The first model specifies that NPS GPA can be predicted by type of major, warfare community, and performance at the Academy as measured by Order of Merit. This model is shown in Figure 2. As shown in Table 3, the order of entry into the regression is Major Group, Community, OOM_PCT.
In this analysis Major Group is a nominal variable; therefore, it is recoded into dummy variables before running the regression. Group 1 is chosen as the standard to compare Group 2 and Group 3 majors against. Because
dummy variables are required, step one of the regression needs two coefficients even though the only variable being analyzed is Major Group. Table 6 shows the results of Model 1.
In the first step both Major Group variables are significant at the 99% level, and both negatively affect Nuclear Power School GPA. However, Group 3 majors suffer a much greater reduction in GPA, almost a quarter of a point. This result is not surprising. More experience in technical courses should aid performance in Nuclear Power School.
Table 6. Hierarchical Logistic Regression Analysis of Predictors of NPS GPA: Model 1 (N=1095)
Standard Variable B Error t p β B Step 1 Constant 3.184 0.015 214.497 0.000 Major: Group 2 -0.080 0.026 -3.005 0.003 -0.092* Major: Group 3 -0.241 0.029 -8.426 0.000 -0.258** Step 2 Constant 3.159 0.016 202.839 0.000 Major: Group 2 -0.090 0.026 -3.408 0.001 -0.104* Major: Group 3 -0.250 0.028 -8.814 0.000 -0.268** Community: Other 0.087 0.067 1.307 0.191 0.038 Community: SWO Nuke 0.132 0.027 4.872 0.000 0.142** Step 3 Constant 3.477 0.019 186.648 0.000 Major: Group 2 -0.067 0.021 -3.126 0.002 -0.078* Major: Group 3 -0.244 0.023 -10.554 0.000 -0.262** Community: Other 0.061 0.055 1.120 0.263 0.027 Community: SWO Nuke 0.092 0.022 4.149 0.000 0.099** OOM_PCT -0.008 0.000 -23.393 0.000 -0.556**
Note. * p < .01; ** p < .001. R2 = .061 for Step 1 (p < .001); ∆R2 = .079 for Step 2
(p < .001); ∆R2
= .386 for Step 3(p < .001). Major Group 2 is dummy coded such that 1 = Math/Science major and 0 = engineering majors; Major Group 3 is dummy coded such that 1= Humanities/Social Science major and 0 = engineering majors; Community: Other is dummy coded such that 1 = any service assignment except SWO Nuke and Subs and 0 = service assigned Subs; Community SWO Nuke is dummy coded such that 1 = service assigned SWO Nuke and 0 = service assigned Subs; OOM_PCT is a fractional variable where a smaller fraction represents a higher class standing and 1 is assigned to the individual at the bottom of the class.
The second step of the regression enters the dummy variables for service community. NUC SUB is chosen as the standard to compare the other communities against. The two dummy variables entered into the regression are NUC SURF and Other.
Adding variables to account for community increases the negative weight of the Major Group variables. The Community: Other variable is not significant. All other variables in the regression are significant at the 99% level. Nuclear surface officers perform better than submariners by about a tenth of a point.
The last step of the regression enters Order of Merit Percentile (OOM_PCT) which is a continuous variable. In this final step every variable is significant at the 99% level except Community: Other. OOM_PCT is inversely related to NPS GPA. OOM_PCT has a range of zero to one, and is derived by the equation:
OOM_PCT = OOM
No in class
The top person in each class has a very small OOM_PCT and the last person’s OOM_PCT is one. Because “better” is smaller the negative coefficient is expected. Do not let the small value of OOM_PCT confuse you. It actually shows a strong effect. Because OOM_PCT is a percent the coefficient really shows that raising Order of Merit by one percent (about 10 places) is reflected in an increase of 0.008 in Nuclear Power School GPA.
The addition of OOM_PCT to the model lessens the impact of the other variables to a small degree. The
percent reduction in the value of its coefficient. The coefficient for Group 2 is reduced by 26 percent while the coefficient for Group 3 remains almost constant.
D. HIERARCHICAL LOGISTIC REGRESSION ANALYSIS OF PREDICTORS OF NUCLEAR POWER SCHOOL GPA (MODEL 2)
The second model specifies that NPS GPA can be predicted by type of major, warfare community, and performance at the Academy as measured by Cumulative Academic Quality Point Rating (CAQPR), Technical Quality Point Rating (TQPR), and Military Quality Point Rating (MQPR). This model is shown in Figure 3. As shown in Table 4, the order of entry into the regression is first Major Group, then Community, and last the performance variables CAQPR, TQPR, and MQPR.
In this analysis Major Group is a nominal variable; therefore, it is recoded into dummy variables before running the regression. Group 1 is chosen as the standard to compare Group 2 and Group 3 majors against. Because dummy variables are required, step one of the regression needs two coefficients even though the only variable being analyzed is Major Group. Table 7 shows the results of Model 2.
In the first step both Major Group variables are significant at the 99% level, and both negatively affect Nuclear Power School GPA. However, Group 3 majors suffer a much greater reduction in GPA, almost a quarter of a point. This result is not surprising. Less experience in technical courses should hurt performance in Nuclear Power School.
Table 7. Hierarchical Logistic Regression Analysis of Predictors of NPS GPA: Model 2 (N=1095)
Standard Variable B Error t p β B Step 1 Constant 3.184 0.015 214.497 0.000 Major: Group 2 -0.080 0.026 -3.005 0.003 -0.092** Major: Group 3 -0.241 0.029 -8.426 0.000 -0.258*** Step 2 Constant 3.159 0.016 202.839 0.000 Major: Group 2 -0.090 0.026 -3.408 0.001 -0.104** Major: Group 3 -0.250 0.028 -8.814 0.000 -0.268*** Community: Other 0.087 0.067 1.307 0.191 0.038 Community: SWO Nuke 0.132 0.027 4.872 0.000 0.142*** Step 3 Constant 1.598 0.094 17.063 0.000 Major: Group 2 -0.087 0.020 -4.272 0.000 -0.100*** Major: Group 3 -0.227 0.024 -9.637 0.000 -0.244*** Community: Other 0.064 0.051 1.256 0.209 0.028 Community: SWO Nuke 0.131 0.021 6.250 0.000 0.141*** CAQPR 0.546 0.057 9.641 0.000 0.589*** TQPR 0.075 0.041 1.828 0.068 0.102* MQPR -0.128 0.039 -3.275 0.001 -0.100**
Note. * p < .1, ** p < .01; *** p < .001. R2 = .061 for Step 1 (p < .001); ∆R2 = .079
for Step 2 (p < .001); ∆R2
= .463 for Step 3(p < .001). Major Group 2 is dummy coded such that 1 = Math/Science major and 0 = engineering majors; Major Group 3 is dummy coded such that 1= Humanities/Social Science major and 0 = engineering majors;
Community: Other is dummy coded such that 1 = any service assignment except SWO Nuke and Subs and 0 = service assigned Subs; Community SWO Nuke is dummy coded such that 1 = service assigned SWO Nuke and 0 = service assigned Subs; CAQPR, TQPR, and MQPR are grade point average like variables with a range of 0 – 4, where 4 is perfect.
The second step of the regression enters the dummy variables for service community. NUC SUB is chosen as the standard to compare the other communities against. The two dummy variables entered into the regression are NUC SURF and Other.
Adding variables to account for community increases the negative weight of the Major Group variables. The Community: Other variable is not significant. All other variables in the regression are significant at the 99 percent level. Nuclear surface officers perform better than submariners by about a tenth of a point.
The last step of the regression enters the Academy performance variables CAQPR, TQPR, and, MQPR. All three of these continuous variables are components of Order of Merit. About 65 percent of Order of Merit is based on academic performance (USNA INSTRUCTION 1531.51A, 1996). CAQPR measures overall academic performance and TQPR measures academic performance in technical classes (math, science, engineering). Military performance accounts for 17.7 percent of Order of Merit (USNA INSTRUCTION 1531.51A, 1996). MQPR measures a Midshipman’s military performance. The rest of Order of Merit (about 18 percent) is based on physical ability and Midshipman conduct (USNA INSTRUCTION 1531.51A, 1996). These two areas are not represented in the model.
In this final step every variable is significant at the 99 percent level except Community: Other and TQPR. TQPR is significant at the 90 percent level while Community: Other remains insignificant. CAQPR and TQPR are both positively related to NPS GPA; however CAQPR is almost six times as powerful as TQPR. This is interesting.
General academic ability is more predictive in Nuclear Power School, a highly technical school, than academic ability in technical classes. Another interesting result is the negative relationship between MQPR and NPS GPA. Better military performance yields lower grades in Nuclear Power School. The magnitude of MQPR’s B is minor; much less than CAQPR and about equal to that of TQPR.
The addition of the three Academy performance variables model lessens the impact of the other variables to a small degree. The greatest change is seen in Major: Group 3, which sees a nine percent reduction in the value of its coefficient. The changes in the coefficients of the remaining variables are very minor.
E. SUMMARY
This chapter shows how the data is analyzed. Two hierarchal regressions are examined. Both models find that Engineering majors perform best at Nuclear Power School and humanities majors the worst. Nuclear surface warfare officers perform better than Submarine officers. Finally, good performance at the Naval Academy has a strong positive effect on NPS GPA.