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TRANSCRIPT
NAVAL POSTGRADUATE SCHOOLv
Monterey, Califolrna C) /
THESISANALYSIS OF U.S. NAVY AIRCRAFT
ACCIDENT RATES IN MAJOR AVIATION COMMANDS
by
Lawrence Charles Bucher
September 1976
Thesis Advisor: G. K. Poock
Approved for public release; distribution unlimited.
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9. PRmOmuFWIN ORGANIZATION NARE AND ADDRSS AAP NSwwmNaval Postgi'aduate School kAa ! ' T"1UwtMonterey, California 93940
11. CONTROLLING OFFICE NAME AND ADDRESS JLaffama nAIL...-
Naval Postgraduate School 1076Monterey, California 93940 _____________
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Naval Postgraduate School UnclassifiedMonterey, California 93940 ,* ~&~iC~~I@NRON
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**Approved for public release; stribution unlimited.
17. OISTRIOUTION STATE[MENT (of M 08oh. abetedM slaoo n l ItW If Eftm u11000)
IS. SUPPLONENTARY MOTIES
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X~imedep3ndent variable measures were obtained for allmajor aircraft accidents between July 1971 and July 1974.Using these time dependent variables and functional formsof these variables, a regression analysis was performed foreach of eight major aviation commands. By using thesefunctional forms of the variables, a relatively high amountof variance in aircraft accident rate was accounted for at
DO ,JAIN,1473 EIINO O6 SOSLT P5~ i/~'2(Page 1) SIX 0102-034-11"01 SECURITY CLASSIFICATION OF TWIS PAGE[ (Us..Dal
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a high confidence level in some commands. When reviewingthe results of the eight major commands considered, it wasparticularly noted that the variables most instrumentalin explaining the variance in aircraft accident rate werenot all pilot oriented but were variables interpreted as4 being related either to pilot experience level, pilotproficiency or aircraft cniin
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DD Form 14731 Jan 43SCCUmI?" CLASSIFICATION OF THIS P&@3tWhs 04NO IRtsIE)SI 102014660
* Analysis of U.*S. Navy AircraftAccident Rates in Major Aviation Commands
by
Lawrence Charles BucherLieutenant Commander, United States Navy
B.S.E.E., Purdue University, 1966
_ - ubmitted in partial fulfillment of -the
requirements for the degree of
MASTER OF SCIENCE IN OPERATIONS RESEARCH
from the
NAVAL POSTGRADUATE SCHOOLSeptember-1976
Auth or
Approved by:Tesis dvisor
econd Reader
Ctirman, Department of perations .esigrc
ABSTRACT
Time dependent variable neasures were obtained for all
major aircraft accidents between July 1971 and July 1974.
Using these time dependent variables and functional forms
of these variables, a regression analysis was performed
for each of eight major aviation commands. By using these
functional forms of the variables, a relatively high amount
of variance in aircraft accident rate was accounted for at
a high confidence level in some commands. When reviewing
the results of the eight major commands considered, it was
particularly noted that the variables most instrumental
in explaining the variance in aircraft accident rate were
not all pilot oriented but were variables interpreted as
being related either to pilot experience level, pilot
proficiency or aircraft condition.
Ii
TABLE OF CONTNTS
I. IM UTO1NCTION -- eeeeee---------------------------- 7
II. PROBLEM DEFINITION ------------------------------ 11
III. ANALYTICAL PROCEDURES ---------------------------- 13
A. DATA SOURCE ---------------------------------- 13
B. DATA SELECTION ........- -------------------- 13
C. PRELIMINARY DATA PREPARATION ------------------ 17
D. THE ANALYSIS TECHNIQUE ---------------------- 18
IV, RESULTS ------------------------------------------ 23
A, COMNAVAIRLANT --------------------- 23
B, MARLANT -------------------------------------- 26
C. COMNAVAIRPAC --------------------------------- 30
D. MARPAC eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee 33
E, CNATRA eeeeeeeeeeeeeeeeeeeeeeee---------- 36
F. NAVAL RESERVES ------------------------------- 39
G, MARTC ---------------------------------------- 42
H. RDT&E/NASC ----------------------------------- 45
V. DISCUSSION --------------------------------------- 48
VI. RECOMMENDATIONS ---------------------------------- 52
APPENDIX As Average Monthly Data Point Values forMajor Commands ------------------------- 53
APPENDIX Bt Aircraft Accidents by Month and byCommand ----------------------------- 64
APPENDIX Cc Forward (Stepwise) Multiple Regression -- 66
APPENDIX D, Statiatical Tests for Significance ------- 69
LIST OF REFERENCES ----------------------------------- 71
INITIAL DISTRIBUTION LIST ---------------------------- 72
5
LIST OF TABLES
I. DATA SET INCLUDED IN CURRENT STUDY ------------ 16
II. CONSTRUCTED VARIABLES ------------- U......--------- 20
III. CONNAVAIRLANT MATRIX OF SIMPLE CORRELATION
COEFFICINTS ------- - ------------------------ 25
IV. COTWAVAIRLANT REGRESSION OUTPUT SUMMARY ---------- 25
V. MARLANT MATRIX OF SIMPLE CORRELATIONCOEFFICIENTS ------------------------------------- 29
VI. MARLANT REGRESSION OUTPUT SUMMARY ---------------- 29
VII. COMNAVAIRPAC MATRIX OF SIMPLE CORRELATIONCOEFFICIENTS -------------------------------------- 32
VIII. COMNAVAIRPAC REGRESSION OUTPUT SUMMARY ...........- 32
IX. MARPAC MATRIX OF SIMPLE CORRELATIONCOEFFICIENTS ------------------------------------- 35
X. MARPAC REGRESSION OUTPUT SUMMARY ----------------- 35
XI. CNATRA MATRIX OF SIMPLE CORRELATIONCOEFFICIENTS ------------------------------------ 38
XII. CNATRA REGRESSION OUTPUT SUMMARY ----------------- 38
XIII. NAVAL RESERVES MATRIX OF SIMPLE CORRELATIONCOEFFICIENTS ------------------------
XIV. NAVAL RESERVES REGRESSION OUTPUT SUMMARY --------- 41
XV. M.ARTC MATRIX OF SIMPLE CORRELATIONCOEFFICIENTS -----------------------------------
XVI. MARTC REGRESSION OUTPUT SUMMARY ------------------ 44
XVII. RDT&E/NASC MATRIX OF SIMPLE CORRELATION 47COEFFICIENTS -------------------------------------
XVIII. RDT&E/NASC REGRESSION OUTPUT SUMMARY -------------- 47
XIX. SIGNS OF CORRELATION COEFFICIENTS ---------------- 49
6
I. INTRODUCTION
Aviation safety is one of the major tools used to obtain
J Navy goal of fleet readiness. The reports necessary to
provide the Naval Safety Center with a means by which to
judge the Navy's progress in aviation safety are delineated
in OPNAVINST 3750.6 (Series). Through analysis of reported
mishaps, the safety center has the ability to determine
correctable material and personnel deficiencies, Through
the administrative effort expended in submitting reports,
the Navy can be repaid many times in the savings of lives
and material.
Due to extensive post aircraft accident analysis by
accident investigation teams, aircraft accidents have been
broadly categorized in terms of causal factors. Causal
factors are not to be confused with environmental factors
but are any event, act, failure/malfunction, circumstance
or occurrence, the presence or absence of which caused the
accident. Contributing to accidents are poorly designed
equipment, supervisory error, improper aircrew training,
failure of a facility to provide adequate runway drainage,
maintenance induced equipment malfunctions, etc.
An accident is designated as a major accident if:
(1) loss of life occurs; (2) complete loss of an aircraft
is involvedi or (3) substantial damage occurs to any
K 7
aircraft involved where substantial damap is defined in
Appendix A of OPAVINST 3750.6 (Series). The most common
cause cited in the literature on aircraft accidents is
pilot error. In a study by Brictson, et al. Z-1969-7,
approximately seventy-eight percent of the accidents stud-
ied attributed pilot error as being the primary causal
factor, with only eight percent being attributed to
support personnel errors, and the remaining thirteen per-
cent being attributed to aircraft failure, equipment failure
and/or weather.
A study conducted for the Royal Air Force by Goorney
E19651, concluded Viat fatigue, personal worries, com-
placency, emotional stress and lack of current flying expe-
rience, directly contributed to pilot error. Goorney's
study states that excessive ground duties prior to flying
attributed to fatigue and that personal worries concerning
marriages, dating, housing, financial and work problems
attributed to emotional stress.
Collicot, et al. Z-1972_ categorized accident causal
factors into pilot error, material failure, maintenance
error, and miscellaneous other causes. The authors compared
Air Force F-4 accidents with Navy-Marine F-4 accidents and
attributed maintenance error disparities to the fact that
Air Force F-4 aircraft only realized one-tenth of the can-
nibalization of parts that Navy-Marine aircraft realized.
The authors also singled out that the Navy-Marine c ricer
job rotational policies resulted in lower in-type flight
8
hours for Navy-Marine aviAtors and thus adversely affectedtheir pilot proficiency. The authors also noted that, in
comparing dual piloted to single piloted aircraft, the dual
piloted aircraft had fewer accidents per ten thousand hours
than the single piloted aircraft. The authors conclusion
was that pilot mental overload was critical in the determina-
tion of a prime factor in pilot error.
As a result of the Collicot study and a study by Kowalsky,
et al. ZE1974J,. the emphasis that pilot induced accidents
were caused by lack of pilot proficiency was shifted to
implications that pilot error accidents may be attributed
to a state of temporary mental overload where the pilots
incorrectly evaluated information inputed to them during the
overload period.
Sinc. the advent of the Naval Safety Center, a great deal
of effort has been expended in maintaining extensive data
banks of accident related information. Statistical Analysis
of available data shnuld enable predictive mathematical
models to be constructed, as much of the data available can
be construed as measuies of pilot proficiency. Myers Z-1974 7
attempted such a statistical analysis, hypothesizing that
measures of pilot proficiency and experience would suffice
to form an adequate foundation for accident rate analysis.
He applied statistical techniques of principle component
analysis and cluster analysis to ten variables obtained from
the Individual Flight Activity Reporting System (IFARS) which
are submi'tted to the Safety Center. Comparing two groups of
9
pilots--one group being involved in aircraft accidents and
the other group being accident free--his. results were not
as pronounced as desired. The fact that each group con-
tained only fifty subjects is reason to believe that this
small sample size suppressed his accident predictivo results.
Maxwell and Stucki Z-1975,J applied regression analysis
techniques to an all Navy study of aircraft accidents for
the period July 1968 to June 1974. Their analysis indicated
that 46.6% of the total accident rate variability is explained
by pilot related variable measures if one wishes to accept
a statistical confidence level of 75% as meaningful. Results
of their study corroborated with the previous studies cited,
that pilot error of one sort or another is the single largest
cause of aircraft accidents.
The author of this Writing agrees with Maxwell and Stucki
that sufficient data should be currently available, from
which predictive capability is extractable. The variable
nature of the monthly accident rate suggests underlying
factors, causal and thus definable in their role of accident
perpetration. Using statistical analysis to isolate variable
measures associated with pilot proficiency and aircraft
maintenance which vary either directly or indirectly with
accident rate, then predictive and thus preventive know-
ledge can assist in lowering the loss of human life and
the dollar loss resulting from aircraft accidents.
10
II. PROBLEM DEFINITION
The Naval Safety Center (NSC), Norfolk, Virginia, has
provided the author with major accident rates computed for
aircraft accidents for eight major commands: (1) Commander
Naval Air Forces Atlantic (COMNAVAIRIANT); (2) Fleet Marine
Forces Atlantic (MARLANT); (3) Commander Naval Air Forces
Pacific (COMNAVAIRPAC); (4) Fleet Mariae Forces Pacific
(MARPAC); (5) Commander Naval Air Training Command (CNATRA),
(6) Commander Marine Training Command (MARTC); (7) Naval
Reserves; (8) Commander Research Development Test and
Evaluation/Naval Air Systems Command (RDT&E/NASC); for
fiscal years 1969 through 1974. The accident rate is defined
as the total number of accidents in a given month multiplied
by a constant factor of ten thousand and then divided by
the total monthly hours flown for a given command. Major
accidents by definition, as delineated in OPNAVINST 3750.6
(Series), are characterized by loss of life, loss of aircraft,
or extensive aircraft damage measured in necessary man-hours
to effect repair.
A variety of approaches to look for consistent trends
or cyclic phenomena in aircraft accident rate of Navy-Marine
accidents was undertaken by Poock [-19762. None were found
that could pass any statistical tests to verify their
existence beyond reasonable elements of chance.
11
The purpose of this paper is to further explore accident
rate dependence on time related variable measures for the
eight major commands listed above in hopes that one or more
of these measures can be identified for later use in the
reduction of accident rates and thus the reduction in the
loss of lives and money.
12
III. ANALYTICAL PROCEDURES
A. DATA SOURCE
OPNAVINST 3750.6 (Series) promulgates the requirements
and procedures for the reporting of each aircraft accident
or incident involving all Navy and Marine aircraft. This
establishes control over accident data with the goal of
increasing aviation safety. The reports are forwarded
to the Naval Safety Center (NSC) for inclusion in their
master data bank. Accident data currently available from
NSC can provide approximately eighty variable measures for
each accident.
B. DATA SELECTION
The NSC data bank provides a ready source of data for
each accident or data set. However, as this is a continuation
of the work of Maxwell and Stucki, the 2110 computer data
cards obtained from NSC for their study were also used in
this study.
The initial step in the conduct of the current accident
rate analysis was to select appropriate variable measures or
data points. A data point for an accident was considered
to be any suitable variable measure associated with the
accident- and a data set consisted of data points for a
L13
specific accident. Specific measures were chosen in mutual
discussions with NSC personnel.
Selection of appropriate data points required that each
point be time dependent. Data point time dependency and
subsequent selection was based on the variable descriptions
contained in the anual of Code Classification for Navy
Aircraft Accident, Incident and Ground Accident Reporting
(Code Manual) promulgated by NSC.
A sufficient number of data sets had to be incorporated
into the analysis to facilitate viable statistical results,
but the span of time defined by the data sets had to be
chosen with care. Unfortunately, of the six fiscal years
of data available to the author, only fiscal years 1972,
1973, and 1974 were used in this study. Fiscal years 1969,
1970, and 1971 were eliminated primarily because some data
sets were either incomplete or entirely void of information.
A change in reporting procedures during 1972 alleviated this
problem. Also, in the fiscal years chosen for the analysis,
a particular accident too often had to be disregarded due to
incomplete data or to the fact that the particular occurrence
involved another aircraft and the other aircraft was deemed
at fault. Therefore, either due to insufficient data or
to an occurrence and not an accident, a total of 636 of
the original 2110 data sets available were used. Data for
each variable of these 636 data sets were complete and there
is absolutely no data missing in the data sets used in
the analysis.
14
Ten data points from each set of the original thirty
data points requested ty" Maxwell and Stucki were selected
for inclusion in the current analysis. Nine of these data
points are the same data points used in the Maxwell and
Stucki study with the addition of the data point "Years
Experience as a Designated Naval Aviation" and the data
point "Flight Purpose Code" deleted. In addition, the data
points selected also allowed the author to construct four
additional variables deemed as measures of experience and
pilot proficiency. Table I lists the basic variables used
in the study. The first ten variables listed are from the
Naval Safety Center and variables eleven through fourteen
are the constructed variables.
Pilot age, years experience as a designated Naval aviator,
experience, age at designation as a Naval aviator and total
flight ti-ne in the aircraft involved in the reported accident
have b'4en considered as measures of pilot experience. If
these variables are true measures of experience they should
exhibit negative correlation with accident rate, assuming
a relationship exists.
There is the age old adage of "practice makes perfect"
which this author construes as a measure of pilot proficiency.
Included in the category of pilot proficiency were totalflight time during the preceding ninety days, total night
flight time during the preceding ninety nights, total day
flight time during the preceding ninety days, the number
of carrier landings in the last thirty days, the number of
carrier landings in the last thirty nights, and the ratio
15
TABLE I
DATA SET INCLUDED IN CURRENT STUDY
1. Accident rate by month (RATE)
2. Pilot's age (AGE)
3. Years experience as a designated Naval aviator (rA)
4. Total flight time in accident involved aircraft model
(TTINE)
5. Total flight time during preceding ninety days (TOT9)
6. Total night flight time during preceding ninety nights(NITE90)
7. Daylight carrier 1-ndings during preceding thirty days(CLDAY)
8. Night carrier land ngs during preceding thirty nights(CIIIT)
9. Number of aircraft tours (ACTOUR)
10. Aircraft flight hours since last major or minorinspection (ACHRS)
11. The ratio of years experience as a designated Navalaviator and total flight time in the accident involvedaircraft model (EXPER=DNA/TTIME)
12. Age at designation as a Naval aviator (WINGS=AGE-DNA)
13. Total flight time during preceding ninety days minustotal night flight time during preceding ninety nights(DAY90=TOT90-NITE90)
14. The ratio of total night flight time during the pre-ceding ninety nights to total day flight time duringthe preceding ninety days (NITEDAY=NITE90/DAY9O)
_16
of night flight time to day flight time during the preceding
ninety days and nights.
To measure airframe age and general condition, two var-
iables were selected. All Navy/%arine aircraft are required
to undergo a Periodic Aircraft Rework (PAR) cycle for analysis
and repair after having accumulated a specific number of
flight hours. Thus, the number of aircraft tours was chosen
as one variable. As a measure of aircraft condition, the
aircraft flight hours since the last major or minor inspection
was also selected as a variab!3.
C. PRELIMINARY DATA PREPARATION
A common theoretical proposition in parametric statistics
states that changes in one variable can be explained by
reference to changes in several other variables. Such a
relationship is described in a simple way by a multiple
linear regression equation as described in Appendix C. To
use this statistical method the relationships between the
variables require the following assumptionst (1) normality;
(2) data must be in the interval measurement scale;
(3) the number of observations exceeds tht number of coef-
ficients to be estimated; and (4) no exact linear relation-
ships exist between any of the explanatory variables.
Normality was assumed by invoking the Central Limit Theorem'
and the technique of averaging by month was used to transform
the data into interval data.
17
Raw data for each of the first ten variables of Table I
was averaged by month for each of the thirty-six months within
the time span selected and was also used to compute the values
for the remairtng variables of Table I.
D. 7E ANALYSIS TECHNIQUE
To conduct the statistical analysis of the data set the
author selected the forward (stepwise) multiple regression
computer program package developed by Jae-On Kim and Frank
J. Kahout at the University of Iowa. The program is included
in the Statistical Package for the Social Sciences (SPSS)
compiled and edited by Nie, et al. Z-1975-7.
Multiple regression may be viewed as a descriptive tool
whereby the linear dependence of one variable on other var-
iables is summarized and decomposed. Kim and Kahout state
that the most important uses of the technique as a descriptive
tool aret
(1) to find the best linear prediction equationand evaluate its prediction accuracy; (2) tocontrol for other confounding factors in orderto evaluate the contribution of a specificvariable or set of variables; and (3) to findstructural relations and provide explanationsfor seemingly complex multivariate relation-ships, such as is done in path analysis.
However, the primary purpose is to evaluate and measure over-
all dependence of a specified (dependent) variable on a set
of other variables (independent). The dependent variable
used for the current study was accident rate and tie inde-
pendent variables consisted of those variables listed as 2
through 14 in Table I and all the variables listed in Table II.
18
To explain the variables listed in Table II it must
again be stated that regression analysis assumes the under-
lying relationships among the variables are linear and addi-
tive. There are man occasions for which such simple linear
models are inadequate. Early efforts by the author dealt
entirely with first order variables but examination of
scatterplots of.the residuals, which are conceived as meas-
ures of the error component, indicated lack of linearity and
the presence of curvilinearity. Therefore, functional terms
were added to the variable list as suggested by Kim and Kahout.
These additional variables are listed in Table II.
The SPSS computer program is designed to provide the user
with a considerable number of control options. The listwise
deletion option was chosen for use by the author as it is
the most conservative and accurate of the options.
The forward (stepwise) multiple regression technique
(Appendix C) is particularly useful in studies of the current
type. Tt is appropriate to enter independent variables one
by one on the basis of a pre-determined statistical ,riteria.
This procedure is used when a researcher desires to isolate
a subset of available predictor variables that will yield an
optimal prediction equation with as few terms as possible.
Draper and Smith [-1966J conclude the following in their
discussion of various regression procedures, "We believe
this (stepwise regression) to be the best of the variable
selection procedures discussed and recommend its use."
The percentage of the accident rate variability explained
19
* TABIR 11
4CONSTRUCTED VAXBES
1. AG32 (AGE)2 20. CLAIa 10CD
k2. TTI32 =(TTIR)2 21 WT = 1.O/Cdt4IT2
3. T0T902 m(TOT90)2 22. ACTCRJRI =1.O/ACTOUR2
4. WINGS2 a (WINGS)2 23. ACHRSI 1.0/ACHRS2
5. DhY902 = (DAY90)2 24. IXIAI = 1.O/DNA2
6. CLDAY2 = (CLDAY) 2 25. EXPERI = 1.0/tExPE2
7. CI&NIT2 = (CLNIT)2 26. WINGSI =1.OAVINGS2
8. ACHRS2 = (ACHRS) 2 27. RTAGE = (AGE) 1
9. EXPER2 = (EXpER)2 28. RTDNA w(DNA)*
10. flNA2 = (DNA)2 29. RTTTU = (TTII )i
*11. NITE902 = (NITE9O) 2 30. RTTOT9O = (TOT9O)i
12. ACTOUR2 = (ACTOUR) 2 31. RTDAY9Or = (DAY90)i13. NITEDAY2 = (NITEDAY)2 32. RTCLDAY = (CLDAY)i
L.14. NITEDAYI = 1.0/NITEDAY2 33. RTCILVIT = (CLNIT)1
15. AGEI = 1.O/AGE2 34. RTACI{RS = (ACHRS)i
16. TTIPMI = 1.0/TTIME2 35. RTEXPER = (EXPER)i
17. TOT90I =1.0/T0T902 36. RTWINGS = (WINGS) 1
18. NITE90I =1.0/AIITE9O2 37. RTNITE90 = (NITE9O)i
19. DAY90I =1.O/DAY902 38. RTACTOUR w(ACTOUR)t
39. RTNITEDAY =(NITEDAY)1
20
by the time related independent variables entered is exactly
the type of statistical output required to ascertain the
causal factors responsible for that variability.
Thirteen separate regression calculations were attempted
for each of the eight couands considered. Each of the
separate regression calculations were permutations of the
variables listed in Table I and the variables listed in
Table I. Regression calculations using only the first
eight variables of Table I or regression calculations using
the first ten variablest of Table I led to the suspicion of
curvilinearity in the data as a result of an inspection of the
residual scatter plots. Therefore, the author attempted
various regression calculations using combinations of the
variables of Table I with either the squares of those var-
iables, the inverse squares of those variables, the square
roots of those variables or any combinations thereof.
There is no unique procedure for selecting the best
criteria and personal judgement is a necessary part of any
decision reached by the analyst. The author set up guide-
lines to choose the "best" equation as follows, (1) the
regression equation would be limited to five or six inde-
pendent variables; (2) the regression equation chosen should
accotut for the highest amount of the variance in aircraft
accident rate; (3) the residual plots would be examined
for the best indication of minimum residuals; and (4) the
statistical significance of each regression would be cal-
culated as outlined in Appendix D and the regression equation
21
* yielding the greatest amount of accountable variance with
the highest confidence level would be the equation selected.
22
IV. RESULTS
A. COWIAVAIRLANT
Early efforts at regression analysis by the author used
only the variables listed in Table I. These efforts led to
the suspicion of curvilinearity as a result of examination of
the residual plots. The order of variable inclusion at the
early stage was, (1) total flight time during the ninety
days preceding the accident (TOT9O)g and (2) aircraft flight
hours since the last major or minor inspection (ACHRS). In
equation form the regression became,
RATE = 0.35295 + o.o0658(TOT9O) + O.O0163(ACHRS)
This equation accounted for 19.5% of the variance in aircraft
accident rate at a 95% confidence level.
Final regression results using functional forms of the
variables indicated that the hierarchical order of variable
inclusion as governed by the individual variable contributions
towards explaining accident rate variance was, (1) the square
root of aircraft flight hours since the lasti major or minor
inspection (RTACHRS)i (2) the square of aircraft flight
hours since the last major or minor inspection (ACHRS2)i
(3) the inverse square of the total flight time during the
ninety days preceding the accident (TOT9OI)i (4) the inverse
square of the quotient years experience as a designated
Naval aviator and total flight time in the accident involved
23
aircraft model (EXPERI)i and (5) the square root of the
quotient years experience as a designated Naval aviator
and total flight time in the accident involved aircraft
model (RTEXPER). Table III lists the simple correlation
coefficients and Table IV is a sumary listing of computer
output provided by the SPSS package. In equation form the
regression becames
RATE = 0.89771 + 0.11823(RTACHRS) - 0.00002(ACHRS2)
- 464 .21653(TOT90I) - 0.00002(EXPRI)
- 4.76996(RTEXPER)
or in terms of Table I variables
RATE = 0.89771 + 0.11823(ACHRS)* - 0.00002(ACHRS) 2
- 464.21653(TOT90)2 ,- 0.00002(TTInE/DINA) 2
4.76996(DNA/TTImE)*
These equations account for 42.9% of the variance in aircraft
accident rate at a 99% confidence level. Therefore, by
using functional forms of the variables, an additional
23.4% of the variance was accounted for--a substantial
improvement in the results.
The net effect of the functional forms of hours since
the last major or minor inspection is positive. The remain-
ing variables are interpreted as being measures of either
pilot experience or pilot proficiency and they have a net
effect of reducing aircraft accident rate.
24
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B. MARLANT
Using the same early methods as those used for COMNAVAIRLANT
the order of variable inclusion at the early stage was:
(1) years experience as a designated Naval aviator (DJA)l
(2) daylight carrier landings during the preceding thirty
days (CLDAY), (3) the quotient of years experience as a
designated Naval aviator and total flight time in the accident
involved aircraft model (EXPER); (4) the quotient of night
flight hours to day flight hours during the preceding ninety
days (NITEDAY); and (5) total flight time in accident
involved aircraft model. In equation form the regression
became:
RATE = 0.96753 + 0.09865(DNA) + o.o8248(CLDAY)
- 20.27987(EXPER) + 1.41098(NITEDAY)
- 0.oo048(TTME)
This equation accounted for 32.6% of the variance in air-
craft accident rate at a 75% confidence level.
Final regression results using functions of the var-
iables indicated that the hierarchical order of variable
inclusion as governed by the individual variable contri-
butions towars explaining accident rate variance was:
(1) the square root of years experience as a designated
Naval aviator (RTI14A); (2) the square root of total
night flight time during the preceding ninety nights
(RTNITE90); (3) total night flight time during the
26
preceding ninety nights (NITE90); (4) the quotient of
years experience as a designated Naval aviator and total
flight time in the accident involved aircraft model (EXPER)l
(5) total flight time in the accident involved aircraft
model (TTDbE); and (6) the square of night carrier land-
ings during the preceding thirty nights (CINIT2). Table V
lists the simple correlation coefficients and Table VI is a
summary listing of computer output provided by the SPSS
package. In equation form the regression became:
RATE = -0.17128 + 0.88657(RTDNA) + 0.52634(RTNITEgo)
-O.06351(NITE9O) - 57.37027(EV.ER) - 0.00115(TTIME)
+ 0.21877(CLNIT2)
or in terms of Table I variables
RATE = -0.17128 + 0.88657(DNA)i + 0.52634(NITE90)*
- 0.06351(NITE90) - 57.37027(DNA/TTIME)
2- 0.00115(TTIME) + 0.21877(CLNIT)
These equations account for 56.5% of the variance in air-
craft accident rate at a 99% confidence level versus the
32.6% accounted for initially. A substantial improvement
was again observed when using functional forms of the
variables in the regression analysis.
When reviewing the correlation matrix (Table V) it is
noted that every variable present in the equation is posi-
tively correlated with accident rate except for EXPER (a
measure of pilot experience) and the square of night
carrier'landings in the last thirty days (a measure of pilot
27
proficiency). The net affect of the functional forms of
night flight hours during the last ninety nights is positive,
an indication that night flying may be a hazardous evolution
and add to accident rate.
28
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C. CMUAVAIRPAC
Initial efforts yielded the following order of variable
inclusions (1) total flight time during the preceding
ninety days (DAY9O); (2) the number of aircraft tours
(ACTOUR)i and (3) years experience as a designated Naval
aviator. In equation form the regression becames
RATE = -0.07944 + 0.01289(DAY90) + 0.10561(ACTOUR)
+ o.04137?(DNA)
This equation accounted for 33.8% of the variance in air-
craft accident rate at a 99% confidence level.
Final regression results using functions of the var-
iables indicated that the hierarchical order of variable
inclusion as governed by the individual variable contri-
butions towards explaining accident rate variance was a
(1) the inverse square of total day flight time during
the preceding ninety days (DAY90I); (2) the square of
the age of the pilot at designation as a Naval aviator
(WINGS2); (3) the number of aircraft tours (ACTOUR);
(4) the inverse square of aircraft hours since the last
major or minor inspection (ACHRSI); and (5) the square
of the hours since the last major or minor inspection
(ACHRS2). Table VII lists the simple correlation coef-
ficients and Table VIII is a sunary listing of computer
output provided by the SPSS package. In equation form the
regression became,
30
RATE = 1.47J4?79 - 670.77272(DAY90I) - O.Ool34(WNMGS2)
+ O.15733(ACTOUR) + 30,.94442(ACHRSI)
+ 0.00001(ACMRS2)
or in terms of Table I variables
RATE = l.474.79 - 670.77272/(DAY90)2 - 0.0013(AGE - tiA)2
+ O.15733(ACTOVR) + 30.944.42(ACHRS) 2
+ 0.0000l(ACHS) 2
These equations account for 45.7% of the variance in air-
craft aocdent rate at a 99.5% confidence level, an increase
of 11.9% in accounting for variance.
It is noted in these equations that the number of
aircraft tours and functional forms of hours since the
last major or minor inspection have a positive effect on
accident rate. Conversely, variables interpreted as
measures of pilot proficiency and experience level have
a negative effect.
31
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32
D. MARPAC
Initial efforts at regression analysis yielded very poor
results for this command. The only variable to be included
in the equation was the quotient of night flight hours to
day flight hours during the preceding ninety days. In
equation form the regression becames
RATE = 1.75337 - 2.47720(NIE90/DAY90)
This equation accounted for 9.2% of the variance in air-
craft accident rate at a 75% confidence level.
Further regression efforts using functions of the var-
iables led to much better results with the hierarchical
order of variable inclusion being: (1) the square of
the number of aircraft tours (ACTOUR2)i (2) the number
of aircraft tours (ACTOUR); (3) the square of total
night flight time during the preceding ninety nights
(NITE902); (4) the square of the quotient total night
flight hours to total day flight hours during the preceding
ninety days (NITEDAY2); (5) aircraft flight hours since
the last major or minor inspection (ACHRS); and (6) the
square of age at designation as a Naval aviator (WINGS2).
Table IX lists the simple correlation coefficients and
Table X is a summary listing of computer output provided
by the SPSS package. In equation form the regression
became:
33
RATE - 1.26335 - 0.32047(ACTOUR2) + 2.2.178(ACTUR)
+ 0.0102(NITR902) - 19.20769(NITEDAY2)
- 0.00565(ACHRS) - 0.00462(uINGS2)
or in terms of Table I variables
RATE = 1.26335 - 0.32O47(ACTOOR)2 + 2.2.178(ACT0IJR)
+ 0.01042(NITE90) 2 _ 19.20769(NITE90/DAY90) 2
- 0.00565(ACHRS) - 0.00462(AGE-DIKA) 2
Either equation accounts for 39.2% of the variance in air-
craft accident rate at a 95% confidence level, a substantial
improvement over the 9.2% of variance accounted for initially.
Reviewing the correlation matrix it is noted that every
variable present in the equation is negatively correlated
with accident rate. However, the intercorrelations of the
variables has the affect of causing some of the signs of
the coefficients in the equation to change, with the net
effect of the functional forms of aircraft tours being
positive.
434
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1. ONATRA
All attempts at regression analysis for this coumand
yielded essentially the same results. Early efforts using
only the variables listed in Table I yielded the following
order of variable inclusion: (1) the quotient of total
night flight hours to total day flight hours during the
preceding ninety days (NITEDAY); (2) total flight time
in accident involved aircraft model (TTIME); (3) the
quotient of total flight time in accident involved aircraft
model to years experience as a designated Naval aviator
(TTD1/ A), (4) aircraft flight hours since the last
major or minor inspection (ACHRS)i and (5) the quotient
of years experience as a designated Naval aviator to total
flight time in accident involved aircraft model. In equation
form the regression became,
RATE = 5.22976 + 51.98496(NITE9O/DAY9O) + 0.00955(TTIME)
- 0.01973(TTIME/DNA) - 0.04198(ACHRS)
- 216.41848(DNA/TTIME)
This equation accounted for 32.3% of the variance in air-
craft accident rate at a 90% confidence level.
Later regression results using functions of the variables
yielded: (1) the square root of aircraft flight hours since
the last major or minor accident (RTACHRS)i (2) the square
of aircraft hours since the last major or minor inspection
36
* (ACmRS), (3) the square of the total day flight hours
flown during the preceding ninety days (DAY902)1 (4) the
square root of the quotient of total flight time in the
accident involved aircraft model to years experience as a
designated Naval aviator (l.O/RTUPER); and (5) the
quotient of total flight time in accident involved air-
craft model and years experience as a designated Naval
aviator. Table XI lists the simple correlation coefficients
and Table XII is a summary listing of computer output pro-
vided by the SPSS package. In equation form the regression
became s
RAT = -0.31346 + 0.11248(RTACHRS) - 0.00003(ACHRS2)
- 0.00002(DAY902) + 0.03J482(l.0/RTEXPER)
- 0.00092(1.0/EXPER)
or in terms of Table I variables
RATE = - 0.31346 + 0.11248(ACHRS)' - 0.00003(ACHRS) 2
- 0.00002(DAY9) 2 + 0.03482(TTIME/DNA)"
- 0.00092(TTIE/DNA)
Either equation accounts for 33.0% of the variance in air-
craft rate at a confidence level of 90%1 representing no
significant change in the results. The functional forms
of aircraft hours since the last major or minor inspection
and the reciprocal forms of EXPER have a net positive
effect while the square of day flight time during the last
ninety days has a negative affect.
37
j n Q%NOCD 0 .41 c4mU.0% Mv~O c 4 0 N 0 LIN
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. I .J P - ' - . . .. -..... . ... --- ' . .. ... W
F. NAVAL J VSW V
Initial efforts yielded the following order of variable
inclusione (1) total night flight time during the preceding
ninety nights (NITB90)s (2) the quotient of total night
flight time and total day flight time during the preceding
ninety days and nights (NITE90/AY90)1 (3) total flight
time during the ninety days preceding the accident (TOT9O)g
and (4) the number of daylight carrier landings during the
preceding thirty days. In equation form the regression
became:
RATE 0.97395 + o.o6986(NITE90) - 1.2294(NiT9o/DAYgO)
- 0.00777(TOT90) - 0.03343(CLDAY)
This equation accounted for 71.4% of the variance in air-
craft accident rate at a 99% confidence level.
Final regression results using functions of the variables
indicated that the hierarchical order of variable inclusion
as governed by the individual variable contributions towards
explaining aircraft accident rate variance was, (1) the
square of total night flight time during the preceding
ninety nights (NITE902); (2) the square of the quotient
of total night flight time and total day flight time during
the preceding ninety days (NITEDAY2); (3) the inverse
square of aircraft flight hours since the last major or
minor inspection (ACHSI); (4) the square root of daylight
carrier landings during the preceding thirty days; and
39
(5) the inverse square of the quotient of years experience
as a designated Naval avia+or and total flight time in the
accident involved aircraft model (EXPRI). Table XIII lists
the simple correlation coefficients and Table XIV is a summary
listing of computer output provided by the SPSS package. In
equation form the regression became:
RATE = 0.83553 + O.00084(NITE902) - 0.56367(NITEDAY2)
-311.23233(ACHRSI) - 0. 22889(RTCLDAY)
+ 0.00002(EXPERI)
or in terms of Table I variables
RATE = 0.83553 + O.00084(NITE90)2 _ 0.56367(NITE90/DAY9O)2
- 311.23233(I.0/ACHRS)2 _ 0.22889(CLDAY)}
+ 0.00002(TTIME/DNA) 2
Either equation accounts for 81.3% of the variance in air-
craft accident rate at a 99.9% confidence level, a 9.9%
increase of accountable variance over initial efforts. The
net effect of the square of night flight hours during the
preceding ninety nights and the quotient of night flight
hours and day flight hours during the preceding ninety
nights and days is negative. This may indicate that the
higher the ratio of night flight hours to day flight hours
(a measure of pilot proficiency), the lower the accident
rate.
4o
va ( 00,1. 00~ .4 .1.% W.00rI CV ~ m000004-
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G. KARTC
Initial efforts using only the variables of Table I
yielded the following order of variable inclusions (1) the
quotient of total night flight hours and total day flight
hours during the preceding ninety days (NITEDAY); (2) total
flight time in accident involved aircraft model (TTIN);
(3) the quotient of total flight time in accident involved
aircraft model and years designated as a Naval aviator
(TTU/M A); (4) age at designation as a Naval aviator
(WINGS); and (5) number of aircraft tours (ACTOUR). In
equation form the regression became:
RATE- - 45.84436 + 2.23927(NITEDAY) + 0.02707(TTIME)
- 0.15004(1.0/EXPER) + 2.20096(WINGS)
- O.75295(ACTOUR)
This equation accounted for 68.0% of the variance in air-
craft accident rate at a 95% confidence level.
Final regression results using functions of the variables
indicated that the hierarchical order of variable inclusion
as governed by the individual variable contributions towards
explaining aircraft accident rate variance was: (1) the
square of the quotient total night flight time and total
day flight time during the preceding ninety days (NITEDAY2);
(2) total flight time in accident involved aircraft model
(TTIME); (3) the inverse square of the quotient years expe-
rience as a designated Naval aviator and total flight time in
* 42
the accident involved aircraft model (EII)i (4) total
night flight time during the preceding ninety nights (NITE9O)l
and (5) the square of age at designation as a Naval aviator
(INGS2). Table XV lists the simple correlation coefficients
and Table XVI is a summary listing of computer output provided
by the SPSS package. In equation form the regression becames
RATE - - 0.36132 + 65.28325(NITEDAY2) + 0.00328(TTINE)
- .O0008(EXPRI) - 0.41913(NITE90)
+ 0.00385(WINGS2)
or in terms of Table I variables
RATE = - 0.36132 + 65.28325(NITE90/DAY90)2 + 0.00328(TTIME)
- 0.00008(TTIME/DNA) 2 _ 0.1+9I3(NITE90)
+ 0.00385(AGE-DNA)2
Either equation accounts for 79.9% of the variance in air-
craft accident rate at a 95% confidence level, a 10.9% increase
of accountable variance over initial efforts.
It should be noted for this command that only one variable
interpreted as a measure of experience (EXPERI) is negatively
correlated with accident rate. Another measure of experience
(WINGS2) and three variables interpreted as measures of pilot
proficiency are all positively correlated with accident rate.
This positive correlation of pilot proficiency and experience
variables is contrary to what the author hypothesized. The
study by Poock Z-1976J also concluded that this command
produced unusual results.
£43
0% fO MVNO 0 Q "M-4CM
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These two conands were grouped together due to the factthat neither command had enough data points to be analyzed
if considered as individual commands. Initial efforts using
only the variables of Table I yielded the following order of
variable inclusions (1) total night flight hours during the
preceding ninety nights (NITB90); (2) the quotient of
years experience as a designated Naval aviator and total
flight time in accident involved aircraft model (EXPER);
and (3) pilot's age. In equation form the regression
became.
RATE = 0.93622 - 0.08430(NITE90) + 0.31653(EXPER)
- 0.01623(AGE)
This equation accounted for 56.5% of the variance in air-
craft accident rate at a 95% confidence level.Final regression results using functions of the variables
indicated that the hierarchical order of variable inclusion
as governed by the individual variable contributions towards
explaining aircraft accident rate variance was, (1) the
square of total night flight during the preceding ninety
nights (NITE902); (2) the square root of total flight
-time in accident involved aircraft model (RTTTIME)i (3) the
inverse square of years experience as a designated Naval
aviator (DNAI); (4) the square root of the inverse quotient
45
of years experience as a designated Naval aviator and
total flight time in the accident involved aircraft model
(1.O )TZXu)i (5) the inverse square of total flighttime during the preceding ninety days (TOT90I) and (6) the
square root of total flight time during the preceding ninety
days (RTTOT90). Table XVII lists the simple correlation
coefficients and Table XVIII is a summary listing of com-
puter output provided by the SPSS package. In equation
form the regression became:
RATE = - 1.21331 + 0.71262(NITE902) + 0.23598(RTTTIME)
+ 19.68521(DNAI) - 0.642I(1.0/RTEXPER)
+ 182.91525(TOT90I) + 0.38527(RTTOT90)
or in terms of Table I variables
RATE = - 1.21331 + 0.71262(NITE90) 2 + 0.23598(TTIME)*
+ 19.68521(1.0/DNA) - o.61421(TTImE/DNA)'
+ 182.91525(1.O/TOT9O) 2 + 0.38527(TOT90)i
Either equation accounts for 80.8% of the varianoe in air-
craft accident rate at a 95% confidence level, a 25.3%
increase o-3r initial efforts.
46
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V. DISCUSSION
Reviewing the results it can be seen that as functional
forms of the variables were introduced into the regression
analysis that more variance in aircraft accident rate was
accounted for at a higher confidence level. This was true
for all eight commands considered.
Observing the signs of the correlation coefficients
listed in Table XIX, it can be seen that the variable EXMPR,
which is the ratio of years experience as a designated
Naval aviator and total flight time in accident involved
aircraft model, was negatively correlated with accident
rate in all cases. This indicates that the more flight
time in a particular aircraft model that a pilot possesses
per year of designated Naval aviator service that he will
become more safe and thus have fewer accidents. This could
suggest that the more experienced a pilot becomes the larger
a repertoire of near tragedies he has to draw from and thus
the more reminders or analogies he has to compare with
current situations.
Conversely, the variable CLNIT, which is the number of
night carrier landings a pilot has during the last thirty
nights, showed positive correlation with aircraft accident
rate in the three commands where the variable was present
(COMNAVAIRLANT, MARLANT, COMNAVAIRPAC). This may indicate
48
E4 +++1+
4-
11I4 11111
4E-
0
* E04
0>w K0> -
0z C I -
* 09
that night, carrier landings are more taxing evolutions
and tend to add to aircraft accident rate.
It has been common belief that pilot proficiency lessens
aircraft accident rate. However, when again reviewing the
correlation coefficients, it is observed that the correlation
of total flight time during the preceding ninety days (TOT90)
and day flight time during the preceding ninety days (DAY90)
is positively correlated with aircraft accident rate except
in the cases of CNATRA and MARTC (both training commands).
It is also observed that the variable night flight time
during the preceding ninety nights is positively correlated
with aircraft accident rate in all commands except CNATRA.
Considering that the training commands are on a schedule
where the pilot should not experience fatigue, the positive
correlation of these variables with aircraft accident rate
would tend to indicate that if flight time is not uniformly
spread out that practice does not necessarily make perfect
and that a possible fatigue factor may be causing an increase
in aircraft accident rate. Fatigue could be construed as
having the majority of flight time during the preceding
ninety days massed into a short period of time instead of
being distributed uniformly over the ninety day period. (It
is understood that data for a thirty day period is now being
recorded.) Another explanation would support Goorney's
supposition that pilot complacency may increase directly
as the number of hours flown and thus contribute to aircraft
accidents. In this case, new pilots in the training command
50
L K ..... ... ... ..... ... . . ... . . .. . ...... . .. . . ...... ...
most likely will not become complacent or they will not
receive their wings.
The rem variables listed in Table XIX did not
indicate a dominant sign of the correlation coefficient
common to all commands. Therefore, the author will not
attempt to explain the rem variables individually.
When reviewing the results of the major commands con-
sidered, it should be noted that the variables most instru-
mental in explaining the variance in aircraft accident
rate are not all pilot oriented variables as was shown in
the Maxwell and Stucki study which was an overall Navy/
Marine study. The overall results don't seem to apply
when taking a more microscopic look at individual commands.
COMNAVAIRLANT, COMNAVAIRPAC, MARPAC, CNATRA and Naval Reseirves
regression equations all contain variables interpreted as
being either related to experience level, pilot proficiency,
or aircraft condition. Only MARIANT, MARTC, and RDT&E/NASC
account for the variance in aircraft accident rate by
variables interpreted as being pilot oriented variables
in their respective regression equations. Condition of
the aircraft must therefore also be considered when attempt-
ing to account for the variance in aircraft accident rate.
51
VI. RECWUKDTCI
The current study includes eight major commands in its
treatment of aircraft accident rate. Functional forms of
the variables produced the best results. For this type of
study however, the author recommends that the distributions
for each variable be ascertained and that these distributions
whether they be gamma, beta, exponential, etc. be used in
an attempt to analyze aircraft accident rate.
This study was limited to consideration of only accident
involved pilots and accident involved aircraft. A future
study could be done comparing these pilots and aircraft
to accident free pilots and aircraft in order to ascertaiA
whether these groups are from the same distribution. It
would then be possible to ascertain critical points in a
pilot's career or the life of an aircraft.
A more microscopic study than this study may seem appro-
priate. However, subdividing the data any further into
Airwings may limit the analyst to only a small number of
data points.
52
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AflWIX C
ee FOWR (SUPWISZ) NULTIPLU RZEGRSSION
The basic principles of regression analysis may be
extended to situations involving two or more independent
variables. The general mathematical form of the (unstand-
ardited) regression is
YO = A+ Bj1X + 2 . +BAC
where Y' represents the estimated value of the dependent
variable, A is the Y intercept, the Bi are regression
coefficients, and the X, are the independent variables.
It is assumed that this is a aomplete set of variables
from which the equation is to be chopen and includes any
functions such as squares and inverse squares thought to
be desirable and necessary.
The A and Bi coefficients are selected in such a way as
to minimize the sum of squared residuals, y-y,)2.By
minimizing the squared residuals, the regression technique
maximizes the correlation between the actual dependent
variable (Y) and the estimated dependent variable (Y')
while the correlation between the independent variables
and the residual values (Y-Y') are reduced.
The proportion of variance of Y explained, i.e., the
goodness of fit of the regression equation can be evaluated
by examining the square of the multiple correlation (R2),
where R2 is calculated by,
66
= - 2
ssy -sr ssre;y
or
variation In Y explained by the combined
R2 linear influence of the independent variablestotal variation in Y
where SSy is the total variation or sum of squares in Y,
SSr is the sum of squared residuals, and SSreg is the
regression of squares.
The forward (stepwise) selection procedure available in
the Statistical Package for the Social Sciences (SPSS ver-sion 6) used for this study inserts variables in turn until
the regression equation is satisfactory. Independent var-
iables are entered only if they meet certain statistical
ctiteria. The order of inclusion is determined by the
respective contribuvion of each variable that explains the
greatest amount of variance previously unexplained by the
variables already in the equation. Th, variable that does
this is the next variable to be entered.
This order of insertion is determined by using the
partial correlation coefficient as a measure of the impor-
tance of variables not yet in the equation. The,basic
procedure is as follows. First select the X most correlated
with Y (suppose it is XI) and find the linear regression
equatiorr Y = f(X1 ). Next find the partial correlation
67
coefficient of X (ijl) and Y (after allowance for Xl),
i.e., find the correlation between the residuals from the
Aregression Y = f(X1 ) and the residuals from another regres-
sion X =f(X). The X. with the highest partial correlation
with Y is now selected and the process continues. As each
variable ib entered into the regression, the following
values are examined,
1. R2, the multiple correlation coefficient;
2. The partial F-test value for the variable most
recently entered, which shows whether the variable
has taken up a significant amount of variation
over that removed by variables previously entered
in the regression.
As soon as the partial F value related to the most recently
entered variable becomes nonsignificant the process is
terminated.
68
APPENDIX D
STATISTICAL TESTS FOR SIGNIFICANCE
Regression procedures per se may be categorized as de-
scriptive statistics. Regression analysis is commonly per-
formed on sample data from which the researcher is either
interested in estimating population parameters from sample
regression statistics or to testing statistical hypothesis
about the population parameters and determining confidence
limits for estimates in testirng the hypothesis.
The overall test for goodness of fit of the regression
equation uses statistical inference procedures to test the
null hypothesis that the sample of observations being analyzed
has been drawn from a population in which the multiple cor-
relation is equal to zero. An equivalent way of stating
the null hypothesis, Ho, is that the next variable to be
added in a forward regression would not add significantly
to the explained variance in the dependent variable, Y,
already accounted for by variables included in the regression
equation. The alternate hypothesis, Hi, directly contradicts
the null hypothesis.The test statistic employed for the overall test is
SSreg/ R2/
-SSres (6-K') (1-R2)/(N-K- )
'" 69
where SS ini the sum of squares explained by the entireregregression equation, SSres is the residual (unexplained)
sum of squares, K is the number of independent variables
in the equation and N is the sample size. The F ratio is
distributed approxiuately as the F distribution with degrees
of freedom K and (N-K-i).
Adjusted R2 is an R2 statistic adjusted for the num-
ber of independent variables in the equation and the number
of cases. It is a more conservative estimate of the percent
of variance explained, especially when the sample size is
small. The adjusted R2 formula uses unbiasec estimates
of the error variance and the total variance of Y in the
population. The formula used by SPSS is:
R2 2K1Adjusted R= R - (1-R)
Becaused Adjusted R2 is a conservative estimate of the per-
cent of variance explained, the author used the following
F statistic to determine confidence levels for the regression
equations obtained for each command considered:
(Adjusted R2 )/K
(1-Adjusted R2 )/(N-K-I)
70
LIST OF FmmCEES
Brictson, C. A., Pitrela, F. D., and Wulfeck, J. W., &-alysisof Aircraft Carrier Land Accidents (1265 to 1969).Dunlap and Associates, CNR, Washingon, D. C., November1969.
Collicott, C. R., Muir, D. Z., and Dell, A. H., U. S. NavalAviation Safety, ORG Study 766, October 1972.
Draper, N. R., and Smith, H., Applied Resreslion Analysis,John Wiley and Sons, Inc., New York, 1966.
Goorney, A. I , The Human Factor in Aircraft Accidents-Investigation of Background Factors of Pilot Error-Related Aircraft Accidents. Flying Personnel ResearchCommittee, Ministry of Defense, Great Britain, July1965.
Kowalseky, N. B., Masters, R. L., Stone, R. B., Bubcock, G.L., and Rypka, E. W., An Analysis of Pilot Error-RelatedAircraft Accidents, NASA Contractor Report 2444, June197T.
Manual of Code Classification for Navy Aircraft Accident,Incident, and Ground Accident Reportin , Records Div-ision, Records and Data Processing Department, NavalSafety Center, 1 July 1972.
Maxwell, J. S., and Stucki, L. V., nalysis of the VariableBehavior Manifested in All Navy/Marine Major AircraftAccident Rates, Unpublished Master's Thesis, NavalPostgraduate School, Monterey, California, September1975.
Myers, H. B., Jr., Pilot Accident Potential as Related toTotal Fliht EZaience and Recency and Frequency ofFlying, Unpublished Master's Thesis, Naval PostgraduateSchool, Monterey, California, September 1974.
Navy Aircraft Accident, Incident and Ground Accident Report-ing Procedures, OPNAVINST 3750.6J of 13 December 1973.
Nie, N. H., Hull, C. H., Jenkins, J. G., Steinbrenner, K.,and Bent, D. H., Statigtical Package for the SocialSciences, Second Editin, McGraw-Hill, New York, 1975.
Poock, G. K., Trends in Major Aircraft Accident Rates, NavalPostgraduate School Report #NPS55Pk76061, Monterey, Cali-fornia, June 1976.
71
INITIAL DISTRIBUTION LIST
No. Copies
1. Defense Documentation Center 2Cameron StationAlexandria, Virginia 22314
2. Chief of Naval Personnel 1
Pero lbDepartment of the NavyWashington, D. C. 20370
3. Library, Code 0212 2Naval Postgraduate SchoolMonterey, California 93940
4. Department Chairman, Code 55 2Department of Operations ResearchNaval Postgraduate SchoolMonterey, California 93940
5. Associate Professor G. K. Poock, Code 55Pk 3Department of Operations ResearchNaval Postgraduate SchoolMonterey, California 93940
6. Assistant Professor D. E. Neil, Code 55Ni 1Department of Operations ResearchNaval Postgraduate SchoolMonterey, California 93940
7. Director, Aviation Safety Programs 1Naval Postgraduate SchoolMonterey, California 93940
8. Naval Safety Center 1Naval Air StationNorfolk, Virginia 23511
9. LCDR R. W. Mister Code 1155 1Naval Safety CenterNaval Air StationNorfolk, Virginia 23511
10. LCDR L. C. Bucher 119 Arbor AvenueTopsham, Maine 04086
72