Research Paper Undergraduate 496 words

PTSD Stress Levels and Troop Numbers in Operation Iraqi Freedom

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Abstract

This paper investigates the linear relationship between the number of U.S. Marines deployed during Operation Iraqi Freedom (OIF) and the stress levels they experienced over the first two years of deployment. Using data reported by Atkinson, Guetz, and Wein (2009), Pearson's correlation coefficient was calculated from eight months of paired observations following the initial invasion. The analysis excluded one outlier corresponding to the initial invasion period. Results indicate a strong positive linear correlation, r(6) = .789, with troop levels explaining approximately 62% of the variance in stress levels (R² = .622). The findings have implications for Veterans Administration planning and mental health resource allocation for returning combat personnel.

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What makes this paper effective

The paper clearly states a null hypothesis, grounding the statistical analysis in standard scientific methodology and making the purpose of the correlation test explicit.
It identifies and addresses a potential outlier (the initial invasion period) before running the correlation, demonstrating awareness of how anomalous data points can distort results.
The use of both r and R² provides a complete picture of the relationship — not just its strength and direction, but also the proportion of variance explained.

Key academic technique demonstrated

The paper demonstrates the application of Pearson's correlation coefficient to real-world military health data. By organizing the raw data into a structured table including X², Y², and XY columns, and then substituting summed values into the correlation formula, the paper models the correct computational workflow for bivariate linear correlation — a technique central to introductory statistics and quantitative research methods courses.

Structure breakdown

The paper opens with a brief literature-based rationale connecting PTSD to OIF troop data, introduces the research question and null hypothesis, describes the dataset and the decision to exclude an outlier, presents the raw data in tabular form, and concludes with the computed Pearson's r and coefficient of determination (R²). This compact structure — rationale, data, analysis, result — reflects a standard short quantitative report format suitable for undergraduate statistics coursework.

Introduction to PTSD and Combat Stress

Post-traumatic stress disorder (PTSD) is a common experience among combat troops, both while in theatre and after returning home (Atkinson, Guetz, & Wein, 2009). The Veterans Administration must prepare for the mental health needs of returning troops, and there is therefore a need for reliable prediction models. Toward this goal, Atkinson and colleagues (2009) examined the reported stress levels for Marines during Operation Iraqi Freedom (OIF).

A total of 67 months of data was available for both groups, though more limited data was available for the number of Marines deployed (Atkinson, Guetz, & Wein, 2009, supplemental data, pp. 62, 66). When the number of Marines deployed is compared to stress levels, a possible linear relationship appears to exist. There appears to be one outlier representing troop levels during the initial invasion, corresponding to a stress level of 0.0072 at troop levels of 66,166.

Data and Outlier Considerations

To determine the amount of stress experienced by Marines deployed during the two years of deployment following the initial invasion of Iraq, troop levels were compared with stress levels using linear correlation. The null hypothesis (H₀) is that stress levels are not associated with deployed troop levels.

After the initial invasion had concluded, the number of Marines deployed in Iraq dwindled to a few thousand. By the beginning of the second year of deployment, however, the number of deployed Marines increased dramatically, as did stress levels. The data used in this analysis are presented in the table below.

Troop Levels and Stress: Observed Trends

Table: Stress levels experienced by OIF Marines in relation to troop levels during the first two years of OIF deployment.

Month 4: Marines Deployed = 22,885 | Stress Level = 0.0014 | X² = 5.24×10⁸ | Y² = 1.96×10⁻⁶ | XY = 32.039
Month 7: Marines Deployed = 6,545 | Stress Level = 0.0000 | X² = 42,837,025 | Y² = 0 | XY = 0
Month 10: Marines Deployed = 2,557 | Stress Level = 0.0004 | X² = 6,538,249 | Y² = 1.6×10⁻⁷ | XY = 1.0228
Month 13: Marines Deployed = 25,568 | Stress Level = 0.0085 | X² = 6.54×10⁸ | Y² = 7.23×10⁻⁵
Month 16: Marines Deployed = 32,636 | Stress Level = 0.0094 | X² = 1.07×10⁹ | Y² = 8.84×10⁻⁵
Month 19: Marines Deployed = 35,216 | Stress Level = 0.0154 | X² = 1.24×10⁹ | Y² = 0.000237
Month 22: Marines Deployed = 30,500 | Stress Level = 0.0144 | X² = 9.3×10⁸ | Y² = 0.000207
Month 25: Marines Deployed = 30,500 | Stress Level = 0.0042 | X² = 9.3×10⁸ | Y² = 1.76×10⁻⁵
Sums: Marines Deployed = 186,407 | Stress Levels = 0.0537 | X² = 5.39×10⁹ | Y² = 0.000625

Pearson's Correlation Analysis

Plugging the values from the bottom row of the table into the formula for Pearson's correlation coefficient (r) reveals a strong relationship between the number of Marines deployed during OIF and the stress levels experienced: r(6) = .789. The amount of variance in stress levels that could be explained by troop levels was R² = .622, or approximately 62%.

Conclusion

Plugging the values from the bottom row of the data table into the formula for Pearson's correlation coefficient reveals a strong relationship between the number of Marines deployed during OIF and the stress levels experienced, r(6) = .789. Approximately 62% of the variance in stress levels is accounted for by troop deployment numbers (R² = .622). These findings support the use of troop-level data in Veterans Administration prediction models for PTSD and related mental health resource planning for returning combat personnel.

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Key Concepts in This Paper

PTSD Linear Correlation Operation Iraqi Freedom Pearson's r Troop Deployment Stress Levels Outlier Exclusion R-squared Veterans Administration Combat Mental Health