The Merging of Statistics Education, Consulting and Research: A Case Study

Figures & data

Table 1. Observed and Estimated Expected Cell Frequencies for Organization X Experiment

Plan i	Plan j
	1	2	3	4	5
1	−	20 (23.4)	22 (20.3)	20 (16.6)	1 (2.7)
2	9 (5.6)	−	6 (9.9)	7 (6.8)	1 (0.7)
3	8 (9.8)	24 (20.0)	−	8 (10.8)	2 (1.3)
4	10 (13.4)	23 (23.2)	21 (18.7)	−	3 (2.2)
5	29 (27.2)	29 (29.3)	27 (27.7)	27 (27.8)	−

Table 2. Ranking Analysis of Alternative Plans

Plan			Ranking
1	0	0.53	2
2	−1.437	0.19	5
3	−0.731	0.36	4
4	−0.213	0.48	3
5	2.302	0.94	1

Table 3. Estimated Pair-wise Preference Probabilities

Plan i	Plan j
	1	2	3	4	5
1	−	0.81	0.67	0.55	0.09
2	0.19	−	0.33	0.23	0.02
3	0.33	0.67	−	0.37	0.05
4	0.45	0.77	0.63	−	0.07
5	0.91	0.98	0.95	0.93	−

Table 4. Sequential Bonferroni Multiple Comparison Procedure

Contrast	ML Est.	Std. Error	z-score	Unadjusted p-value	Sequential Bonferroni Adjusted p-value
α1 - α2	1.437	0.294	4.88	1.06 × 10^−6	6.39 × 10^−6   **
α1 - α3	0.731	0.269	2.71	6.77 × 10^−3	2.71 × 10^−2
α1 - α4	0.213	0.264	0.81	4.20 × 10^−1	4.20 × 10^−1
α1 - α5	−2.302	0.416	5.53	3.12 × 10^−8	2.18 × 10^−7
α2 - α3	−0.706	0.280	2.52	1.18 × 10^−2	3.53 × 10^−2
α2 - α4	−1.223	0.288	4.24	2.19 × 10^−5	1.10 × 10^−4
α2 - α5	−3.739	0.450	8.31	9.62 × 10^−17	9.62 × 10^−16
α3 - α4	−0.517	0.267	1.94	5.25 × 10^−2	1.05 × 10^−1
α3 - α5	−3.033	0.431	7.03	2.07 × 10^−12	1.86 × 10^−11
α4 - α5	−2.516	0.420	5.98	2.17 × 10^−9	1.74 × 10^−8

Figure 1. Multiple Comparison Groupings of Plans (5% Significance Level)

Table 5. Monte-Carlo Power of Balanced and Cyclic Designs for Various Alternatives

Alternative (α1,…, α5)	Power
	Balanced Design	Cyclic Design
(1.0,1.0,1.0,1.0,1.0)	.06	.05
(1.0,1.0,1.0,1.0,1.2)	.11	.08
(1.0,1.0,1.0,1.2,1.2)	.18	.10
(1.0,1.0,1.2,1.2,1.2)	.18	.078
(1.0,1.0,1.0,1.0,1.5)	.54	.38
(1.0,1.0,1.0,1.5,1.5)	.74	.34
(1.0,1.0,1.5,1.5,1.5)	.78	.38
(1.0,1.5,1.0,1.0,1.0)	.54	.65
(1.0,1.5,1.0,1.5,1.0)	.75	.95
(1.0,1.0,1.0,1.0,1.8)	.95	.77
(1.0,1.0,1.0,1.8,1.8)	.99	.75
(1.0,1.0,1.8,1.8,1.8)	.99	.80
(1.0,1.2,1.2,1.2,1.2)	.12	.074
(1.0,1.5,1.5,1.5,1.5)	.55	.37

Table 6. Monte-Carlo Standard Error Estimates for the Pair-Wise

Contrasts under the Alternative (1.0,1.0,1.0,1.0,1.0)

Contrast	Estimated Standard Errors
	Balanced Design	Cyclic Design
α1 - α2	.23	.24
α1 - α3	.23	.33
α1 - α4	.24	.42
α1 - α5	.24	.48
α2 - α3	.23	.24
α2 - α4	.23	.34
α2 - α5	.24	.41
α3 - α4	.24	.24
α3 - α5	.24	.33
α4 - α5	.24	.24

Table 7. Timeline and Principal Activities Associated with Consulting Project

Academic Quarter	CC Involved?	CRA Involved?	Principal Activities
Winter 2005	Yes	Yes	Proposal writing and submission
Spring 2005	No	No	Proposal reviewed by Organization X and project cost was negotiated. Proposal eventually approved.
Summer 2005	No	Yes	ML analysis of Bradley-Terry model with R program. Multiple client meetings with Organization X.
Fall 2005	Yes	Yes	Goodness-of-fit test, analysis of cyclic design, power and precision study, linear model analyses. Client meeting with Organization X.
Winter 2006	No	No	Organization X reviews results and uses R code to analyze new data sets on their own.
Spring 2006	Yes	No	Multiple comparisons analyses. Weak vs. Strong control for multiple comparison methods. Final client meeting with Organization X. Client is billed for the work.