                                                                                 45.77    47.69        62.51
                                                                                 60.21    47.51        44.92
Note: If you have set equal population                                           46.37    50.80
variances, then the F test should not
                                                                                 60.18    59.27
reject H0: s12 = s22. A rejection would be
                                                                                 59.88    55.62
a Type I error.
                                                                                 61.17    32.78
Conversely, if you have set unequal
population variances, then the F test                                            Sample statistics     Sample statistics
                                                                           2
should reject H0: s12 = s22. A failure to                             s1            126.1291              255.4152
reject would be a Type II error.                                      s 22           87.1210              140.1400
                                                                  2        2
                                                     F calc = s1 /s2                  1.4477                  1.8226
                                             2   2            2        2
                    Folded F calc = max(s1 ,s2 )/min(s 1 ,s 2 )                       1.4477                  1.8226
                                                 Sample size n 1                        10                      6
                                                 Sample size n 2                        10                     10
                                                        df1 = n 1-1                      9                      5
                                                        df2 = n 2-1                      9                      9
                              p -value = 2 x P (F > F calc) -->                       0.5903                  0.4089
                               Conclude unqual variances?                               No                      No
         Press F9 key to get a different set of samples.


         Group 2             Group 1      Group 2          Group 1     Group 2
            50                  50           50               50          50
            10                  10           10               10          10
              100                100            100           100            100

Random samples                 Random samples                Random samples
       Group 2               Group 1 Group 2               Group 1 Group 2
         55.64                 46.96    52.62                48.04    44.04
         65.75                 76.27    51.16                42.65    60.12
         49.28                 63.71    50.13                55.59    83.53
         39.93                 38.53    52.29                50.79    47.25
         61.02                 38.94    47.21                42.47    44.35
         30.15                 71.60                         55.92    41.22
         41.60                 54.69
         32.71                 60.61
         38.59                 39.84
         47.90                 58.11

Sample statistics               Sample statistics            Sample statistics
   255.4152                        185.4082                      35.610
   140.1400                            4.7324                    261.732
     1.8226                          39.1787                         0.136
     1.8226                          39.1787                         7.350
        6                               10                            6
       10                                5                            6
        5                                9                            5
        9                                4                            5
     0.4089                            0.0030                       0.0472
       No                                Yes                          Yes

								
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