Defense Acquisition Research Journal Issue 95

January 2021

Bonferroni Test The research question we are attempting to answer in this section is: • When all the survey responses for each subgroup are taken individually, are there statistical differences in the responses? Table 5 shows a sampling of the results from the Bonferroni test. While the previous parametric Hotelling test looks at all subcategories in each group compared to all the subcategories in the second group, the paramet ric Bonferroni test compares one pair of the subgroups at a time, like the t -test. The difference is the Bonferroni test accounts for the added degrees of freedom with multiple simultaneous pairwise tests.

TABLE 5. BONFERRONI TEST Simultaneous Confidence Intervals Mean Difference of Null is 0 Model Inputs: VAR48; VAR 148; C1

VAR49; VAR 149; C2

VAR50; VAR 150; C3

VAR51; VAR 151; C4

Mean Difference

0.0522

-0.3283

-0.0152

-0.0457

Variance Group 1

1.6917

1.5336

0.8024

0.5850

Variance Group 2

1.4105

0.5553

0.3658

0.5553

Pooled Variance

1.2496

1.0393

0.7746

0.7558

F-Critical

2.6190

2.6190

2.6190

2.6190

T-Critical

3.3620

3.3620

3.3620

3.3620

Standard Error

0.3820

0.3178

0.2368

0.2311

Lower Confidence

-1.2323

-1.3966

-0.8115

-0.8225

Upper Confidence

1.3366

0.7401

0.7810

0.7312

Within Confidence?

Yes

Yes

Yes

Yes

Bonferroni Critical

2.6127

2.6127

2.6127

2.6127

Lower Confidence

-1.4760

-1.5993

-0.9626

-0.9700

Upper Confidence

1.5803

0.9428

0.9321

0.8786

Within Confidence?

Yes

Yes

Yes

Yes

Null hypothesis: The individual expected differences are equal to zero.

We conclude that: • In all the tests, we did not detect any statistical significance, and find that all subgroups are statistically identical. This implies that additional testing is required.

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Defense ARJ, January 2021, Vol. 28 No. 1 : 2-39