Skip to main content

Full text of "DTIC AD1049442: Examining Manning Relationships Between US Air Force Enterprises and Career Fields"

See other formats


EXAMINING MANNING RELATIONSHIPS BETWEEN US AIR FORCE ENTERPRISES AND CAREER 

FIELDS 


A US Air Force (USAF) dataset containing 6 attributes and over 400,000 funded authorizations (paid workforce 
positions) is analyzed for significant manning relationships among 12 Service Core Functions (SCFs) and 32 
functional areas. The authorizations are collapsed into 375 groups of 32 functional equities ranging from 
Acquisitions to Weather career fields. The SCFs are managed by 7 Core Function Leads (CFLs) who are 
typically Major Command (MAJCOM) commanders. Logistic fit analyses via logistic odds ratio (OR) 
comparisons and contingency table analyses reveal significant manning shortfalls in all 12 CFLs. The results of 
the analysis hope to better inform the USAF Strategic, Planning & Programming Process (SP3). The SP3 is a 
Chief of Staff of the Air Force (CSAF)-approved framework that guides strategic decision making. 

Keywords: Logistic Regression, Personnel risk, Relative Risk, Strategic risk, Odds Ratio 

Introduction 


The primary objective of this cross-sectional observational study is to examine ways to assess manning data that may help 
senior Air Force leaders manage personnel capability and enhance maximization of readiness. The desired endstate is a 
more defensible, rigorous methodology to better inform SCF (Figure 1) strategic risk assessments. This would enable 
SCF personnel planners to assess manning shortages to more accurately inform the USAF budget, thereby, enabling the 
CSAF to better manage personnel combat capability. Manning is defined as the ratio of the number of personnel and the 
number of funded authorizations: 


Manning = 


Number of ( assigned ) personnel 
Number of funded authorizations' 


Each USAF unit has a unit manning document (UMD) which stipulates the number of personnel and funded 
authorizations. Each authorization represents a funded position. Ideally, funded authorizations should have assigned, 
trained personnel filling the positions, but this is usually not achieved across the USAF. 


Air Force Core Functions 


r 

Nuclear Deterrence Ops 

)( 

Global Precision Attack 

i 

Air Superiority 

II 

Special Operations 

L 

Space Superiority 

JL 

Rapid Global Mobility 


r 

Cyberspace Superiority 

T 

Personnel Recovery 

L 

Command and Control 

JL 

Agile Combat Support 


L 

Global Integrated ISR 

JL 



Personnel & Training 


Figure 1: USAF Service Core Functions (SP3 2011) 

Career fields are often undermanned, which results in a stressed, overworked workforce that equates to increased military 
risk. As of July 2016, there were over 400,000 active duty military and civil servants in the USAF. Of the 400,000+ 
personnel, 55% are enlisted, 13% are officer and the remaining 32% are civil servants (See Appendix II). The USAF has 
over 300 career field specialties or Air Force Specialties (AFS). AFSs are further compartmentalized into Air Force 


1 


















Specialty Codes or AFSCs. The AFSCs are condensed into 32 functional equities (FEs) across the 12 SCFs. A mapping 
of the career fields to the functional equities is provided in Figure 2. 


Mapping from AFS to Functional area 

Acq 

60C, 63A/F/G/S 

Distribution 

25E. 2F0, 2P0, 2TX, 2XX 

Mx 

21A, 2AX, 2M0, 2R0, 2R1 

S&T 

61X, 62X, 8E0 

Airfld Ops 

1AX, IPX, 1TX 

Fin 

65X, 6F0, 6F5 

Materiel 

2S0 

Safety 

ISO, 1S1 

C2 Sys Ops 

1CX 

Force Supt 

30X, 34X, 36-38X, 3DX, 

3M, 3R03SX 

Msn Assur 

17X, 81-83, 85, 8X, 90G, 92X, 95-99, 9X 

1B0,1B4,1F4, 39X, 3AX, 3F4, 3T0, 3V0, 

69E, 6A3, 72, 75, 76, 7D 

Sec Forces 

31F, 31P, 3 IS, 3P0 

CE 

32E/G/S, 3EX 

Health Srvs 

40-48X, 4X, 9S1 

Muns 

21M, 2WX 

Space/Miss 

13X 

Chaplain 

52R, 5R0 

Hist 

3H0, 84H 

Ops Mgt 

86M, 86P 

SpecInv 

71, 71S, 750 

Combat Sys 

12X 

Inspection 

87G/I/Q, 8IO/T 

Ops Plans 

10C,16X 

Wx 

151,15W, 1W0 

Comm- 

33S7 33V7-3€fr"3Cl 

Intelligence 

14N, 1NX 

Pilot 

11X 



CC 

20C, 80C, 91C, 91W 

Legal 

5LI, 5J0 

PA 

35X, 3NX 



Cons 

64A, 64P, 6C0 

Log Plans 

21G/L/R/T, 221, 2G0 

RPA 

18X, 1V0 





Figure 2: Functional Equity Mapping 

This results in a dataset of 375 observations 1 . Figure 3 is a bi-chart which shows the assigned USAF personnel by the 12 
SCFs along with associated manning rates. Figure 4 shows manning rates by FE. The mean and median are the same for 
the FEs. The SCFs are unequally weighted (i.e. the amount of personnel differs by the SCF). Each of the twelve SCFs are 
supported by Core Function Support Plans (CFSPs) and developed and approved by one of the seven CFLs. CFSPs 
translate the vision for the specific CFs into risk-informed, resource-constrained, planning force proposals that guide 
follow-on Program Objective Memorandum (POM) and Science & Technology (S&T) decisions and activities (NAP, 
2014). 


1 The reader should be advised not all 32 functional equities are represented in every SCF, so although 32 x 12 is 384, there are 
actually only 375 observations. 


2 
























Figure 3: USAF SCF Manning Summary 



Figure 4: USAF Functional Equity Manning Summary 


Data Overview 

This study consists of over 416,485 authorizations collapsed into 375 subsets as of July of 2016 from the Air Force 
Manpower, Personnel and Services database. Each subset represents a group of FE by SCF. Each observation contains 6 
variables listed in Table 1. The variable type characteristics are categorical (to include nominal and ordinal) and numeric. 


3 

























Table 1: Variables for categorical analysis 


Name 

Description and effect type 

Type 

Levels and notes 

SCF 

Service Core Function (Fixed) 

Nom. 

There are 12 USAF SCFs. 

Functional Equity 
(FE) 

Career Field Family (Fixed) 

Nom. 

There are 32 FEs. 

Manning category 

Binned manning categories between 
> 100% and < 80% (Fixed) 

Ord. 

6 ordered categories 

Manning rate 

Assigned personnel vs Authorizations 

(Used to determine ‘Fully Manned’ & ‘Manning 

category’) 

Cont. 

This is a continuous value. 

Fully Manned (Y/N) 

Factor which consists of (Fixed) 
either fully manned or not 

Nom. 

Binomial variable 
(outcome) 

Overage/Shortage (-) 

Number of surplus/shortage of 
authorizations (Fixed) 

Disc. 

This is a discrete value. 


Research Question & Application of Techniques 

In the world of doing either the same amount of workload or less workload with fewer resources, how does one 
effectively manage resources with respect to assessing personnel capability? In the past, USAF has developed numerous 
MAJCOM manpower assessments using various techniques. However, since 2010, the USAF has adopted a broader 
enterprise-level approach via the SCF. A SCF may utilize several MAJCOMs in order to execute its mission. One 
enduring challenge is accurately assessing personnel deficiencies across the USAF by SCF. If planners could more 
accurately assess and identify the personnel SCF sight picture, this would help substantiate the risk associated with a lack 
of required manpower to deliver wartime and peacetime capability. A valid manning assessment can help identify 
capability gaps and serve as a good planning tool as a means of validating risk. This further enables senior leaders to 
qualify risk with analysis and increase the odds of filling or mitigating personnel capability gaps. The improved strategic 
manning assessment could then be used to improve the strategic planning & programming process and enable the CSAF 
to better advocate for personnel resources. The subsequent research questions and hypothesis (a = 0.05) are as follows: 

• Is there a meaningful manning relationship between USAF SCFs and full manning levels? 

Null Hypothesis (H 0 ): There is an association between SCF and Full manning levels. 

Alternate Hypothesis (H A ): There is no association between SCF and Full manning levels. 

• Given, SCFs are unique: is there a rigorous way to compare manning levels among SCFs and FEs? 

USAF manning levels typically do not vary much during non-presidential election years and historically, attempts at 
trying to predict manning beyond a given Fiscal Year Defense Plan (FYDP) have been mostly fruitless. The goal of this 
study is not to develop a model to predict future manning levels. The goal of this study is to build a SCF and FE 
comparative manning assessment that strategic leaders can utilize for personnel capability advocacy. Techniques 
explored will focus on logistic analysis in the form of contingency tables, logistic odd ratios and other methods to 
compare the SCFs and FEs against the manning levels. 


4 












Exploratory Analyses 

The next portion uses descriptive statistics to examine if the 12 SCF populations that consist of primarily 32 functional 
equities are statistically similar. The analysis is performed using JMP 11 Pro. The study uses a significance level (also 
known as a) of 0.05 or simply there is a 5% likelihood of committing a Type I error (rejecting the null hypothesis, when it 
is true). Figure 5 provides standard box and whisker plots by SCF population size intersected by a grand mean; lists the 
respective SCF standard deviations; and shows a Tukey test pairwise comparison among the SCF means. The plots show 
evidence of SCF dissimilarity. The standard deviation range among the SCFs is relatively large. The majority of the 
Tukey test results reveal the SCFs are statistically dissimilar. 


130% • 

120 %- 

110 %- 

100% 

90%“ 

S0% 

? 70%“ 

c 

c 

^ 60%“ 
50% 
40%- 

30%~ 

20 % 

io%- 

0 % 




P 


[1 


ACS - 
AS - 
C2 - 

cs - 

GISR - 
GM - 
GPA 

NDO 
P &T 
PR 

SO ■ 

ss ■ 


■Agile Combat Support 
Air Superiority 
■ Command & Control 
Cyberspace Superiority 

- Global ISR 

- Global Mobility 

- Global Precision Attack 

- Nuclear Deterrence Ops 

- Personnel & Training 

- Personnel Recovery 
-Special Ops 

- Space Superiority 


CJ 0 : g 
13 

SCF 


0.14 

0.12 

0.10 

0.08 



* 

• 


* 




* 


* 

0.06 

0.04 

0.02 

0.00 

• 

• 



• 


« 


• 


* 



ACS AS C2 CS GISR GM GPA NDO P&T PR SO SS 
SCF 


Std dev manning range: 4% -12.5% (i.e. large) 


< 

Cl. 

O 

Q 

TL 

(— 

Cl. 

Connecting Letters Report 


Level 

Mean 


GM A 

10309713 


PR B 

10051307 


ACS c 

0399745! 


C2 D 

0.9665473 


SS E 

09365637 


GISR F 

09331010 


SO G 

03235S5O 


P&T G 

09232152 


NDO H 

031*1729 


GPA | 

0-90SS132 


CS 1 

0-9071673 


AS 

J 03971833 


Levels net connected by seme letter ere siflnif ieently different, 


O ' $ 


Figure 5: Descriptive Statistics of SCF Manning Levels 


Contingency Analyses 

The main outcome variable or response is a binary categorical variable (i.e. > 100% manned or not) and the other factors 
are fixed nominal and ordinal variables. We use contingency analysis to examine if there are meaningful associations 
between SCFs and manning levels as well as studying associations between SCFs and FEs (Figure 6). 


5 























T Contingency Analysis ol Fully Manned(Y/N) By SCF 
4 Mosaic Plot 



SCF 


Tests 

u 

DF 

-LogLtke 

RSquare(U) 

375 

11 

13.907225 

0.0613 

Test 


ChiSquare 

Frob>Chi5q 

Likelihood Ratio 

27.314 

0.0035* 


^ * Contingency Analysis of Fully Manned[Y/N> By Functional Equity 
J Mosaic Plot 



FuriftiOnal Equity 


Tests 

N DF -LogUke R Square 0U3 

375 31 25,203551 01120 

Test CbiSquare Prob>ChiSq 

Likelihood Ratio 50.407 0.0153* 


Figure 6: SCF and FE manning Contingency Analysis 

Figure 6 via the Likelihood Ratio test statistic shows the chi-square values from the SCF and FE observations, which are 
27.814 and 50.507 respectively. Since, the p-value is less than a (0.05) this demonstrates there is a significant association 
between manning levels and SCF. 

The manning categorical variable (‘Mann_Cat’) is an ordinal response with six levels. We test this response for 
homogeneity among the SCF and FE variables. Since, the Likelihood ratio p-values are smaller than a, the results of tests 
suggests the difference in manning levels across SCF and FE are statistically significant (Figure 7). 


6 

































A 


Test Response H om ogeneity 


Test ChISquare Prob>ChiSq 

Likelihood Ratio 75.1017 0.0371* 




M.ann Cat 




100% 

or 

more 

95-99% 

90-94% 

85-89% 

80-84% 

<80% 


117 

41 

74 

54 

35 

54 

375 

31.20 

10.93 

19.73 

14.40 

9.33 

14.40 



32 

32 

32 

28 

32 

32 

32 

32 

32 

21 

32 

3 2 

375 


Share Chart 


Acquisition 
A«rficld Operations 
C2 Systems Ops 


CE_ 

Chaplaincy 

Combat Systems (12XJ 

Commarader/Sr Leader 

[Contracting 

Distribution 

Fi nal nee 

Force Su pport 

Health Services 

Historian 

Inspections _ 

]ntelli pence 

Legal _ 

Logistics Plans 
. Main tenance 
Materiel 

Mission Assurance 
Munitions 

Ops Mqt 

■Ops Planning 


JPA 

Pilot 

RPA 

SfltT 

Safety 

SF_ 

Spacc/N uke/Mbsi le Ops 

Sotrial Invest. _ 

Wither 




Test Response Homogeneity 

Test ChtSquare Prab>Chi5q 

Likelihood Ratio 247.623 <.0001* 


Figure 7: Ordinal Categorical Analysis 


Modeling Approach 


Although, the focus of this study is to explore not to necessarily predict manning levels among SCFs and FEs, the data are 
investigated to see if a nominal logistic regression model can provide more meaningful insight among the SCFs and FEs 
as it relates to being fully manned or not. Logistic regression analysis describes how a binary (0 or 1) response variable is 
associated with a set of explanatory variables (categorical or continuous). The general logistic function is n(x ) = 


e (oc+/?x) 

1 + e (0C+/?x) 


odds 

1+odds 


where x is the independent variable or factor and e is the exponential function, and 7r(x) is the 


probability of being at least 100% manned. For this nominal outcome variable, each factor is examined individually and 
associated model statistics are compared to a joint (combined) model. The manning categorical (ordinal) factor is not a 
statistically significant effect in any of the models as the p-values for the parameter estimates were greater than a. Figure 
8 provides a summary of the results. 


7 




































































































































































Whole Model Test 


Model 

Difference 

Full 

Reduced 


-Log Likelihood 

41.69940 

183.43230 

225.13170 


DF Ch[Square 

42 83.39879 

Combined 


Prob>ChiSq 

0 . 0001 * 


RSquare(U) 

AICc 

BIC 

Observations (or Sum Wgts) 

Measure 

Entropy RSquare 
Generalized RSquare 
Mean -Log p 
RMSE 

Mean Abs Dev 
Miselassification Rate 


0,1852 

464.297 

621,722 

375 


Goodness Of 

Fit Statistic 

Chi Square 

DF 

Prob>ChiSq 

Pearson 

362.3808 

332 

0,1209 

Deviance 

366.3646 

332 

0,09] 

LI 


N 


Training Definition 

0.1852 1-Logllke[model)/Loglike(0) 

0.2853 (1 -(L(0)/L(model)) A (2/n))/a - L£0) A (2/n)) 
0,4892 X-Log(p(j])/n 
0.4026 VX(y[j]-ptj])Vn 
0.3253 X|y|J]-plj]|M AUC 

0.2400 X(p(j]*pMax)/n 0.78223 

375 n 


Figure 8: SCF & FE manning Model Comparison 

Results from the joint model from the ‘Whole Model Test’ shows significance. The accuracy rates (1- misclassification 
rate) regarding predictability classifies success 76% of the time. The Goodness of Fit (GoF) statistic suggest the model is 
adequate as the Deviance values are above a. The joint model has an Area under the Curve (AUC) of 0.782. This 
suggests the modeling predictions have more than a ‘chance’ of being accurate. In fact, a strict interpretation of this 
model is that when presented randomly with a given number of SCF and FE manning observations that are > 100% and < 
100%, there is a 78.2% chance of correct classification. Figure 9 depicts the model probability estimates of being 100% 
or more manned by SCF and FE. 


8 









ACS | 

AS | 

C2 | 

es | 

GISR 1 

GM | 

GPA | 

MDO | 

F&T | 

PR | 

SO I 

SS 

Acquisition 

04193 

0234 

02514 

0.4613 

02036 

0.6146 

0234 

02514 

0.4606 

. 

0.1658 

0.5777 

Airfield Operations 

0.2576 

0.1665 

0.1387 

0.2816 

01122 

0.4334 

0.1665 

0.1387 

0.2305 

0.5211 

0,0371 

9,3961 

C2 Systems Ops 

0.3523 

0.2383 

0.202 

0.3923 

0,1658 

0.5458 

0,2389 

0.202 

0.3816 

0.S31 

0,1304 

0,5078 

CE 

0.3523 

0.2383 

0202 

0 3923 

0.1658 

0.5459 

0.2389 

0202 

03816 

0.631 

0.1304 

0.507G 

Chaplaincy 

0.2064 

0.1302 

01077 

0.2358 

00865 

0.3644 

0.1302 

0.1077 

02348 


0 0667 

03296 

Combat Systems f!2X 

0.1656 

0.1026 

0.0844 

0.1906 

0.0674 

0.3Q44 

0.1026 

0.0844 

0.1898 

0.3837 

0,0518 

0.2723 

CC/SL 

0.7222 

05394 

0,5468 

0,7551 

0.4864 

0.8514 

0,5334 

0,5468 

0.7541 

0.8307 

0,4168 

0.3308 

Contracting 

0.4433 

03135 

02746 

0.4318 

0.2231 

0.6426 

0.3135 

0.2746 

0.4304 

0.7133 

0.1832 

0.6066 

Distribution 

0.4433 

03195 

02746 

0.4918 

0.2291 

0.6426 

03195 

0.2746 

0.4904 

0,7139 

0,1832 

0.6066 

Finance 

0.0732 

0.0472 

0.0384 

0.0926 

0,0304 

0.1594 

0.0472 

0.0384 

0.0821 

0.2124 

0.0231 

0.1338 

Force Support 

0,165$ 

0.1026 

0.0844 

01906 

0.0674 

0,3044 

0,1026 

0.0344 

01898 

0.3837 

00518 

0.2728 

Health Services 

0.165S 

01026 

00844 

0.1306 

0 0674 

0.3044 

0.1026 

0.0844 

0.1898 

0.3837 

0.0518 

02729 

Historian 

0.4196 

0.294 

0,2514 

0.4619 

0.2086 

0.6146 

0294 

0.2514 

0.4606 

v| 

0.1659 

0,5777 

Inspections 

0.0732 

Oj0472 

0.0384 

0.0326 

0.0304| 

0.1584 

O.0472 

O.0384 

0.0821 

0,2124 

0.0231 

0.1338 

Intelligence 

0.4433 

0.3135 

02746 

0,4318 

0.2231 

0,6426 

0,3195 

0.2746 

0.4904 

0.7139 

0.1832 

08066 

Legal 

0.16S6 

01026 

00844 

0.1306 

0 0674 

0.3044 

OJ026 

0.0844 

01898 

0.3837 

0.0518 

02729 

Logistics Plans 

0.0732 

0.0472 

0.0384 

0.0926 

0.0304 

0.1534 

0.0472 

0.0384 

0.0821 

0.2124 

0,0231 

n 1333 

Maintenance 

0.3523 

0.2389 

0.202 

0.3923 

0.1658 

0,5459 

0,2383 

0.202 

0.3816 

0.631 

0.1304 

0.5078 

Materiel 

01656 

01026 

0.0844 

0.1306 

0 0674 

0.3044 

0.1026 

0.0844 

01899 

03837 

0.0518 

0.2729 

Mission Assurance 

0.3529 

0.2389 

0.202 

0.3329 

0.1858 

0.5453 

0.2389 

0.202 

03916 

0.631 

0.13O4 

05076 

Munitions 

0.3523 

0.2389 

0.202 

0.3929 

0.1658 

0.5453 

0.2383 

0.202 

0.3816 

0.631 

G.1304 

0.5078 

Ops Mgt 

0.2576 

0.1685 

0.1337 

0,2316 

0.1122 

0.4334 

0,1665 

0.1387 

0.2905 

0.5211 

0,0871 

0,3381 

Ops Planning 

0.4433 

03195 

02746 

0.4318 

0.2231 

0.6426 

0.3135 

0.2746 

O.4304 

0.7139 

0.1832 

06066 

Pilot 

0.335 

0.2731 

0.2325 


0.1921 

0.59 

0.2731 

0.2325 

0.4352 

0.6718 

0,1522 

0.5524 

PA 

0.5442 

0.4073 

0.3565 

0.5862 

0.3031 

0.7247 

0.4073 

0.3565 

0.5843 

0.7832 

0.2471 

0.893 

FSPA 

0.6036 

0.4871 

0.4141 

. 

0,3568 

0.7705 

04671 

0,4141 

0,6425 

0.8269 

0.2351 

07422 

S&T 

3E-08 

2E-08 

2E-08 

4E-08 

IE-08 

7E-06 

21-08 

2E-03 

4E-08| 

IE-07 

3E-03 

GE-OB 

Safely 

0.41SS 

0294 

02514 

0.4813 

0.2086 

0.6146 

0,294 

02514 

O.4606 

| 

0.1659 

05777 

SF 

3E03 

2E-0S 

2E-08 

4E 08 

IE 08 

7E08 

2E08 

2EC3 

4E 08l 

IE-07 

9E-09 

8E-0S 

Space/Muke/Missile C 

0.2576 

0.1665 

01337 

0.2916 

0,1*22 

0,4334 

01665 

0.1387 

02905 

0.5211 

0.0871 

0.3381 

Special Invest/ 

0335 

02731 

0.2325 

■ 

0.1921 

0.53 

0.2731 

0.2325 

0.4352 

0.6718 

0.1522 

05524 

leather 

0.4737 

0.3412 

0,2946 

. 

0.2469 

0.6648 

0.3412 

0.2946 

0.515 


0,1833 

0,6298 


Likelihood oft 100% manning 

x < 0.15 Low 
| 0.15 < x > 0.25 Mod. 
0.25 <x> 0.4 Sig 
1.0 < x > 0.4 High 


Figure 9: SCF and FE Likelihood being fully manned 2 


The results suggest none of the FEs by SCF are likely to be 100% manned or more. Notably, the Science & Technology 
(S&T) and Security Forces (SFs) FEs are highly likely to not be fully manned in any SCF or FE. Conversely, the 
commander or senior leader FEs has the potential in the Global Mobility (GM) and Personnel Recovery (PR) SCFs to 
have 100% or more manning. This is illustrated via the likelihood color palette scale in Figure 9. Arguably, rows (FEs) 
in red are highly less likely to be 100% or more manned. 


Model Results 


Figure 10 is a matrix of the modeling interpretations of the success/failure probabilities of the 375 observations. 
Probability of Success (( 1+e i 0 g it[n ( X ) ] )) is considered 100% or more manned or a green ‘Y\ otherwise a red ‘N’ in the 
matrix of cells. 


2 Cells without values indicate the FE was not represented in the SCF. 


9 















































Acquisition [ 

Airfield Operations [ 

C2 Systems Ops 

CIE 

Chapin nog 

Combat Systems (12X) | 

CCfSL 

Contracting 

Distribution 

Finance 

Force Support 

Health Services 

Historian 

Inspections j 

Intelligence 

Legal j 

Logistics Plans 

Maintenance 

Materiel 

Mission Assurance 

Munitions 

Ops Mqt 

Ops Planning 

Pilot ( 

p A 

FIP A 

S&T 

Safety | 

SF 

Sp a ce/Nuk e/Mis si] e Ops 1 

Special Invest/ | 

Weather | 



Figure 10: Likelihood of 100% manning in binary form 
The full joint model equation is listed in Appendix I. 

Odds Ratio Analyses 

The outcome variable is a success/fail response variable so Odds Ratios (ORs) via logistic transformations (logits) are 
computed and compared among SCFs and FEs. The logistic odds is represented as Logit[n(x)] = log(odds) = 

log = Po + + ••• P p X p where /? 0 is the intercept, /? p (the parameter) is the log OR of one unit increase in x 

whereas e (P) is the OR of one unit increase in x (Agresti, 2013). The ORs are computed from the joint model previously 

P P 

discussed. A total of 1,034 (12 2 + 32 2) ORs are computed and compared of which 45 (34%) and 160 (16%) are 

considered ‘statistically significantly different than one,’ respectively. These overview statistics suggest there are 
significant differences in full manning levels among SCFs and FEs. Figure 11 is a matrix of the SCF ORs accompanied 
with a scale to aid in interpretation. 


10 











































































ACS - Agile Combat Support 
AS -AirSuperiority 
C2 - Command & Control 
CS - Cyberspace Superiority 
GISR - Global ISR 
GM -Global Mobility 
GPA -Global Precision Attack 
NDO - Nuclear Deterrence Ops 
P &T-Personnel & Training 
PR - Personnel Recovery 
SO -Special Ops 
SS - Space Superiority 

SO SS 


ACS 
AS 
C2 
CS 

GISR 
GM 
GPA 
NDO 
P&T 
PR 
SO 
SS 

Relative Comparative Difference Scale 

x>6 High 
- 6 > x > 3 Sig 

■ 3 > x > 1 Mod 

■ 1 1 > x > 0 Low 


^ 1.737 

0.576 

^ 0.464 

1.186 

0.364 

2.204 

0.576 

0.464 

1.18 

3.135 

0.275 

1.89 

- 

0.806 

2.061 

0.633 

3.83 

1 

0.806 

2.05 

5.448 

0.478 

3.284 

2.155 

1.24 

- 

2.557 

0.785 

4.75 

1.24 

1 

2.543 

6.757 

0.592 

4.074 

0.843 

0.485 

0.391 

- 

0.307 

1.858 

0.485 

0.391 

0.995 

2.643 

0.232 

1.593 

2.745 

1.58 

1.274 

3.257 

- 

6.051 

1.58 

1.274 

3.239 

8.607 

0.755 

5.189 

0.454 

0.261 

0.211 

0.538 

0.165 

- 

0.261 

0.211 

0.535 

1.423 

0.125 

0.858 

1.737 

1 

0.806 

2.061 

0.633 

3.83 

- 

0.806 

2.05 

5.448 

0.478 

3.284 

2.155 

1.24 

1 

2.557 

0.785 

4.75 

1.24 

- 

2.543 

6.757 

0.592 

4.074 

0.847 

0.488 

0.393 

1.005 

0.309 

1.868 

0.488 

0.393 

- 

2.657 

0.233 

1.602 

0.319 

0.184 

0.148 

0.378 

0.116 

0.703 

0.184 

0.148 

0.376 

- 

0.088 

0.603 

3.638 

2.094 

1.688 

4.316 

1.325 

8.018 

2.094 

1.688 

4.292 

11.406 

- 

6.876 

0.529 

0.304 

0.245 

0.628 

0.193 

1.166 

0.304 

0.245 

0.624 

1.659 

0.145 



Interpretation of OR 



ACS 


AS 


CS 


GISR 


GM 


GPA 


NDO 


P&T 


PR 


Figure 11: SCF OR Comparison 


The matrix should be examined from left to right by row. For example, the Air Superiority (AS) SCF compared to the 
Agile Combat Support (ACS) SCF has 0.576, or low odds, of being fully manned. Conversely, ACS has 1.737 odds, or 
moderate odds, of being fully manned when compared to AS. The top 3 SCFs with better odds of full manning levels 
are Personnel Recovery, Global Mobility and Space Superiority. This is fairly intuitive as these rows are more green. 
The bottom 4 SCFs with lesser odds of full manning levels are Command & Control, Nuclear Deterrence Options, Global 
ISR and Special Operations. Further, the same matrix from Figure 11 overlaid with turquoise outlines is used in Figure 
12 to illustrate which SCF ORs are considered significantly different. Similar analysis is performed by FE. The FE 
results are listed in Appendices III and IV. 



ACS 

AS 

C2 

CS 

GISR 

GM 

GPA 

NDO 

P &T 

PR 

SO 

SS 

Comparisons 

Total OR 

ACS 

- 

0.576 

0.464 

1.186 

0.364 

2.204 

0.576 

0.464 

1.18 

3.135 

0.275 

1.89 

61 

12.314 

AS 

1.737 

- 

0.806 

2.061 

0.633 

3.83 

1 

0.806 

2.05 

5.448 

0.478 

3.284 

60 

22.133 

C2 

2.155 

1.24 

- 

2.557 

0.785 

4.75 

1.24 

1 

2.543 

6.757 

0.592 

4.074 

80 

27.693 

CS 

0.843 

0.485 

0.391 

- 

0.307 

1.858 

0.485 

0.391 

0.995 

2.643 

0.232 

1.593 

40 

10.223 

GISR 

2.745 

1.58 

1.274 

3.257 

- 

6.051 

1.58 

1.274 

3.239 

8,607 

0.755 

5.189 

100 

35.551 

GM 

0.454 | 

0.261 

0.211 

0.538 

0.165 

- 

0.261 

0.211 

0.535 

1.423 

0.125 

0.858 

10 

5.042 

GPA 

1.737 

1 

0.806 

2.061 

0.633 

3.83 

- 

0.806 

2.05 

5.448 

0.478 

3.284 

60 

22.133 

NDO 

2.155 

1.24 

1 

2.557 

0.785 

4.75 

1.24 

- 

2.543 

6,757 

0.592 

4.074 

SO 

27.693 

> &T 

0.847 

0.488 

0.393 

1.005 

0.309 

1.868 

0.488 

0.393 

- 

2.657 

0.233 

1.602 

30 

10.283 

PR 

0.319 

0.184 

0.148 

0.378 

0.116 

0.703 

0.184 

0.148 

0.376 

- 

0.088 

0.603 

0 

3.247 

SO 

3.638 

2.094 

1.688 

4.316 

1.325 

8.018 

2.094 

1.688 

4.292 

11.406 

- 

6,876 

110 

47.435 

SS 

0.529 

0.304 

0.245 

0.628 

0.193 

1.166 

0.304 

0.245 

0.624 

1.659 

0.145 

- 

20 

6,042 


Considered Statistically Different 


Figure 12: SCF OR Comparison with Significance Indicators 


11 




















































Figure 12’s results reveal the Global Mobility, Personnel Recovery and Space Superiority SCFs have statistically different 
manning levels as it relates to being fully manned or not. 

Relative Risk 

Relative risk ratios (RRR) which are comparative ratios of the probabilities of success (i.e. a given SCF and FE being 
fully manned) is another quantitative way to compare categories. As the number of categorical levels increases, the 
number of relative comparisons grows quite large. For example, 12 SCF and FE RRR one-way comparisons is 4,224 

P 

(12 2 combinations *32 FEs) possibilities. In this instance, we will only explore relative comparisons to the ACS SCF. 

The probabilities of success are taken from the joint model results depicted in Figure 9. If the RRR is equal to 1, we 
conclude independence or FEi with respect to a given SCF is neither more likely nor less likely of occurring than FE 2 with 
respect to the same SCF. If the RRR is less than 1, we conclude FEi with respect to a given SCF is less likely of 
occurring than FE 2 with respect to the same SCF. If the RRR is greater than 1, we conclude FEi with respect to a given 
SCF is more likely of occurring than FE 2 with respect to the same SCF. The RRRs are computed and shown in Figure 
13. 



ACS 

AS 

C2 

CS 

GISR 

GM 

GPA 

NDO | 

1 P&T 1 

PR | 

1 SO 

SS 

Acquisition 

1 

1.43 

1.67 

0.31 

2.01 

0.63 

1.43 

1.67 

0.31 

- 

2.53 

0.73 

Airfield Operations 

1.63 

1.55 

1.36 

0.33 

2.3 

0.53 

1.55 

1.36 

0.33 

0.43 

2.36 

0.65 

C2 Systems Ops 

1.13 

1.48 

1.75 

0.3 

2.13 

0.65 

1.43 

1.75 

0.3 

0.56 

2.71 

0.7 

CE 

1.13 

1.48 

1.75 

0.3 

2.13 

0.65 

1.43 

1.75 

0.3 

0.56 

2.71 

0.7 

Chaplaincy 

2.03 

1.53 

1.32 

0.33 

2.33 

0.57 

1.53 

1.32 

0.33 

- 

3.03 

0.63 

Combat Systems (12X) 

2 53 

1.62 

1.36 

0.37 

2.46 

0.54 

1.82 

1.36 

0.37 

0.43 

3.2 

0.61 

CC/SL 

0.53 

1.2 

1.32 

0.36 

1.43 

0.35 

1.2 

1.32 

0.36 

0.31 

1.73 

0.37 

Contracting 

0.33 

1.41 

1.64 

0.31 

1.38 

0.7 

1.41 

1.64 

0.32 

0.82 

2.45 

0.74 

Distribution 

0.33 

1.41 

1.64 

0.31 

1.38 

0.7 

1.41 

1.64 

0.32 

0.82 

2.45 

0.74 

Finance 

5.3 

1.68 

2.06 

0.36 

2.81 

0.5 

1.83 

2.06 

0.36 

0.37 

3.43 

0.57 

Force Support 

2.53 

1.62 

1.36 

0.37 

2.46 

0.54 

1.82 

1.36 

0.37 

0.43 

3.2 

0.61 

Health Services 

253 

1.62 

1.36 

0.37 

2.46 

0.54 

1.62 

1.36 

0.37 

0.43 

3.2 

0.61 

Historian 

1 

1.43 

1.67 

0.31 

2.01 

0.63 

1.43 

1.67 

0.31 

- 

2.53 

0.73 

Inspections 

5.3 

1.68 

2.06 

0.36 

2.61 

0.5 

1.63 

2.06 

0.36 

0.37 

3.43 

0.57 

Intelligence 

0.33 

1.41 

1.64 

0.31 

1.36 

0.7 

1.41 

1.64 

0.32 

0.62 

2.45 

0.74 

Legal 

2 53 

1.62 

1.36 

0.37 

2.46 

0.54 

1.82 

1.36 

0.37 

0.43 

3.2 

0.61 

Logistics Plans 

5.3 

1.68 

2.06 

0.36 

2.61 

0.5 

1.63 

2.06 

0.36 

0.37 

3.43 

0.57 

Maintenance 

1.13 

1.43 

1.75 

0.3 

2.13 

0.65 

1.43 

1.75 

0.3 

0.56 

2.71 

0.7 

Materiel 

2.53 

1.62 

1.36 

0.37 

2.46 

0.54 

1.82 

1.36 

0.37 

0.43 

3.2 

0.61 

Mission Assurance 

1.13 

1.48 

1.75 

0.3 

2.13 

0.65 

1.43 

1.75 

0.3 

0.56 

2.71 

0.7 

Munitions 

1.13 

1.43 

1.75 

0.3 

2.13 

0.65 

1.43 

1.75 

0.3 

0.56 

2.71 

0.7 

Ops Mgt 

1.63 

1.55 

1.36 

0.33 

2.3 

0.53 

1.55 

1.36 

0.33 

0.43 

2.36 

0.65 

Ops Planning 

0.33 

1.41 

1.64 

0.31 

1.36 

0.7 

1.41 

1.64 

0.32 

0.62 

2.45 

0.74 

Pilot 

1.06 

1.45 

1.7 

" 

2.06 

0.67 

1.45 

1.7 

0.31 

0.53 

2.6 

0.72 

PA 

0.77 

1.34 

1.53 

0.33 

1.3 

0.75 

1.34 

1.53 

0.33 

0.63 

2.2 

0.73 

RPA 

0.7 

1.23 

1.46 

_ 

1.63 

0.73 

1.23 

1.46 

0.34 

0.73 

2.05 

0.31 

S&T 

1E+07 

1.74 

2.16 

0.34 

2.75 

0.45 

1.74 

2.16 

0.35 

0.32 

3.64 

0.53 

Safety 

1 

1.43 

1.67 

0.31 

2.01 

0.83 

1.43 

1.67 

0.31 

- 

2.53 

0.73 

SF 

1E+07 

1.74 

2.16 

0.34 

2.75 

0.45 

1.74 

2.16 

0.35 

0.32 

3.64 

0.53 

Space/Nuke/Missile Ops 

1.63 

1.55 

1.36 

0.33 

2.3 

0.53 

1.55 

1.36 

0.33 

0.43 

2.36 

0.65 

Special Invest/ 

1.06 

1.45 

1.7 

- 

2.06 

0.67 

1.45 

1.7 

0.31 

0.53 

2.6 

0.72 

Weather 

0.33 

1.33 

1.61 

- 

1.32 

0.71 

1.33 

1.61 

0.32 

- 

2.33 

0.75 


Figure 13: SCF/FE Relative Risk Ratio table 


12 
























































In the ACS column of Figure 13, the Acquisition FE is held fixed compared to the other FEs within the ACS SCF. If we 
refer to the Airfield Operations and Acquisition FEs within the ACS SCF, we see a RRR of 1.63. The interpretation is 
within the ACS SCF, the Acquisition FE is 1.63 times likely of being 100% or more manned than Airfield Operations. 

For the rest of the columns (AS-SS), the RRRs are compared within each row or the FE is held fixed relative to the ACS 
SCF. For example, the 1.43 RRR at the intersection of the Acquisition FE and AS SCF, infers within the Acquisitions FE, 
the Air Combat Support SCF is 1.43 times likely of being 100% or more manned than the Air Superiority SCF. Similarly, 
at the intersection of the Acquisition FE and C2 SCF, infers within the Acquisitions FE, the Air Combat Support SCF is 
1.67 times likely of being 100% or more manned than the Command and Control SCF. A takeaway from Figure 13 is 
ACS has a relative moderate risk to the other SCFs with regards to being 100% or more manned. 

SCF and FE Prioritization 

Strategic Decision Makers need a concise way to prioritize SCF and FE manning groups. One way is to rank them by 
level of manning deficiencies. Computing the odds ratios from the logits and examining the odds between SCFs and FEs 
affords a quantitative opportunity to assess, compare and establish a ranking. There are several methods. 

The first ranking method is to compare the values of the ORs of a given SCF to all of the other SCF ORs in the 
population. For example, ACS’ ORs would be compared to the other 11 SCF ORs. We compare them by summing the 
count of all ACS ORs not greater than the other 11 SCF ORs. From the computed analysis, we know this value to be 61. 
This means out of the 121 possibilities for ACS ORs to be less than the other SCFs, ACS has lesser manning odds than 
about half of the other SCFs. We apply this technique across all SCFs and obtain a list ranked from least to greatest. The 
SCF with the greatest number of counts is ranked last. From Figure 12, Special Ops (SO) is ranked last and Personnel 
Recovery is ranked first. The same technique is applied to the FEs. 

The second ranking method is to simply compare the size or magnitude of the OR of a given SCF to all of the other SCF 
ORs in the population. We do this by summing the ORs of each SCF by row and obtain a list ranked from least to 
greatest. For example, the sum of the ACS’ ORs is 12.314. The SCFs with the greatest and least values are ranked last 
and first respectively. The same technique is applied to the FEs. 

The third ranking method takes into account the amount of shortages and overages of a given SCF or FE. Table 2 
provides a list the overages and shortages by SCF and FE. 


13 



Table 2: SCF and FE Overages and Shortages (-) 





□ug^Sht(-) 


Ovg/ShtH 

Acquisition 

Airfield Operations 

-573 

45 

ACS 

-32 

C2 Systems Ops 

747 

AS 

-2076 

CE 

-374 

C2 

-674 

Chaplaincy 

Combat Systems (12XJ 

-34 

-250 

CS 

-1136 

CC^SL 

105 

GISR 

-1363 

Contracting 

-31 



Distribution 

-333 

GM 

1519 

Finance 

3 

GPA 

-5320 

Force Support 

1725 

NDQ 

-1995 

Health Services 

373 



Historian 

-14 

P &T 

-1323 

Inspections 

-37 

PR 

23 

Intelligence 

-442 

SO 

-633 

Legal 

-311 

SS 

-11^6 

Logistics Flans 

-71 

Maintenance 

2133 



Materiel 

-461 



Mission Assurance 

220 



Munitions 

-1234 



Ops Mgt 

-41 



Ops Planning 

-476 



Pilot 

-373 



PA 

43 



RFA 

-134 



S6tT 

-550 



Safety 

44 



SF 

-1363 



SpaceHNuke^Missile Ops 

-73 



Special Invest^ 

-135 



Veather 

-41 


The overages/shortages are ranked from greatest to least. For example, the PR SCF is ranked first since it has the highest 
number of overages. Conversely, Global Precision Attack (GPA) is ranked last because it has the highest number of 
shortages. 

The issue with the first three methods is rank ties are common. A way to minimize rank ties is to apply a composition 
technique. The fourth method is a composite of the first three methods with some additional computations. The 
composite method involves three components; summing the first three methods’ rankings; computing a dampening factor 
which takes into account the actual manning rate; and computing a weight by accounting for the number of authorizations 
per SCF or FE. This method is called the composite value denoted by /? * co * r where /? = 1 + (1 — M) represents the 

i i* i jt * j i of auths per SCF or FE. . 

dampening factor which M is the manning rate; co = 1 + (-) and 

* ’ v Total auths y 

r = ^ ith Rank(j), where i = SCF or FE and j = 1,. .3. 

This procedure takes into account the size of the population (SCF or FE), population manning rate, population 
overage/shortage and population odds of being fully manned. The composite values are then ranked from least to 
greatest. Figure 14 shows the final ranked SCFs with regards to the least likely to be fully manned. 


14 



ACS - Agile Combat Support 
AS - Air Superiority 
C2 - Co mma nd & Control 
CS - Cyberspace Superiority 
GISR-Global ISR 
GM - Global Mobility 
GPA - Global Precision Attack 
NDO - Nuclear Deterrence Ops 
P & T- Personnel & Training 
PR - Personnel Recovery 
SO -Special Ops 
SS -Space Super' 

ACS 


ACS 

AS 

C2 

cs 

GISR 

GM 

GFA 

NDO 

P8T 

PR 

SO 

SS 


1.737 

2.155 

0.343 

2.745 

0.454 

1.737 

2.155 

0.847 

0.319 

3.638 

0.529 



Comp. 


M Dampen inn 

cu 

T 





Value 

Ovg/ShtH Manning 

Faaor 

Weight 

Total 





23.4647 

-32 

0 9993 

1.0002 

138 

17.00 





27,7906 

-2076 

0.8972 

1.1028 

1.05 

24.00 





23,80 

-674 

0.9671 

1.0329 

1.05 

22.00 





16.8770 

-1136 

0.9076 

1.0924 

1.03 

15.00 





33.6074 

-1363 

0.9331 

1.0669 

1.05 

30.00 





5.42472 

1519 

1.0313 

0.9687 

1.12 

5.00 





31,0992 

-5320 

0,9063 

1.0912 

1.14 

25,00 





32,0128 

1995 

0,9214 

1.0786 

106 

28.00 





20.5377 

-1826 

0.9236 

1.0764 

1.06 

18.00 





4.01738 

23 

1.0056 

0.9944 

101 

4.00 





31.7578 

-683 

0.9366 

1.0632 

103 

29.00 





14.5435 

-1146 

0.9243 

1.0757 

104 

13.00 




AS 

C2 

CS 

GISR GM 

GPA 

NDO P&T 

PR 

50 

SS 

RANK 

0.576 

0.464 

1.136 

0.364 2.204 

0.576 

0.464 1.18 

3.135 

0.275 

1.39 

6 

- 

0.806 

2.061 

0.633 3.83 

1 

0.806 2.05 

5.448 

0.478 

3.284 

3 

1.24 

- 

2.557 

0.785 4.75 

1.24 

1 2343 

6.757 

0.592 

4.074 

7 

0.485 

0.391 

- 

0.307 1.858 

0.485 

0.391 0.995 

2.643 

0.232 

1.593 

4 

1.58 

1.274 

3.257 

6.051 

1.58 

1.274 3.239 

8.607 

0.755 

5.189 

12 

0.261 

0.211 

0.538 

0,165 

0.261 

0.211 0.535 

1.423 

0.125 

0.853 

2 

1 

0.806 

2.061 

0,633 3.83 

- 

0.806 2.05 

5.448 

0.478 

3.284 

9 

1.24 

1 

2.557 

0785 4.75 

1.24 

- 2.543 

6.757 

0.592 

4.074 

11 

0.438 

0.393 

1.005 

0309 1.868 

0.483 

0.393 - 

2.657 

0.233 

1.602 

5 

0.184 

0.148 

0.378 

0116 0.703 

0.184 

0.148 0.376 

- 

0.088 

0.603 

1 

2.094 

1.688 

4.316 

1.325 8.018 

2,094 

1.688 4.292 

11.406 

■ 

6.876 

10 

0.304 

0.24S 

0.628 

0.193 1.166 

0.304 

0.245 0.624 

1.659 

0.145 

* 

3 


Figure 14: SCF Prioritization Technique 

Results from Figure 13 show the top 3 SCFs with lower odds of not being fully manned are Personnel Recovery, Global 
Mobility and Space Superiority. Conversely, the bottom 3 SCFs with higher odds of not being fully manned are Global 
ISR, Nuclear Deterrence Ops and Special Ops. A comparison of the ranking methods is listed in Table 3. 


15 



Table 3: Ranking methodology Comparison with respect to being not fully manned 



OR Comp. 

Sum OR 

Ovg/Sht 

Composite 


Rankl 

Rank2 

Rank3 

Rank4 

ACS 

S 

G 

3 

G 

AS 

6 

7 

11 

8 

C2 

9 

9 

4 

7 

CS 

5 

4 

G 

4 

GISR 

11 

11 

8 

12 

GM 

2 

2 

1 

2 

GPA 

6 

7 

12 

9 

NDO 

9 

9 

10 

11 

P &T 

4 

5 

9 

5 

PR 

1 

1 

2 

1 

SO 

12 

12 

5 

10 

SS 

3 

3 

7 

3 


Final Remarks 

This research presents an alternative method of assessing USAF manning by SCF and FE by using logistic regression 
functions and contingency analyses. Statistically, there is an association between SCFs or FEs and full manning levels. 
Manning relationships among CFLs or FEs can be rigorously prioritized by OR comparisons. Further, this research can 
inform Strategic Decision Makers of manning capability gaps and substantiate advocacy for more resources to meet 
combat and peacetime requirements. There are no SCFs fully manned in the USAF. Overall, across the USAF, 
‘commanders or senior leaders’ is the only FE of 32 likely to be fully manned. This methodology enables senior decision 
makers to better qualify risk and enhance the strategic planning & programming process risk assessment, which enables 
the CSAF to better substantiate and advocate for personnel resources. 


16 






















References 


Agresti, Alan (2013). Categorical Data Analysis (3rd ed.). p. 119-122. Hoboken, New Jersey: John Wiley & Sons, Inc. 

NAP of Science, Eng. & Medicine. (2014). “Development Planning: A Strategic Approach to Future Air Force 
Capabilities” https://www.nap.edu/read/18971/chapter74. Accessed Feb 2017 


-There are no DOIs associated with these references. 


17 



Appendix I. (Joint Model) 


2.00205380064806 + Matchf. SCF, 

"ACS", -0.169625541949248, "AS", 0.382773594328361, "C2", 0.598187339531182, "CS", -0.340458443926399, 
"GISR", 0.840216482139152, "GM", -0.959983538960857, "GPA", 0.382773594328361, 

"NDO", 0.598187339531182, 

"P & T", -0.335101203204821, "PR", —1.3124077302221, "SO", 1.1217617567933, "SS", -0.806323648388117) + 
Match (= Functional Equity, 

"Acquisition", — 1.50895901227517, “Airfield Operations", —0.774050445307, "C2 Systems Ops", 
-1.22630715465715, "CE", -1.22630715465715, "Chaplaincy", -0.485653424612526, "Combat Systems (12 X)", 
-0.215625028117114, "Commander/SrLeaded', -2.78780240085377, "Contracting", -1.6287434114286, 
"Distribution", — 1.6287434114286, "Finance", 0.620987265633101, "Force Support", -0.215625028117114, 
"Health Services", -0.215625028117114, "Historian", -1.50895901227517, "Inspections", 0.620987265633101, 
"Intelligence", — 1.6287434114286, "Legal", -0.215625028117114, "Logistics Plans", 0.620987265633102, 
"Maintenance", — 1.22630715465715, "Materiel", —0.215625028117114, "Mission Assurance", 
-1.22630715465715, "Munitions", -1.22630715465715, "Ops Mpt", -0.774050445307, "Ops Planning", 
-1.6287434114286, "PA", -2.00975916866181, "Pilot", -1.40608660852006, "RPA", -2.25311850963814, 
"S&r", 15.3930762469828, "Safety", -1.50895901227517, "SF", 15.3930762472812, 

"Space/Nuke/Missile Ops", —0.774050445307, "Special Invest. ", —1.40608660852006, 

"Weather", -1.72694463802467). 


18 



Appendix II. (SCF and FE Assigned Manning levels by Demographic) 



Appendix Figure 1 


FE Assigned by Demographic 

^ %of Total(Sum of Assgncnl) & 2 more vs. Function 

40% 



I % of Tot*l($um of AwgnenQ 
1 % of ToUl(Som of Awgnoff) 
1 % of ToUl[Sum of Assent rv) 


% of Total = 


Sum of Assigned of Demographic Functional Area 
Total Assigned of Functional Area 


Appendix Figure 2 


19 























Appendix III. FE Manning OR Analyses 


Rank 


Acq lirfld 0[j2 Sys 0| 

CE | Chap. | Nays 

raSL| Contr. 

□ist. 

Fin. 

Dree Sujealth Srj 

Hist. 

Insp. 

| Intel. | 

le 

LG PlanJ 

Mk | 

| Mat'l | 

[isnAs^ Muns |Dps Mg|)ps Plar| Pilot | 

PA | 

RPA | 

S&T 

1 SE I 

SF 

le/NukeJ 

SI | 

Vk 

19 

Acq 


0.48 

0.754 

0.754 

0.359 

0.274 

3.582 

1.127 

1.127 

0.119 

0.274 

0.274 

1 

0.118 

1.127 

0.274 

0.118 

0.754 

0.274 

0.754 

0.754 

0.43 

1.127 

0.802 

1.65 

2.105 

0 

1 

0 

0.43 

0.902 

1.244 

14 

Airfld Ops 

2.085 


1.572 

1.572 

0.748 

0.572 

7.481 

2.351 

2.351 

0.248 

0.572 

0.572 

2.085 

0.248 

2.351 

0.572 

0.248 

1.572 

0.572 

1.572 

1.572 

1 

2.351 

1.831 

3.441 

4.338 

0 

2.035 

0 

1 

1.331 

2.583 

7 

C2 Sys Ops 

1.327 

0.64 


1 

0.477 

0.364 

4.766 

1.485 

1.485 

0.158 

0.364 

0.364 

1.327 

0.153 

1.485 

0.364 

0.153 

1 

0.364 

1 

1 

0.636 

1.485 

1.187 

2.138 

2.782 

0 

1.327 

0 

0.636 

1.187 

1.65 

21 

CE 

1.327 

0.64 

1 


0.477 

0.364 

4.766 

1.485 

1.485 

0.158 

0.364 

0.364 

1.327 

0.153 

1.485 

0.364 

0.153 

1 

0.364 

1 

1 

0.636 

1.485 

1.187 

2.138 

2.782 

0 

1.327 

0 

0.636 

1.187 

1.65 

25 

Chap. 

2.782 

1.33 

2.087 

2.087 

- 

0.763 

8.886 

3.136 

3.136 

0.331 

0.763 

0.763 

2.782 

0.331 

3.136 

0.763 

0.331 

2.087 

0.763 

2.087 

2.087 

1.334 

3.136 

2.51 

4.581 

5.356 

0 

2.732 

0 

1.334 

2.51 

3.46 

26 

Navs 

3.645 

1.75 

2.747 

2.747 

1.31 


13.08 

4.108 

4.108 

0.433 

1 

1 

3.645 

0.433 

4.108 

1 

0.433 

2.747 

1 

2.747 

2.747 

1.743 

4.108 

3.238 

6.014 

7.671 

0 

3.645 

0 

1.743 

3.238 

4.533 

1 

CC^SL 

0.278 

0.13 

0.21 

0.21 

0.1 

0.076 

■ 

0.314 

0.314 

0.033 

0.076 

0.076 

0.278 

0.033 

0.314 

0.076 

0.033 

0.21 

0.076 

0.21 

0.21 

0.133 

0.314 

0.251 

0.458 

0.536 

0 

0.273 

0 

0.133 

0.251 

0.346 

4 

Contr. 

0.887 

0.43 

0.668 

0.668 

0.318 

0.243 

3.187 - 1 

0.105 

0.243 

0.243 

0.387 

0.105 

1 

0.243 

0.105 

0.668 

0.243 

0.668 

0.668 

0.425 

1 

0.3 

1.464 

1.367 

0 

0.337 

0 

0.425 

0.3 

1.103 

13 

□ist. 

0.887 

0.43 

0.668 

0.668 

0.318 

0.243 

3.187 

1 


0.105 

0.243 

0.243 

0.337 

0.105 

1 

0.243 

0.105 

0.668 

0.243 

0.668 

0.668 

0.425 

1 

0.3 

1.464 

1.367 

0 

0.337 

0 

0.425 

0.3 

1.103 

24 

Fin. 

8.414 

4.04 

6.343 

6.343 

3.024 

2.308 

30.23 

8.485 

8.485 


2.308 

2.308 

3.414 

1 

8.435 

2.308 

1 

6.343 

2.308 

6.343 

6.343 

4.035 

8.435 

7.582 

13.83 

17.71 

0 

3.414 

0 

4.035 

7.582 

10.46 

17 

Force Supt 

3.645 

1.75 

2.747 

2.747 

1.31 

1 

13.08 

4.108 

4.108 

0.433 

1 

3.645 

0.433 

4.108 

1 

0.433 

2.747 

1 

2.747 

2.747 

1.743 

4.108 

3.238 

6.014 

7.671 

0 

3.645 

0 

1.743 

3.238 

4.533 

18 

Health Srus 

3.645 

1.75 

2.747 

2.747 

1.31 

1 

13.08 

4.108 

4.108 

0.433 

1 


3.645 

0.433 

4.108 

1 

0.433 

2.747 

1 

2.747 

2.747 

1.743 

4.108 

3.238 

6.014 

7.671 

0 

3.645 

0 

1.743 

3.238 

4.533 

8 

Hist. 

1 

0.48 

0.754 

0.754 

0.358 

0.274 

3.582 

1.127 

1.127 

0.118 

0.274 

0.274 


0.118 

1.127 

0.274 

0.118 

0.754 

0.274 

0.754 

0.754 

0.43 

1.127 

0.802 

1.65 

2.105 

0 

1 

0 

0.43 

0.802 

1.244 

30 

Insp. 

8.414 

4.04 

6.343 

6.343 

3.024 

2.308 

30.23 

8.485 

8.485 

1 

2.308 

2.308 

3.414 


8.435 

2.308 

1 

6.343 

2.308 

6.343 

6.343 

4.035 

8.435 

7.582 

13.33 

17.71 

0 

3.414 

0 

4.035 

7.582 

10.46 

11 

Intel. 

0.887 

0.43 

0.668 

0.668 

0.318 

0.243 

3.187 

1 

1 

0.105 

0.243 

0.243 

0.337 

0.105 


0.243 

0.105 

0.668 

0.243 

0.668 

0.668 

0.425 

1 

0.3 

1.464 

1.367 

0 

0.337 

0 

0.425 

0.3 

1.103 

28 

LE 

3.645 

1.75 

2.747 

2.747 

1.31 

1 

13.08 

4.108 

4.108 

0.433 

1 

1 

3.645 

0.433 

4.108 


0.433 

2.747 

1 

2.747 

2.747 

1.743 

4.108 

3.238 

6.014 

7.671 

0 

3.645 

0 

1.743 

3.238 

4.533 

27 

LG Plans 

8.414 

4.04 

6.343 

6.343 

3.024 

2.308 

30.23 

8.485 

8.485 

1 

2.308 

2.308 

3.414 

1 

8.435 

2.308 


6.343 

2.308 

6.343 

6.343 

4.035 

8.435 

7.582 

13.33 

17.71 

0 

3.414 

0 

4.035 

7.582 

10.46 

8 

Mh 

1.327 

0.64 

1 

1 

0.477 

0.364 

4.766 

1.485 

1.485 

0.158 

0.364 

0.364 

1.327 

0.153 

1.485 

0.364 

0.153 

- 

0.364 

1 

1 

0.636 

1.485 

1.187 

2.138 

2.782 

0 

1.327 

0 

0.636 

1.187 

1.65 

28 

Mafl 

3.645 

1.75 

2.747 

2.747 

1.31 

1 

13.08 

4.108 

4.108 

0.433 

1 

1 

3.645 

0.433 

4.108 

1 

0.433 

2.747 


2.747 

2.747 

1.743 

4.108 

3.238 

6.014 

7.671 

0 

3.645 

0 

1.743 

3.238 

4.533 

10 

Msn Assr. 

1.327 

0.64 

1 

1 

0.477 

0.364 

4.766 

1.485 

1.485 

0.158 

0.364 

0.364 

1.327 

0.153 

1.485 

0.364 

0.153 

1 

0.364 

■ 

1 

0.636 

1.485 

1.187 

2.138 

2.782 

0 

1.327 

0 

0.636 

1.187 

1.65 

23 

Muns 

1.327 

0.64 

1 

1 

0.477 

0.364 

4.766 

1.485 

1.485 

0.158 

0.364 

0.364 

1.327 

0.153 

1.485 

0.364 

0.153 

1 

0.364 

1 


0.636 

1.485 

1.187 

2.138 

2.782 

0 

1.327 

0 

0.636 

1.187 

1.65 

20 

Ops Mgt 

2.085 

1 

1.572 

1.572 

0.749 

0.572 

7.491 

2.351 

2.351 

0.248 

0.572 

0.572 

2.035 

0.243 

2.351 

0.572 

0.243 

1.572 

0.572 

1.572 

1.572 


2.351 

1.331 

3.441 

4.338 

0 

2.035 

0 

1 

1.331 

2.583 

12 

Ops Plans 

0.887 

0.43 

0.668 

0.668 

0.318 

0.243 

3.187 

1 

1 

0.105 

0.243 

0.243 

0.887 

0.105 

1 

0.243 

0.105 

0.668 

0.243 

0.668 

0.668 

0.425 


0.3 

1.464 

1.367 

0 

0.337 

0 

0.425 

0.3 

1.103 

15 

Pilot 

1.108 

0.53 

0.835 

0.835 

0.388 

0.304 

3.882 

1.248 

1.248 

0.132 

0.304 

0.304 

1.103 

0.132 

1.248 

0.304 

0.132 

0.335 

0.304 

0.335 

0.335 

0.532 

1.248 


1.328 

2.333 

0 

1.103 

0 

0.532 

1 

1.373 

2 

PA 

0.606 

0.28 

0.457 

0.457 

0.218 

0.166 

2.177 

0.683 

0.683 

0.072 

0.166 

0.166 

0.606 

0.072 

0.633 

0.166 

0.072 

0.457 

0.166 

0.457 

0.457 

0.281 

0.633 

0.547 

1.276 

0 

0.606 

0 

0.281 

0.547 

0.754 

5 

RPA 

0.475 

0.23 

0.358 

0.358 

0.171 

0.13 

1.707 

0.536 

0.536 

0.056 

0.13 

0.13 

0.475 

0.056 

0.536 

0.13 

0.056 

0.353 

0.13 

0.353 

0.353 

0.223 

0.536 

0.428 

0.734 


0 

0.475 

0 

0.228 

0.428 

0.581 

31 

S&T 

2E+07 

1E+07 

2E+07 

2E+07 

8E+06 

6E+06 8E+07 

2E+07 

2E+07 

3E+06 

6E+06 

6E+06 

2E+07 

3E+06 

2E+07 

6E+06 

3E+06 

2E+07 

6E+06 

2E+07 

2E+07 

1E+07 

2E+07 

2E+07 

4E+07 

5E+07 

- 

2E+07 

1 

1E+07 

2E+07 

3E+07 

6 

SE 

1 

0.48 

0.754 

0.754 

0.358 

0.274 

3.582 

1.127 

1.127 

0.118 

0.274 

0.274 

1 

0.118 

1.127 

0.274 

0.118 

0.754 

0.274 

0.754 

0.754 

0.43 

1.127 

0.802 

1.65 

2.105 

0 


0 

0.43 

0.802 

1.244 

32 

SF 

2E+07 

1E+07 

2E+07 

2E+07 

8E+06 

6E+06 

8E+07 2E+07 

2E+07 

3E+06 

6E+06 

6E+06 

2E+07 

3E+06 

2E+07 

6E+06 

3E+06 

2E+07 

6E+06 

2E+07 

2E+07 

1E+07 

2E+07 

2E+07 

4E+07 

5E+07 

1 

2E+07 


1E+07 

2E+07 

3E+07 

22 

Space^Nuke^M.O. 

2.085 

1 

1.572 

1.572 

0.748 

0.572 

7.481 

2.351 

2.351 

0.248 

0.572 

0.572 

2.035 

0.243 

2.351 

0.572 

0.243 

1.572 

0.572 

1.572 

1.572 

1 

2.351 

1.331 

3.441 

4.338 

0 

2.035 

0 


1.331 

2.583 

16 

SI 

1.108 

0.53 

0.835 

0.835 

0.388 

0.304 

3.882 

1.248 

1.248 

0.132 

0.304 

0.304 

1.103 

0.132 

1.248 

0.304 

0.132 

0.335 

0.304 

0.335 

0.335 

0.532 

1.248 

1 

1.328 

2.333 

0 

1.103 

0 

0.532 

■ 

1.373 

3 

Vk 

0.804 

0.38 

0.606 

0.606 

0.288 

0.221 

2.888 

0.806 

0.806 

0.086 

0.221 

0.221 

0.304 

0.086 

0.806 

0.221 

0.086 

0.606 

0.221 

0.606 

0.606 

0.386 

0.806 

0.726 

1.327 

1.682 

0 

0.304 

0 

0.336 

0.726 



FE odds of not being fully manned 



x>1000 High 
1000 > x > 100 Sig 
100 > x > 1 Mod 
1 > x > 0 Low 


Appendix Figure 3 


20 





























































Appendix IV. FE Significant Difference in Manning OR Analyses 



Acq lirfld Orf2 Sys Oj 

CE 

| Chap. | 

Naus 

ICC/SLl 

Contr. 

□ist. 

Fin. 

Dree Sule-alth Srj 

Hist. 

Insp. | 

| Intel. | 

LE 

LG Plan) 

| Mk | 

| Mafl I 

[isn As^ 

Muns pps Mg[)ps Plar| 

Pilot | 

PA | 

RPA 

1 S&T 1 

1 SE 1 

1 SF 1 

eiT.JukeJ 

SI | 

Wk 

Acq 


0.40 

0.754 

0.754 

0.359 

0.274 

3.592 

1.127 

1.127 

0.119 

0.274 

0.274 

1 

0.119 

1.127 

0.274 

0.119 

0.754 

0.274 

0.754 

0.754 

0.46 

1.127 

0.902 

1.65 

2.105 

0 

1 

0 

0.4@ 

0.902 

1.244 

Airfld Ops 

2.035 


1.572 

1.572 

0.749 

0.572 

7.491 

2.351 

2.351 

0.249 

0.572 

0.572 

2.005 

0.249 

2.351 

0.572 

0.249 

1.572 

0.572 

1.572 

1.572 

1 

2.351 

1.001 

3.441 

4.399 

0 

2.005 

0 

1 

1.001 

2.593 

C2 Sys Ops 

1.327 

0.64 


1 

0.477 

0.364 

4.766 

1.495 

1.495 

0.150 

0.364 

0.364 

1.327 

0.150 

1.495 

0.364 

0.150 

1 

0.364 

1 

1 

0.636 

1.495 

1.197 

2.109 

2.792 

non 

1.327 

0 

0.636 

1.197 

1.65 

CE 

1.327 

0.64 

1 


0.477 

0.364 

4.766 

1.495 

1.495 

0.150 

0.364 

0.364 

1.327 

0.150 

1.495 

0.364 

0.150 

1 

0.364 

1 

1 

0.636 

1.495 

1.197 

2.109 

2.792 

0 

1.327 

0 

0.636 

1.197 

1.65 

Chap. 

2.702 

1.33 

2.097 

2.097 


0.763 

9.996 

3.136 

3.136 

0.331 

0.763 

0.763 

2.702 

0.331 

3.136 

0.763 

0.331 

2.097 

0.763 

2.097 

2.097 

1.334 

3.136 

2.51 

4.591 

5.956 

0 

2.702 

0 

1.334 

2.51 

3.46 

Naus 

3.645 

1.75 

2.747 

2.747 

1.31 


13.09 

4.109 

4.109 

0.433 

1 

1 

3.645 

0.433 

4.109 

1 

0.433 

2.747 

1 

2.747 

2.747 

1.746 

4.109 

3.299 

6.014 

7.671 

0 

3.645 

0 

1.746 

3.299 

4.533 

CC/SL 

0.270 

0.13 

0.21 

0.21 

0.1 

0.076 

- 

0.314 

0.314 

0.033 

0.076 

0.076 

0.276 

0.033 

0.314 

0.076 

0.033 

0.21 

0.076 

0.21 

0.21 

0.133 

0.314 

0.251 

0.459 

0.566 

rol 

0.276 

0 

0.133 

0.251 

0.346 

Contr. 

0.007 

0.43 

0.669 

0.669 

0.319 

0.243 

3.197 


1 

0.105 

0.243 

0.243 

0.007 

0.105 

1 

0.243 

0.105 

0.669 

0.243 

0.669 

0.669 

0.425 

1 

0.0 

1.464 

1.067 

0 

0.007 

0 

0.425 

0.0 

1.103 

□ist. 

0.007 

0.43 

0.669 

0.669 

0.319 

0.243 

3.107 

1 


0.105 

0.243 

0.243 

0.007 

0.105 

1 

0.243 

0.105 

0.669 

0.243 

0.669 

0.669 

0.425 

1 

0.0 

1.464 

1.067 

0 

0.007 

0 

0.425 

0.0 

1.103 

Fin. 

0.414 

4.04 

6.343 

6.343 

3.024 

2.309 

30.23 

9.495 

9.465 


2.309 

2.309 

0.414 

1 

9.495 

2.309 

1 

6.343 

2.309 

6.343 

6.343 

4.035 

9.465 

7.592 

13.00 

17.71 

0 

0.414 

0 

4.035 

7.592 

10.46 

Force Supt 

3.645 

1.75 

2.747 

2.747 

1.31 

1 

13.09 

4.109 

4.109 

0.433 


1 

3.645 

0.433 

4.109 

1 

0.433 

2.747 

1 

2.747 

2.747 

1.743 

4.109 

3.299 

6.014 

7.671 

0 

3.645 

0 

1.743 

3.299 

4.533 

Health Srus 

3.645 

1.75 

2.747 

2.747 

1.31 

1 

13.09 

4.109 

4.109 

0.433 

1 


3.645 

0.433 

4.109 

1 

0.433 

2.747 

1 

2.747 

2.747 

1.740 

4.109 

3.299 

6.014 

7.671 

0 

3.645 

0 

1.740 

3.299 

4.533 

Hist. 

1 

0.40 

0.754 

0.754 

0.359 

0.274 

3.592 

1.127 

1.127 

0.119 

0.274 

0.274 

■ 

0.119 

1.127 

0.274 0.119 

0.754 

0.274 

0.754 

0.754 

0.40 

1.127 

0.902 

1.65 

2.105 

0 

1 

0 

0.40 

0.902 

1.244 

Insp. 

0.414 

4.04 

6.343 

6.343 

3.024 

2.309 

30.23 

9.495 

9.495 

1 

2.309 

2.309 

0.414 


9.495 

2.309 

1 

6.343 

2.309 

6.343 

6.343 

4.035 

9.495 

7.592 

13.00 

17.71 

0 

0.414 

0 

4.035 

7.592 

10.46 

Intel. 

0.007 

0.43 

0.669 

0.669 

0.319 

0.243 

3.107 

1 

1 0.105 

0.243 

0.243 

0.007 

0.105 

1 - 

0.243 0.105 

0.669 

0.243 

0.669 

0.669 

0.425 

1 

0.0 

1.464 

1.067 

0 

0.007 

0 

0.425 

0.0 

1.103 

LE 

3.645 

1.75 

2.747 

2.747 

1.31 

1 

13.09 

4.109 

4.109 

0.433 

1 

1 

3.645 

0.433 

4.109 


0.433 

2.747 

1 

2.747 

2.747 

1.740 

4.109 

3.209 

6.014 

7.671 

0 

3.645 

0 

1.740 

3.209 

4.533 

LG Plans 

6.414 

4.04 

6.343 

6.343 

3.024 

2.309 

30.23 

9.495 

9.495 

1 

2.309 

2.309 

0.414 

1 

9.495 

2.309 


6.343 

2.309 

6.343 

6.343 

4.035 

9.495 

7.592 

13.06 

17.71 

0 

0.414 

0 

4.035 

7.592 

10.46 

Mh 

1.327 

0.64 

1 

1 

0.477 

0.364 

4.766 

1.495 

1.495 

0.150 

0.364 

0.364 

1.327 

0.150 

1.495 

0.364 

0.150 


0.364 

1 

1 

0.636 

1.495 

1.197 

2.109 

2.792 

rol 

1.327 

0 

0.636 

1.197 

1.65 

Mat'l 

3.645 

1.75 

2.747 

2.747 

1.31 

1 

13.09 

4.109 

4.109 

0.433 

1 

1 

3.645 

0.433 

4.109 

1 

0.433 

2.747 


2.747 

2.747 

1.746 

4.109 

3.299 

6.014 

7.671 

0 

3.645 

0 

1.746 

3.299 

4.533 

Msn Assr. 

1.327 

0.64 

1 

1 

0.477 

0.364 

4.766 

1.495 

1.495 

0.150 

0.364 

0.364 

1.327 

0.150 

1.495 

0.364 

0.150 

1 

0.364 


1 

0.636 

1.495 

1.197 

2.199 

2.792 

0 

1.327 

0 

0.636 

1.197 

1.65 

Muns 

1.327 

0.64 

1 

1 

0.477 

0.364 

4.766 

1.495 

1.495 

0.150 

0.364 

0.364 

1.327 

0.150 

1.495 

0.364 

0.150 

1 

0.364 

1 


0.636 

1.495 

1.197 

2.199 

2.792 

0 

1.327 

0 

0.636 

1.197 

1.65 

Ops Mqt 

2.065 

1 

1.572 

1.572 

0.749 

0.572 

7.491 

2.351 

2.351 

0.240 

0.572 

0.572 

2.005 

0.240 

2.351 

0.572 

0.240 

1.572 

0.572 

1.572 

1.572 


2.351 

1.001 

3.441 

4.399 

0 

2.005 

0 

1 

1.001 

2.593 

Ops Plans 

0.007 

0.43 

0.669 

0.669 

0.319 

0.243 

3.197 

1 

1 

0.105 

0.243 

0.243 

0.007 

0.105 

1 

0.243 

0.105 

0.669 

0.243 

0.669 

0.669 

0.425 


0.0 

1.464 

1.967 

0 

0.007 

0 

0.425 

0.0 

1.103 

Pilot 

1.100 

0.53 

0.035 

0.035 

0.390 

0.304 

3.902 

1.249 

1.249 

0.132 

0.304 

0.304 

1.100 

0.132 

1.249 

0.304 

0.132 

0.035 

0.304 

0.035 

0.035 

0.532 

1.249 


1.029 

2.333 

0 

1.100 

0 

0.532 

1 

1.370 

PA 

0.606 

0.29 

0.457 

0.457 

0.210 

0.166 

2.177 

0.603 

0.603 

0.072 

0.166 

0.166 

0.606 

0.072 

0.603 

0.166 

0.072 

0.457 

0.166 

0.457 

0.457 

0.291 

0.603 

0.547 


1.276 

0 

0.606 

0 

0.291 

0.547 

0.754 

RPA 

0.475 

0.23 

0.350 

0.350 

0.171 

0.13 

1.707 

0.536 

0.536 

0.056 

0.13 

0.13 

0.475 

0.056 

0.536 

0.13 

0.056 

0.350 

0.13 

0.350 

0.353 

0.226 

0.536 

0.429 

0.794 


0 

0.475 

0 

0.229 

0.429 

0.591 

S&T 

2E+07 

1E+07 2E+07 2E+07 6E*06 

6E+06 0E+O7 2E+07 2E+07 

3E+06 

6E+06 

6E+06 

2E+07 

3E+06 

2E+07 

6E+06 

3E+06 

2E+07 

6E+06 

2E+07 2E+07 

1E+07 

2E+07 2E+07 4E+07 

5E+07 


2E+07 

1 

1E+07 2E+07 

3E+07 

SE 

1 

0.46 

0.754 

0.754 

0.359 

0.274 

3.592 

1.127 

1.127 

0.119 

0.274 

0.274 

1 

0.119 

1.127 

0.274 

0.119 

0.754 

0.274 

0.754 

0.754 

0.40 

1.127 

0.902 

1.65 

2.105 

0 


0 

0.40 

0.902 

1.244 

SF 

2E+07 

1E+07 2E+07 2E+07 0E*O6 6E+06 0E+O7 2E + 07 2E+07 

3E+06 

6E+06 6E+06 2E+07 

3E+06 

2E+07 6E+06 

3E+06 

2E+07 6E+06 2E+07 2E+07 1E+07 2E+07 2E*07 4E+07 5E + 07 

1 

2E+07 


1E+07 2E+07 

3E+07 

Space^Nuke^M.O. 

2.065 

1 

1.572 

1.572 

0.749 

0.572 

7.491 

2.351 

2.351 

0.249 

0.572 

0.572 

2.065 

0.249 

2.351 

0.572 

0.249 

1.572 

0.572 

1.572 

1.572 

1 

2.351 

1.001 

3.441 

4.369 

0 

2.065 

0 


1.001 

2.593 

SI 

1.100 

0.53 

0.035 

0.035 

0.399 

0.304 

3.992 

1.249 

1.249 

0.132 

0.304 

0.304 

1.100 

0.132 

1.249 

0.304 

0.132 

0.035 

0.304 

0.035 

0.035 

0.532 

1.249 

1 

1.629 

2.333 

0 

1.100 

0 

0.532 


1.370 

Wk 

0.004 

0.39 

0.606 

0.606 

0.209 

0.221 

2.009 

0.906 

0.906 

0.096 

0.221 

0.221 

0.004 

0.096 

0.906 

0.221 

0.096 

0.606 

0.221 

0.606 

0.606 

0.306 

0.906 

0.726 

1.327 

1.692 

n o j 

0.004 

0 

0.306 

0.726 



Appendix Figure 4 


Considered statistically 
different 


21