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Combining DOD Test Information from Disparate Test Events

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### Combining DOD Test Information from Disparate Test Events

Mark London

May 12, 2012

NAVAIR Public Release YY-2012-530

Contents

- Introduction
- Preliminary Comments
- Problem Statement
- Proposed Solution: Meta-Analysis
- Test Setup and Data Set
- Data Analysis
- Data Results
- Conclusions
- Summary
- References

NAVAIR Public Release YY-2012-530

Introduction

- Declining DOD budgets require improvements in DOD T&E Acquisition processes
- DT&E, IT&E, and OT&E need to provide system performance results in a more efficient manner
- Design of Experiments is useful but doesn’t solve all problems
- Methods of combining information from multiple test sources must be developed
- Meta-Analysis
- Bayesian Analysis
- Bayesian Meta-Analysis (combination of both)

NAVAIR Public Release YY-2012-530

Preliminary Comments

Cost Influence of T&E:

Early detection of system issues can dramatically influence total program expenditures.

(Image courtesy of DAU Test and Evaluation Management Guide 2005)

Defense Acquisition University. Test and Evaluation Management Guide. The Defense Acquisition University Press, Ft. Belvoir, VA. 2005.

NAVAIR Public Release YY-2012-530

Preliminary Comments

SE Realization Processes

(right side of the “V”))

Testers verify that products

at each level meet their requirements

Before integration at next higher level

SE Design Processes

(left side of the “V”)

Testers are involved in writing

the verification procedures for requirements at each level

(Image adapted from URL source: http://ops.fhwa.dot.gov/publications/seitsguide/section3.htm)

US Dept. of Transportation Federal Highway Administration, Web.

URL: http://ops.fhwa.dot.gov/publications/seitsguide/section3.htm)

NAVAIR Public Release YY-2012-530

Preliminary Comments

Product Lifecycle Test Phases

(Image adapted from Systems Engineering Guide (2011), Mitre Corporation.)

- Multiple test phases
- Test phases provide different sets of test data
- Different sets of data answer different questions about the system

Mitre Corporation. (2011). Systems Engineering Guide: Test and Evaluation. Web.

URL: http://www.mitre.org/work/systems_engineering/guide/se_lifecycle_building_blocks/test_evaluation/.

NAVAIR Public Release YY-2012-530

Problem Statement

- We need to find ways of combining test data from disparate test events and test phases
- Two “normative” inferential statistical methods available
- Meta-Analysis
- Bayesian Estimation
- We will focus on Meta-Analysis
- Purpose of Study:Determine utility of Meta-Analysis for simple analysis of multiple flight test data sets.

NAVAIR Public Release YY-2012-530

Problem Statement

What’s our goal?... To integrate multiple test data sets into (hopefully) amore statistically significant set of data results

NAVAIR Public Release YY-2012-530

Proposed Solution: Meta-Analysis

- What IS Meta-Analysis?
- Combines results from several studies to address a set of related research hypotheses
- The statistical synthesis of results from a series of studies (Borenstein, 2009)
- Where is Meta-Analysis used?
- Health (Sandelowski, 2000), Medicine, Pharmacology, Education, Psychology, Business, Finance, Computer Simulations (Reese, 1996)
- Almost anywhere there is a need to assemble a summary of research studies on a given topic

Borenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2009). Introduction to Meta-Analysis. John Wiley & Sons, West Sussex, UK.

Reese, C. S., Wilson, A. G., Hamada, M. S., Martz H. F., & Ryan, K. J. (1996). Integrated Analysis of Computer and Physical Experiments. Los Alamos National Labs, Report No. LA-UR-00-2915.

Sandelowski (M. (2000). Focus on Research methods: Combining Qualitative and Quantitative Sampling, Data Collection, and Analysis Techniques in Mixed-Method Studies. Research in Nursing & Health, 23, 246-258.

NAVAIR Public Release YY-2012-530

Proposed Solution: Meta-Analysis

- What can Meta-Analysis provide?
- Way to combine results from multiple studies
- Way to broadly cover large amounts of studies/tests
- Limitations of Meta-Analysis? (Aguinas, 2011)
- Viewed with suspicion in technical fields
- File drawer problem
- Mixing apples & oranges
- Some studies may be ignored

Aguinas, H., Pierce, C. A., Bosco, F. A., Dalton, D. R., & Dalton, C. M. (2011). Debunking Myths and Urban Legends about Meta-Analysis. Organizational Research Methods, 14(2), 306-331.

NAVAIR Public Release YY-2012-530

Proposed Solution: Meta-Analysis

- Different “flavors” of Meta-Analysis
- Fixed Effects Model
- Random Effects Model
- “Effect Sizes” - measure the strength of relationship between variables and are the summary statistic in Meta-Analysis (Shelby, 2008)
- Effects may be use different models:
- d-family (Hedges, g) – compares mean difference
- r-family –compares correlation coefficients

Shelby, L. B. & Vaske, J. J. (2008). Understanding Meta-Analysis: A Review of the Methodological Literature. Leisure Sciences, 30, 96-110.

NAVAIR Public Release YY-2012-530

Proposed Solution: Meta-Analysis

(Adapted from Shelby & Vaske, 2008 and Lipsey & Wilson, 2001)

Lipsey, M. W. & Wilson, D. B. (2001). Practical meta-analysis. Thousand Oaks, CA: Sage.

Shelby, L. B. & Vaske, J. J. (2008). Understanding Meta-Analysis: A Review of the Methodological Literature. Leisure Sciences, 30, 96-110.

NAVAIR Public Release YY-2012-530

Test Setup and Data Set

- Laser spot tracking “miss” distance
- Airborne FLIR/Laser system
- Tested at NAS Patuxent River
- 5 separate data sets collected
- “Effect” is impact of flight environment on mean of laser spot placement.
- Fixed Effects model IAW (Ruzni, 2010)

Improved Mobile IR Signature Target System

Ruzni, N., Idris, N., & Saidin, N. (2010). The Effects of the Choice of Meta-Analysis Model in the Overall Estimates for Continuous Data with Missing Standard Deviations. 2nd International Conference on Computer Engineering and Applications, 369-373.

NAVAIR Public Release YY-2012-530

Test Setup and Data Set

Improved Mobile IR Signature Target System (IMISTS)

Table: IMISTS parameters

NAVAIR Public Release YY-2012-530

Test Setup and Data Set

Ground Test Measure Static Laser System Boresight Error (“Control”)

Flight Test Measures pointing accuracy under flight conditions (“Experiment”)

Flight Test Approach Video of Laser Spot on IMISTS Sample Data Points

NAVAIR Public Release YY-2012-530

Test Setup and Data Set

- Each of 5 ground data sets are “Control” group
- Ground data simulated in Matlab
- Data radial offset distance simulated as N(0,0.1)
- Data polar angle simulated as U(0,2π)
- # simulated points for each set matched corresponding # measured data points
- Each of 5 flight data sets are “Experimental” group to consider effect of flight environment

NAVAIR Public Release YY-2012-530

Data Analysis

PLOTS OF SIMULATED GROUND TEST DATA

- All simulated data modeled as N(0,0.1) in radius and U(0,2π) in polar angle.
- Results shown are averaged over 1000 simulations.

NAVAIR Public Release YY-2012-530

Data Analysis

PLOTS OF FLIGHT TEST DATA

- Note difference of grouping for each separate flight test event
- Most data contained within 2 radius “units”

NAVAIR Public Release YY-2012-530

Data Analysis

- Descriptive Statistics of Simulated data sets

Table: Simulated data set statistics for average of 1000 simulations.

- Descriptive Statistics of Flight data sets

Table: Flight test data Statistics

NAVAIR Public Release YY-2012-530

Data Analysis

Combining data sets into a Summary Table

Table: Summary table of all data sets.

NAVAIR Public Release YY-2012-530

Data Analysis

Calculating the Cohen Effect Size, d, using Direct Calculation Method for

each of the data sets we use the standard formulas (Borenstein, 2009):

the variance, Vd,, and Standard Error, SEd, are given by

where: i = data set number (i=1,2,…,5); XF,XS = sample means

sF, sS = sample SDs; nF, nS = 300 = # samples for each set.

Borenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2009). Introduction to Meta-Analysis. John Wiley & Sons, West Sussex, UK.

NAVAIR Public Release YY-2012-530

Data Analysis

Our resulting table of Cohen effect sizes becomes:

Table: Calculated Cohen d effect size parameter.

These Effect Sizes d are VERY Small! (d < 0.1)

NAVAIR Public Release YY-2012-530

Data Analysis

But, the Cohen d effect size parameter tends to overestimate

our effect size so we apply the Hedges J conversions using:

Table: Bias conversion using Hedges J parameter.

Borenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2009). Introduction to Meta-Analysis. John Wiley & Sons, West Sussex, UK.

NAVAIR Public Release YY-2012-530

Data Analysis

So we calculate our Hedges g effect size parameter using the

following formula:

And the variance, Vg,, and Standard Error, SEg, are given by

Table: Calculation of Hedges g parameter using J conversion.

NAVAIR Public Release YY-2012-530

Data ResultsBorenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2009). Introduction to Meta-Analysis. John Wiley & Sons, West Sussex, UK.

- But, for our Fixed Effects model we also need the respective weighting effects of each data set using:
- The weighting factor, Wi:
- The relative weighting factor, Wr:
- Product of Wi and Effect Size parameter, g
- Sum of Wi and Wi *g

Table: Calculation of Weighting Factors.

NAVAIR Public Release YY-2012-530

Data ResultsBorenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2009). Introduction to Meta-Analysis. John Wiley & Sons, West Sussex, UK.

- Finally to compute our Summary Effect statistics we use the following:
- And calculate our upper and lower 95% confidence levels as:
- Producing the summary effects of the flight vs. simulated data

NAVAIR Public Release YY-2012-530

Data Results

- A forest plot of our g effect sizes and Summary M effect produces:

NAVAIR Public Release YY-2012-530

Data ResultsBorenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2009). Introduction to Meta-Analysis. John Wiley & Sons, West Sussex, UK.

- But…we need to confirm Homogeneity of data sets using Cochrane’s Q statistic:
- Produces a Q value of Q=3002!!
- Our Chi-Square Critical Value (p=0.05, df=5-1=4) is: 9.488
- Since our Q is inside the CV (9.488 < 3002) we reject the null hypothesis that our variability is due to sampling error
- Homogeneity is NOT confirmed!
- To continue we would consider Meta-Regression analysis.

NAVAIR Public Release YY-2012-530

Data Results

(Adapted from Shelby & Vaske, 2008 and Lipsey & Wilson, 2001)

Lipsey, M. W. & Wilson, D. B. (2001). Practical meta-analysis. Thousand Oaks, CA: Sage.

Shelby, L. B. & Vaske, J. J. (2008). Understanding Meta-Analysis: A Review of the Methodological Literature. Leisure Sciences, 30, 96-110.

NAVAIR Public Release YY-2012-530

Conclusions

- Results of preliminary Meta-Analysis:
- Very small effect sizes (d, g, M all < 0.1)
- Flight data does not produce significant statistical difference from Ground data
- Large data sets of same dimensions
- Significant overlap between Flight vs. Ground
- Homogeneity NOT confirmed via Q test
- Random Effects models probably more accurate
- Meta-Regression probably needed
- Application to flight test data problematic
- Future Work should include:
- Complete full Meta-Regression for Random Effects model
- Explore analysis of other flight test regimes
- Compare & Contrast with Bayesian methods

NAVAIR Public Release YY-2012-530

Summary

Purpose of Study:Determine utility of Meta-Analysis for simple analysis of multiple flight test data sets.

Did our study succeed?—Not as originally planned!

Additional Observations:

- Need to ensure sufficient number of data sets
- Meta-Analysis more complicated than initially thought
- Homogeneity of data sets of primary importance
- Advanced methods (e.g. Meta-Regression) start to look more like conventional ANOVA or Multiple-Regression
- Application to Flight Test Data still unclear

NAVAIR Public Release YY-2012-530

ReferencesBorenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2009). Introduction to Meta-Analysis. John Wiley & Sons, West Sussex, UK.

Shelby, L. B. & Vaske, J. J. (2008). Understanding Meta-Analysis: A Review of the Methodological Literature. Leisure Sciences, 30, 96-110.

Anderson-Cook, C. M. (2009). Opportunities and issues in Multiple Data Type Meta-Analyses. Quality Engineering, 21, 243-253.

Aguinas, H., Pierce, C. A., Bosco, F. A., Dalton, D. R., & Dalton, C. M. (2011). Debunking Myths and Urban Legends about Meta-Analysis. Organizational Research Methods, 14(2), 306-331.

Defense Acquisition University. Test and Evaluation Management Guide. The Defense Acquisition University Press, Ft. Belvoir, VA. 2005.

Lipsey, M. W. & Wilson, D. B. (2001). Practical meta-analysis. Thousand Oaks, CA: Sage.

Mitre Corporation. (2011). Systems Engineering Guide: Test and Evaluation. Web. URL: http://www.mitre.org/work/systems_engineering/guide/se_lifecycle_building_blocks/test_evaluation/.

Reese, C. S., Wilson, A. G., Hamada, M. S., Martz H. F., & Ryan, K. J. (1996). Integrated Analysis of Computer and Physical Experiments. Los Alamos National Labs, Report No. LA-UR-00-2915.

Ruzni, N., Idris, N., & Saidin, N. (2010). The Effects of the Choice of Meta-Analysis Model in the Overall Estimates for Continuous Data with Missing Standard Deviations. 2nd International Conference on Computer Engineering and Applications, 369-373.

Sandelowski (M. (2000). Focus on Research methods: Combining Qualitative and Quantitative Sampling, Data Collection, and Analysis Techniques in Mixed-Method Studies. Research in Nursing & Health, 23, 246-258.

US Dept. of Transportation Federal Highway Administration, Web. URL: http://ops.fhwa.dot.gov/publications/seitsguide/section3.htm)

NAVAIR Public Release YY-2012-530

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