ML20149E735

Applicant Exhibit A-21,consisting of Undated Article, Note on X2 Test W/Applications to Road Accidents in Const Zones, Published in Vol 12 of Accident Analysis & Prevention.Copyright Matl

ML20149E735
Person / Time
Site:	Seabrook
Issue date:	11/05/1987
From:	Ceder A, Dressler O TECHNION-ISRAEL INSTITUTE OF TECHNOLOGY, HAIFA, ISRAE
To:
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OL-A-021, OL-A-21, NUDOCS 8802110257
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i A NOTE ON Tile x' TEST WITil APPLICATIONS TO '88 FEB -2 A9 :28

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f ROAD ACCIDENTS IN CONSTRUCTION ZONES

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OFFICE N S&tW /

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00CKEllNG A 'iEHv!CI:

AYisilAt Croca and OrEn Dusstn BR t.NCH g

Transportation Research !nstitute,Technion-Israellastitute of Technology, 1

j liaifa, Israel 1

1 IReceited 20 february 1979;la cri,istJ/orni M Afay 1979) l

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d' Atdract-The routine use of the chi-square tests has perhaps led to an incorrect considerat;on of basic l

underlying data in two articles in the accident and transportation fields.This paper emphasites the necessity of comparing actual measurcJ (observed. resultant, etc.) units with those which are enrected. The two detected errors found in the literature serve as a e arning stimulus in using proportions or transformed units instead of the actual nurnbers in chi-square tests. Several caamples of data preparation are exhibitcJ in G

detail in addition, road accidents in construction oc rnaintenance tones are ana! ped as an application of v

l correct usage of the basic availabie data, f

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l. INTRODtJCTION it has occurred to us that it might be useful to note possible misjudgments of statistical data 8

when incorrectly utilizing chi square (x ) tests. This note lias been primarily motivated by two articles, found incidentally, in the accident [Quandt,1974], and transportation [Ilorton and h

2 Louviere,1974) literature. These two articles incorrectly use the 1 test, as will be shown in the y

discussion below; furthermore, in one of the artichs[Quandt,1974), this has led to wrong a

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conclusions.

i Our investigation of road accidents in construction zones serves as a stimulus in extending 2

the discussion of possible incorrect x testi beyond what can be seen as a trivial and basic j

argument. All the wrong treatments of the x' test mentioned in this note fall into the category b

i of non usage of the actual size of samples and/or the actual numbers in each attribute class.

Q Though it is well known, particularly to statisticians, that the x test cannot be performed when 4

2 only the percentages or proportions of each class are known, there are other commonly used 8

transformed units or rneasurements which are utilized for an 2 test instead of the actual and I-correct numbers.

This paper: (1) exhibits several examples of data preparation (incorrectly and correctly) for h

the.g' test;(2) presents and proves errors found in the two mentioned articles (QuanJt 1974; Q

llotton and Louviere 1974), regarding the x' test; and (3) demonstrates results and x' analysis of road accidents occurring along sections of roadways which were partially and temporarily closed r

due to construction and/or maintenance work, p

2. EX AhlpLES Following are two examples of what are frequently called contingency tables.

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Example 1 j

Assuming that one is interested in cor, paring the safety level of three cities over a given period of time. A typical safety measure shown in the reports of the Israel Central Bureau of g

j Statistics for each city is the number of fatal accidents per 1,000 inhabitants (N). Data for three cities A, B and C are:

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'j City g

4 Measure A

B C

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10' 10' 5 x 10' 1

F 100 9tM (00 t

N 1.0 0.9 1.2 d

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I chere P = number of inhabitants and T = number of fatal accidents. The null hypothesis is that there is no significant di!Ierence between the safety level of the three cities. llence, the c

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expected N value becomes (1600/16 x 10')x 1000 = 1.0 and the sum of the (deviation square f i f divided by the (expected number) is then calculated to te A'= 0.05. Ilowever, from the x c

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distribution with two degrees of freedom, and at the probability level of 5%, A/(0,05) = 5.99, th p

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0 null hypothesis is not rejected, is this correct 7.....certainly not!

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y As remarked earlier, the usage of transformed measure of accidents is prohibited;instead, T

actual values should be considered. In the above example, the expected F numbers are to be i

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' p, 'i analyzed, i.e. the ulues (1600/16 x 10') 10' = 100,1000 and 500 for city A, city B and city C, t

j respectively. The latter leads to a calculation of x =30 which leads one to reject the null 8

,g hypothesis.

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[& ~'*f" p,e Example 2 Assume that a new treatment for road maintenance is being tested. The comparison between jy the old and the new treatments is performed using tge frequencies of three types of road

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defects: pavement, shoulder and friction defects. Seventy kilometers have been tested. A unit ig length of the roadway is defined defective if it contains one or more defects. The number of i, l 3

S M,-y defective units for each defect's type is the criterion in comparing the two treatments. The data g

reflecting the annual cumulative effect after performing each treatment were couected on a f,N

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,.D meter-unit basis for each type of defect along the considered 70km; the data have also

.-l & M transformed to defective units of kilometers and miles as follows:

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h M.'.Q % j Number of defective units nyLlb l* I W$%$)

,.c Old Treatment New Treatment 8

• 1 &g,&,4 3."

. > ~~ i V l meters km miles meters km miles defect type 7 3.'.

l4 pavement 24000 24 15 16000 16 10 y,[7.:. ! '

shoulders 40000 40 25 32000 32 20

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., Q friction 16000' 16 10 24000 24 15

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The null hypothesis that there is no significant difference between the two treatments is

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' l.[pk :,.H obviously rejected when considering the actua' measured units (meters)in which the calculated O

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x = 8266. On the other hand, if one, for some reason, (e.g. standardized units) changes the 8

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units to either km or miles, then the calculated A which equal to 8.266 or 5.166, respectively, 8

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leads to the opposite conclusion (say, at ITc level) about the nuu hypothesis, la fact, any

1. ' y A, d transformation of the actual units distorts the x test. It is simple to show that if the observed (0) and the expected (E) frequencies are multiplied by k, then the calculated A'is equal to k j

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times the corrected x' value. That is, Il(AO,- LE)'/IE] = AI[(0,- E)2/E).

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4 3.CillSQU ARE ERRORS IN TWO ARTICLES

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in Quandt[1974), one section of the article attempts to test the null hypothesis that no

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preference is given by hijackers to flight on any certain day. Accordingly, Quandt concluded

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J that the risk of being hijacked does not vary significantly, on the average, during the week.

lh Quandt (on p.117, based on Table 3), hypothesized that the relative frequency of flights on if. G],?,1 Monday through Friday is 16% each, and on Saturday and Sunday 107c. Then he used the x' O

g test for the total hijackings (in percentagel) by day of week from 1 % 8-1972: 16% (Mon),

@M g.] U l1%(Tues.),187c(Wed.),12ro (Thurs.), 23%(Fri.),1(y7e(Sat.), and 10",(Sun.). Consequently,

[.y '"'[@y the calculated 'is 5.81 and therefore, the null hypothesis is not rejected at the 5% level w here A

r.'t0.05) = 12.59. llowever, there were a total of 2% hijackings, and the calculations yield

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A = 29.9 for which the null hypothesis is rejected,

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i In the second article, llotton and Louviere[IS74J, provide what they called a short range f W&

monitoring denice for the collection of data on the level of sen' ice of various aspects of a new 6

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public bus system.1 hey conducted two surveys: before and after major changes of a bus

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A note on the f test riscations to real accidents in construction zones 9

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system in Iowa City in 1971 across 24 attribute items, and attempted to find wh:ch attribute (fare, frequency of service, route coverage, safely, comfort, waiting time, etc.), is deemed critical to the patronage level. In each survey, the remonses to each attribute ranged on a scale 8

from saliffactory to ur.rafisfactory. The autho s' conclusions are based almost solely on the 2 f

test, without any indication of the sample size of each survey. For example,let us introduce in Table 1 the complete Table 3 of Ilotton and Louvierelp.172]. In this table, the bus system routes were grouped into those which were unchanged, slightly changed and completely

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changed af ter the utilization of the new system.

l TaNe 1. TaNe 3 of Iloiton & touvierel1974l comparison of responses grouping accorJing to changes in route coverage New Routes No Change Some Change l

t Satisf act.

22.7 35.1 27.9 i

I Some Sat.

19 9 15.7 13.2 i

Neither 23.5 19 0 23.3 Before I

Some Unsat.

13 9 14 8 11.9 i

Unsatisfact.

19 8 15.2 18.5 l

New Routes No Change Some Change j

l Sadiract.

39 4 52.7 51 0 Some Sat.

38 7 32.3 29.8 Neither 10.3 7.5 9.1 After Some Unsat.

55 26 4.5 Unsatisfact.

5.9 4.5 5.3 Chi-square Anal) sis of Route Responsest i

No Change Some Change New Routes 9Rd8 01 1.7nll 55 No Change 4.13/4 28 Defore No Change Some Change New Poutes 8.16/9.33 584/5.74 After No Change 2.11;1.46 1probabihty of a Chi square vahie eaceeding 9 49 mith 4 d.f. is 0.05; prob.

abikty of a Chi-square salue exceedirig 13.28 is 0.01; probability of a Chi. square value eacceding 14 86 is 0.003.

Though not indicated, the entries on this Table are probably in percentages (sum to 99.8 and 2

99.6 for each group before and after, respectively). Also, two x values are given for each comparison vecause of the alternate choice of c.ipccted frequency. Nonetheless, the above J

mentioned discussion clearly emphasizes the necessity of the actual response counts for each category, and hence, the 3 values show n in Table I cannot serve as a basis for any concrete 8

conclusions.

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4. ROAD S AFETY AN ALYSIS IN CONSTRUCTION ZONES in a recently held discussion at the lload Safety Centre on research allocation priorities for l'

highway safety, some participants claimed that the safety level in construction zones is not a crucialissue. Their (our null) hypothesis w as that in 4-lane roadways, with ADT (Average Daily Traffic) greater than 10,000, the accident distribution among roadway sections is unchanged

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during construction and/or maintenance work. In other words, for the same roadway sections, the distribution of accidents before and after is not significantly different from the distribution of accidents during constructionimnintenance work.

The analysis has been directed towards data for 1976 and for four 4-lane sections. These sections have been exposed to construction and maintenance work by lane closure situations.

The 1976 data is gathered and shown in Table 2, where ADT's before and after are found to be the same as during lane closure, and relate only to fatal and personal injury accidents. As 2

mentioned earlier, only actual rucasures or results can be subjected to the x test, and consequently, the last two rows of Table 2 are the correct distributions for testing the nu!!

hypothess.

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The calculation leads to r'-(48 and the null hypothesis is rejected (u'(0.05) = 7.81). This r

observation is not surprising since conditions change for the driver passing through the I

roadway work zones. The on going activities in the sicinity of lane closure creates substantial hazards to both the workmen and motorists. Anderson [1976), stresses the need for eficctive action regarding these hazards in highway work zones. Ile reported that in ten construction

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Table 2. Accidea data for 4-lane sections b 1976

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Roado ay numberi i

12 13 13, 15 Kilometer ranget H0 1-53 1-21 14-21, 0-14 s

Daily lane closure total i

length 3m.)

8 8

7 8

No. of lane

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closure days 104 18 47 49 s

Accidenti/Im

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- S lane closure 4.1 3.4 8.8 1.7 1

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Espected number

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.t of accidents during fl i

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lane closure t9.3 1.3 7.9 L.8

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N Actual number of accidents during

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lane closure 32 4

7 5

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t According to the Isrnel Central Bureau of Statistics' Reports.

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Ie 3 4.1 8 104/365 = 9.3.

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l rone studies in California in 1%5, fatal accident rates increased from 3.?5 deaths per 100

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y million miles traveled to 9.18 during the construction period. Also, in 1976, the National rj yg j.3 Transportation Safety Board study found that injury accidents had more than doubled during f

hf,.}:0 the construction / maintenance period.

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This final application of the x' test for accident data in construction zones crophasizes the

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merit of a correct statistical treatment. Perhaps the rc,utine use of the x test (and other 8

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common analyses) in today's prog;ammable pocket-calculator environment, reduce our con-sciousness of basic underlying principles of analyses.

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REFERENCES

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Anderson R. W. Proccedings, fmproeing Saftry la Highway && Zones-A Matter of EAics. 20th Conference of the

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llotton l'. E. med toutiere J.1, Behavioural analysis and transrottation plannir : Input to transit planning. Trans-years Americart Association for Automotive Medicine, Atlanta, Georgia,1976.

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[.gt portatios 3, 165, 1974.

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J jf;M Quandt R. E., Some statisGcal characteruations of aircraft hijackJeg. Accio'. And l'rre. 6, l15,1974.

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UNITED STATES NUCLEAR REGULATORY COMMISSION o

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wAssmoTow, p. c. 20sse s.,*....j Itay 26, 1987 i

MEMORANDUM FOR:

John Milligan Technassociates FROM:

Emile L. Julian Kcting Chief Docketing and Service Branch

SUBJECT:

SEABRook EXHIBITS Any documents filed on the o sen record in the $5.AReek pro-ceeding and made a part of tie official hearing record as an exhibit is considered exempt from the provisions of the United States Copyright Act, unless it was originally filed under seal with the court expressly because of copyright concerns.

All of the documents sent to TI for processing fall within the exempt classification.

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