Analysis of Variances by ChrisCaflish

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```									                                          Analysis of Variance (ANOVA) - F Test
Cost Data Integrity Project
Various New Treatments to Improve Timesheets
What is the purpose of ANOVA?

Several different treatments or procedures can help improve the current critical process. In order to implement immediate
results with minimal change, which of the following treatments is the best?

Treatment 1 - All Project Managers review and approve timesheets with each pay cycle.
Treatment 2 - All new employees must complete timesheet training within two weeks
Treatment 3 - Employees not submitting timesheets receive an email notification within 24 hours

ANOVA helps assess the impact of different treatments for improving a critical process. In this test, we will use
the F Test to determine if differences in treatments is due to random chance or is it statistically significant?

Test the Treatments against Four Projects:

< - - - - - - - - - - - Projects - - - - - - - - - - - >
Treatment               QC02            LB02        VM01            GS02          Mean   Variance
1                            2              1             3               0     1.50      1.67
2                            4              4             2               3     3.25      0.92
3                            1              1             0               2     1.00      0.67
Mean                                  2.33            2.00        1.67            1.67       1.92      1.08
Difference                            0.42            0.08       -0.25           -0.25
Variance of Means                                                                                      1.40
F Ratio =>                                                                                             5.15
Number of Treatments                                   3
Reduce for Estimating Error                            1
Degrees of Freedom (numerator)                         2 Input for F Distribution Value
Number of Projects Sampled                             4
Degrees of Freedom (denominator)                       9 Input for F Distribution Value
Risk in Relation to Confidence Level                0.05 Input for F Distribution Value
F Distribution (Critical Value)                     4.26                                          Compare

Each Project is managed differently and tends to introduce some variation, now block out the
variation introduced by each project and recalculate the F Ratio and F Distribution Value:
ANOVA - F Test with Blocking
< - - - - - - - - - - - Projects - - - - - - - - - - - >
Treatment              QC02            LB02        VM01            GS02        Mean   Variance
1                           2              1             3               0   1.50      1.66
2                           4              4             2               3   3.25      0.52
3                           1              1             0               2   1.00      0.77
Mean                                 1.92            1.92        1.92            1.92     1.92      1.47
Difference                           0.00            0.00        0.00            0.00
Variance of Means                                                                                   1.40
F Ratio =>                                                                                          3.79
Number of Treatments                                    3
Reduce for Estimating Error                             1
Degrees of Freedom (numerator)                          2 Input for F Distribution Value
Number of Projects Sampled                              4
Degrees of Freedom (denominator)                        9 Input for F Distribution Value
Fewer Degrees of Freedom                                3 Input for F Distribution Value
Risk in Relation to Confidence Level                 0.05 Input for F Distribution Value
F Distribution (Critical Value)                      5.14                                      Compare

Cost Data Integrity Project                                                  1                                            F Test - Timesheets
Conclusion regarding ANOVA - F Test for Treatments to Improve Timesheet Process

Without blocking for each project, we would wrongly conclude that there is significant differences between each of the
three treatments for improving timesheet processing. When we block out variation between projects, we conclude that
there really isn't that much difference since the F Ratio of 3.79 is lower than the F Distribution Value of 5.14.

Cost Data Integrity Project                                      2                                               F Test - Timesheets
Analysis of Variance (ANOVA) - F Test
Cost Data Integrity Project
Various New Treatments to Improve Invoices
What is the purpose of ANOVA?

Several different treatments or procedures can help improve the current critical process. In order to implement immediate
results with minimal change, which of the following treatments is the best?

Treatment 1 - All projects are receiving copies of vendor invoices for entering into PMS
Treatment 2 - All projects have a reconciliation / review procedure against the General Ledger
Treatment 3 - All projects have at least one person trained in posting invoices into PMS

ANOVA helps assess the impact of different treatments for improving a critical process. In this test, we will use
the F Test to determine if differences in treatments is due to random chance or is it statistically significant?

Test the Treatments against Four Projects:

< - - - - - - - - - - - Projects - - - - - - - - - - - >
Treatment               QC02            LB02        VM01            GS02          Mean   Variance
1                            6              2             1               4     3.25      4.92
2                            2              0             0               1     0.75      0.92
3                            7              4             2               2     3.75      5.58
Mean                                  5.00            2.00        1.00            2.33       2.58      3.81
Difference                            2.42           -0.58       -1.58           -0.25
Variance of Means                                                                                      2.58
F Ratio =>                                                                                             2.72
Number of Treatments                                   3
Reduce for Estimating Error                            1
Degrees of Freedom (numerator)                         2 Input for F Distribution Value
Number of Projects Sampled                             4
Degrees of Freedom (denominator)                       9 Input for F Distribution Value
Risk in Relation to Confidence Level                0.05 Input for F Distribution Value
F Distribution (Critical Value)                     4.26                                          Compare

Each Project is managed differently and tends to introduce some variation, now block out the
variation introduced by each project and recalculate the F Ratio and F Distribution Value:
ANOVA - F Test with Blocking
< - - - - - - - - - - - Projects - - - - - - - - - - - >
Treatment              QC02            LB02        VM01            GS02        Mean   Variance
1                           4              3             3               4   3.25      0.67
2                           0              1             2               1   0.75      0.78
3                           5              5             4               2   3.75      1.22
Mean                                 2.58            2.58        2.58            2.58     2.58      1.33
Difference                           0.00            0.00        0.00            0.00
Variance of Means                                                                                   2.58
F Ratio =>                                                                                          7.75
Number of Treatments                                    3
Reduce for Estimating Error                             1
Degrees of Freedom (numerator)                          2 Input for F Distribution Value
Number of Projects Sampled                              4
Degrees of Freedom (denominator)                        9 Input for F Distribution Value
Fewer Degrees of Freedom                                3 Input for F Distribution Value
Risk in Relation to Confidence Level                 0.05 Input for F Distribution Value
F Distribution (Critical Value)                      5.14                                      Compare

Cost Data Integrity Project                                                  3                                            F Test - Invoices
Conclusion regarding ANOVA - F Test for Treatments to Improve Invoice Processing

Without blocking for each project, we would wrongly conclude that there is no real significant differences between each of the
three treatments for improving invoice processing. When we block out variation between projects, we conclude that there
is a difference between the three treatments since the F Ratio of 7.75 is higher than the F Distribution Value of 5.14.

Cost Data Integrity Project                                       4                                                  F Test - Invoices

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