Linear Correlation

Stress Levels experienced by Marines during Operation Iraqi Freedom

Post-traumatic stress disorder (PTSD) is a common experience among combat troops, both when in theatre and after returning home (Atkinson, Guetz, & Wein, 2009). The Veterans Administration must prepare for the mental health needs of the troops returning home, therefore there is a need for prediction models. Towards this goal, Atkinson and colleagues (2012) examined the reported stress levels for Marines during Operation Iraqi Freedom (OIF). A total of 67 months of data was available for both groups, but more limited data was available for the number of Marines deployed (Atkinson, Guetz, & Wien, 2009, supplemental data, p. 62, 66. If the number of Marines deployed is compared to stress levels (Figure), a possible linear relationship appears to exist. There appears to be one outlier representing troop levels during the initial invasion, representing a stress level of 00.0072 at troop levels of 66,166. 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 (Ho) is stress levels are not associated with deployed troop levels.

Figure

. Scatter plot of relationship between the numbers of Marines deployed during OIF and stress levels. The data to be compared is presented in the Table. After the initial invasion had completed, 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.

Table.

Stress levels experienced by OIF Marines in relation to troop levels during the first 2 years of OIF deployment.

Month

Marines Deployed

Stress Levels

X^2

Y^2

XY

4

22,885

0.0014

5.24E+08

1.96E-06

32.039

7

6,545

0.0000

42837025

0

0

10

2,557

0.0004

6538249

1.6E-07

1.0228

13

25,568

0.0085

6.54E+08

7.23E-05

16

32,636

0.0094

1.07E+09

8.84E-05

19

35,216

0.0154

1.24E+09

0.000237

22

30,500

0.0144

9.3E+08

0.000207

25

30,500

0.0042

9.3E+08

1.76E-05

Sums =

186407

0.0537

5.39E+09

0.000625

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

Reference

Atkinson, M.P., Guetz, A., & Wein, L.M. (2009). A dynamic model for posttraumatic stress disorder among U.S. troops in Operation Iraqi Freedom. Management Science, 55(9), 1454-68.