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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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