The influence of quality control programs on evaluation of laboratory data

T H E I N F L U E N C E OF Q U A L I T Y C O N T R O L PROGRAMS ON E V A L U A T I O N OF L A B O R A T O R Y DATA S o m e Statistical O b s e r v a t i o n s o n R e f e r e n c e Sera* t Joseph H. Riddich, fl., M.D.S

Abstract A review o f tim d e v e l o p m e n t o f multichannel analysis in tim clinical laboratory is p r e s e n t e d with a discussion o f its influence on the d e v e l o p m e n t o f h a n d and c o m p u t e r i z e d charting teclmiques for quality control, attd regional quality control progrmns. An example o f the effectiveness o f o n e such regional quality control p r o g r m n is presented in the f o r m o f a statistical analysis o f the effects o f changing m a n u f a c t u r e r s o f calibrating serum for the S*IA 1_9/60. Graphical representations, two way analysis o f variance, mad Student's t test o f means are used to d o c u m e n t these effects. In addition, a proposal to c o m p e n sate for these effects for i m p r o v e d accuracy is presented.

Some I0 )'ears have passed since the a p p e a r a n c e o f nmltichannel analyzers in the clinical laboratory. D u r i n g this time considerable e x p e r i e n c e with the weaknesses o f these machines Ires accunmlated. Single point standardization, nonlinear s t a n d a r d curves, and the complete lack o f r e f e r e n c e m e t h o d s against which to check accuracy have been constant sources o f

uncertainty for clinical chemists accust o m e d to traditional carefully controlled batch methods. F u r t h e r m o r e , the m e c h a n ical limitations o f the analyzers have forced the use o f p o o r m e t h o d o l o g y by chemists who knew better but had no choice but to meet the economic competition. Several investigators lmve recently questioned the accuracy o f n m n u f a c t u r e r s '

*Supported in part by National Institutes of iteahh grant 5-PO7-FR-00016, I)eparunel~t of Biomeny, Medical College of Virginia, Richnmnd, Virginia. tI)r. S.J. Kilpatrick,Jr., and the staff of the Biometry Department at Medical College of Virginia provided statistical and computational assistance in the preparation of this material and provided the use of their IBM 1130 computer. -Associate Professor of Pa!hology, Medical College of Virginia. Associate I)irector of I.aboratories and Chief of Clinical l'athology, McGuire Veterans Administration l lospltal, l/ichmond, Virginia.

31

HUMAN PATIIOLOGY--VOLUME 4, NUMBER

32

assay values for pooled lmman serum preparations as calibrating standards and quality control materials?" Althougll the printed values accompanying each lot of this material are Said to represent the pooled results of a number of reference laboratory assays, the accuracy of these printed results cannot be assessed because of turbidity, lack of primary standards for enzymes, and the impossibility of the use of water or other simple solvent standards because of viscosity and dialysis problems inherent in multiclmnnel analyzers. The only present avenues open to the laboratory director for improving tim perfornmnce of these extremely nsefld machines is to compare his resuhs with those of others tln'oughout tim country using the same methodology and qnality control materials and to try to approacli the pooled mean values of these participants and their pooled variability as a,1 apln'oximation of increased accuracy and precision. As an initial attempt at accuracy evalnation, various regional quality control programs lmve evolved, the basis for their effectiveness being very large serum pools suitable for use by many subscribers, and fairly rapid interlaboratory data transmi.ssion. Initially these p r o g r a m s used modifieda Shewhart 4 industrial control charts with a single serum pool large enough for many months of consecutive assays by participating laboratories. Variations of available quality control charting methodology inclnded tim average cusum,5 split sample, Ga and analysis of variance. 8,'a Nonlinearity of standard curves made it necessary to expand tim single pool methods to include a second "abnornml" pool to evaluate precision, and to some extent accuracy, of extreme values. The ilood of data produced by these enlarged quality control programs has stimulated a high degree of computerization bot]i in tim central office of tim quality control programs as well as locally in the clinical laboratory. Seligson m has recently summarized the overall effect of computerization on accuracy and precision in the clinical laboratory. In addition, specific computerization of charting teclmiqnes now includes average C H S l i n l , 11 split sample, r-''ta modified Shewhart, 14 one and two way analyses of variance, ~a and complete

l - - M a r c h 1973

quality control data base maintenance by relnote

t e r l n i n a l . 16

Resuhs fl'om one such regional quality control program in this laboratory recently led to an extensive graphical and statistical analysis of quality control resuhs comparing two manufacturers' lots of calibrating serum for the S*IA 12/60. This report describes the findings of the study. MATERIALS A N D M E T H O D S

Two lots of calibrating sermn w e r e purchased fi'om two different manufacturers during the seven months of the study. Each was stored in the laboratory refi'igerator at 5~ C. for no more than one month at a time prior to use and was supplied by the local dealer on a montldy basis. The first lot lasted four and 9he-half months and the second, two and one-half months. These were prepared daily and used according to manufacturer's recommendations with reference serum cups placed between every 10 positions on the sampler plate of the SMA 12/60. In addition, two lots of control sera were obtained in tim form of an abnormal and a normal serum pool from tim Virginia Regional Quality Control Program,* which were sufficient for the seven months of the study. A portion of the statistical analysis prepared by tiffs regional program is reported in this paper. These control sera were dispensed daily as blind random nornml and abnormal pool samples for assay by the SMA 12/60 during this study. Results were snbmitted t o tim Virginia Regional Quality Control l'rogram on a montldy basis for routine computerized statistical analysis. This analysis included monthly colnputation of individual means, standard deviations, and coefficients of variation as well as pooled values over all participants. In addition, ctnnulative parameters were provided as ah'eady described as well as Youdon plots for each assay metlmd. All chemical assays were performed ""q)r. Russell Briere, Director, Regional Quality Control l'rogranl, Virginia Society for Pathology, 3801 Patterson Avenue, Riclunond, Virginia 23221.

QUALITY CONTROL PROGRAMS AND LABORATORY DATA--RmDICK

on a Survey model SMA 12/61) with albumin, alkaline phosplmtase, bilirnbin, calcium, cholesterol, glucose, lactic dehydrogenase, phosphorus, total protein, transaminase, urea nitrogen, and uric acid with standard Technicon methodology. ~r No changes in methodology occurred during the stud)'. Additional statistical analyses to be described were perfornted on an IBM 1800 laboratory digital computer equipped with four disk and two tape drives, a card reader, line printer, 32k words of core, a ke)'board typewriter, and an analogue to digital converter for on-line data acquisition. Some studies were also performed on the IBM 1130 digital computer in the Biometry Department, which was equipped with a line printer, keyboard typewriter, card reader, disk drive, and 16k words of core. STATISTICAL ANALYSIS

ht addition to tile computations provided by tile Virginia Regional Quality Control Program, several other graphical and statistical maneuvers were performed in order to document the effects of the change in lots of calibrating serum. First, linear plots of time against laboratory results for each consituent were performed by computer using a line printer plotting program developed in this laboratory by the author. Results from portions of tltese plots in tim time region of interest are shown in Figure 1. In addition, two way analysis of variance (ANOVA) of the nornml-abnormal pool results for each constituent was performed by computer for tile duration of the study and then repeated with data obtained before the change of the mannfacturer's lot of calibrating serum and repeated again with data derived from tile other manufacturer's lot of calibrating serum. This effectively partitioned off another source of variation, "between manufacturer" variation. Details of this program and its computations appear in another work. ~5 Finally, al)propriate Student t tests of means TM were performed to test the null 1Wimthesis that the mean values of the individual constituents of the two lots

of calibrating sera were identical after determining homogeneity of variance. ~9

RESULTS

Examination of tile time course plots for tlm montll during which tile calibrating sertnn lots changed revealed striking trends upward or downward beginning on day 20, as shown in Figure 1 for both normal and abnormal pool results. The nornml pools for albumin, alkaline phosphatase, bilirubin, calcium, glucose, lactic d e h y d r o g e n a s e , l)ilosplIorus, t r a n s a m inase, and urea nitrogen showed definite trends. The abnormal pools for alkaline phosplmtase, bilirubin, calcium, glucose, lactic dehydrogenase, plmsplmrus, transaminase, and urea nitrogen also showed these trends. Trends observed in both abnormal and normal pools for the same test were observed to be in the same direction, indicating a possible intercept change as the standard curve for the method. T h e changes in the time course plots, which suggested mean change in nearly all channels of the SMA 12/60, were filrther confirmed by the monthly snmntary from the Virginia Regional Quality Control l'rogram for tile month in which the second lot of calibrating serum was instituted. These changes can be observed in Table 1 by comparing standard deviations of this laboratory with pooled standard deviations of all participants for each method. It would be expected tlmt the individual laboratory standard deviations would, on tile average, be less than that of all participants pooled, since tim latter standard deviation includes a between-laboratory error source that is not included in tile individual laboratory standard deviation. In this case nearly half tlm laboratory standard deviations actually exceeded the pooled method standard deviation, indicating tlmt a very large error source was influencing many channels of tile SMA 12/60 of this laboratory during tim month in which the lots of calibrating serum were cllanged. Examination of results from the two way ANOVA of the data fi'om this study revealed that all channels of the SMA 12160 except for glucose, plmsphorus, and total protein sltowed a drop in F ratios (Text continued on page 39.)

33

I]UMAN

PATItOLOGY--VOLUME

l - - M a r c h 1973

4, N U M B E R

NORMALPOOL 41

NORMAL POOL 48-

NORMALPOOL

18 I

40

t

],9 ~

4~

~

38

3.7

~.6

I

~

I 20

I

DAY

30

I01

20

30

DAY

DAY

NORMAL POOL

195 -

NORMAL POOL

87

NORMAL R3(X.

log

IO"5 Q, I

104 r 83

175 ~ io.3

IOZ

i

I00

i

DAY

C~Ay

2O

30

Z0

30

DAY

Figure I. Time course plots of quality control resuhs from assay of normal (A) and abm)rmal (B) serum pools from tile Virginia Regional Quality Control Program. Striking trends are al)parent for alkaline phosphatase, bilirubin, calcium, glucose, lactic dehydrogenase, phosphorus, transaminase, and uric nitrogen for both normal and abnormal pools. Similar trends are apparent in the normal albumin plot and the abnormal total protein plot. These changes occurred on day 20 concurrent with the installation of a new manufacturer's calibrating serum. (Figure 1 continued on pagcs 35 to 37.)

34

QUALITY CONTROL PROGRAMS AND LABORATORY. DATA--RIDDxcK

42

NORMALPOOL

NORMAL~ NORMALPOOL

75

1

E

146 P-..

74

40'

-.j 7.3

131

I

I

20

30

39

DAY

72

ZO

I

DAY

20 DAY

3O

NORMAL POOL 46

N O R M A L POOL

NORMALPOOL

IG

6~

0.0<

4.5

k r~ cL 44

A

E

15

~

4z

41

14

i 20

43

i

20 DAY

DAY

30

3O 40 I

20 OAY

30

Figure IA. Continued

35

H U M A N I ' A T H O L O G Y - - V O L U M E 4, NUMBER l - M a r c h 1973

188

ABNORMAL~>OOL

ABNORMAL POOL

29

ABNORMALPOOL 40 39 38 37 36 35 34

171 33

31 3O 29 30 2.7 26 I

27

z 20

2.5

I

30

I 20

15"I I

DAY

I

24

3O

I 20

DAY

l 3O

DAY

ABNORMAL POOL 130

ABNORMALPOOL

ABNORMAL POOL

133

265 k.

k

124

,3 Z60 124

255 115 1

2

.

1

2

0

1

i

I

20

30

DAY DAY

Figure lB.

36

i

ZO

I

DAY

I

30

QUALITY CONTROL PROGRAMS AND .LABORATORV DATA--RIDDICK

645 -

6.8

ABNORMALPOOL

ABNORMALPOOL ABNORMALPOOL

57

625

6.7

56 k

605

k 66

~ 55

585

g 6.5

565

6.4

545 20

30

OAY

i

54

i

i

20

30

1 0

53

DAY

a 3O

ABNORMAL POOL

222

ABNORMALPOOL

IO fi

ABNORMAL POOL 52

IO2 k

L. 99

l ~

E 178 t~

20 DAY

154 I

20

J 30

96

L 3O

9.(1

I

20 DAY

30

DAY

Figure lB. Contimted

37

T A B L E 1. VIRGINIA REGIONAL QUALITY CONTROL PROGRAM RESULTS FOR TIlE MONTI! DURING '~,VIIICll CALIBRATING REFERENCE SERUM LOTS I,VERE CIIANGEI) ~:

Test Name

Laboratory Standard Deviation

Pool

Units

Pooled Method Standard Deviation

gin. per 100 nil. gin. per 100 nil.

0.09 0.08

mU./ml. mU./ml.

2.23* 7.15*

Albumin

Normal Abnormal

0.08 0.05

Alkaline phostflmtase

Normal Abnormal

2.70 10.74

Bilirvbin

Normal Abnormal

0.26 0.53

rag. per 100 nd. rag. per 100 rid.

0.09* 0.24*

Calcium

Normal Abnormal

- 0.20 0.26

rag. per 100 ml. mg. per 100 ml.

0.20 0.24*

Cholesterol

Normal Abnormal

4.95 4.56

rag. per 100 ml. rag. per 100 nd.

6.84 5.37

Glucose

Normal Abnormal

0.72 4.88

rag. per 100 ml. nag. per I00 ml.

2.73 -t.88

Lactic dehydrogenase

Normal Abnormal

6.88 24.53

l'hosphorus

Normal Abnormal

0.07 0.12

rag. per 100 ml. rag. per 100 ml.

0.09 0.12

Total protein

Normal Abnormal

0.11 0.10

gin. per 100 ml. gin. per 100 nil.

0.14 0.11

Transanfinase

Normal Abnormal

5.26 20.03

Urea nitrogeq

Normal Abnormal

0.59 0.72

rag. per 100 ml. nag. per 100 nil.

0.86 2.73

Uric acid

Normal Abnormal

0.17 0.33

rag. per 100 ml. nag. per 100 nil.

0.14" 0.13*

mU./ml. mU./ml.

5.70* 18.41"

mU./ml. mU./nil.

3.83* 14.67"

* T h e asterisks indicate tile laboratory standard deviation exceeding method standard deviation and point to a major error affecting m a n y channels. T A B L E 2. COMI'ARISON OF TWO-~rAY A N O V A ov ENTIRE SEVEN MONTIIS' DATA WITII F RATIOS COMPUTED SEPARATELY BEFORE DAY 20 AND FROM DAY 2{) ONe"

Between, Days F Ratio Test Name Albumin

38

Entire 7 Months

Before Day 20

After Day 20

Additivity F Ratio Entire 7 Months

8.12*

1.83"

2.00*

19.11"

Alkaline phosl~hatase

15.60"

1.69"

2.66*

938.40*

Before Day 20 16.80* 1.69 NS

Bilirubin

61.2(}*

3.32*

5.33*

1388.64"

95.69*

Calcium

6.0-t*

3.27*

3.87*

24.56*

6.8-t*

Cholesterol

2.66*

Glucose

1.36 NS

l.actic d e h ) d r o g c n a s e

4.38*

1.92"

After Day 20 10.61" 19.26" (}.24 NS 11.34 ~`

5.13"

5.37*

15.10"

14.38"

11.09"

13.44"

35.43*

! 17.87"

110.66"

296.22*

19A}3"

19.19" 286.84*

1.43 NS

l'hosphorus

2.18"

17.8(}*

9.16"

47.0t*

682.28*:

Total protein

4.33*

4.99*

2.59*

15.17*

283.58*

Tra,lsaminase

i 6.31 *

2.30*

3.31"

896.07*

2.62 NS

Urea nitrogen

2.41 *

3.87"

4.80"

20.13*

12.03*

Uric acid

3.Ot*

2.01"

3.19*

62.68*

24.32"

0.05 NS

74.95* 18.74* 5.06 NS 41.60*

t A new lot of calibrating reference serum Was begun on day 20. Note tile p r o f o u n d drop in most F ratios when between lot variation is partitioned o u t b y this method. * T h e asterisk indicates that the value exceeds tile critical value at p = .95. NS = not significant.

QUALITY

CONTROL

I'P, O G R A M S

for eitlmr between days or additivity partitions in COlnparisons o f resnlts front the entire seven months with tim results o f c o l n p u t i n g separate A N O V A b e f o r e and a f t e r the lot change (Table 2). Eaclt o f tltose large F ratios over the entire seven montlts o f the study indicates significant "runs" d u r i n g tim study, ntany o f wlticlt becante less significant when A N O V A was r e p e a t e d a f t e r segregating "between malmfacttlrers"

error.

T h e actual mean vahles and coefficients o f variation o f quality control restilts for the two lots o f calibrating sel'unt are shown in Table 3; results o f Student's t test o f means are also indicated in this table. All channels showed significant (p = .95) m e a n differences between quality

AND

LABORATORY

DATA--RIDDICK

control results obtained fi'Oln each o f tim two lots o f calibrating serunt, with the exception o f cholesterol, glucose, phosp h o r n s , and ui'ic acid. Cholesterol and p h o s p h o r u s were borderline cases in that the normal pool mean clmnges were not significant but the abnorntal pool ineans differed sigifificantly. T h e coefficients o f variation o f those tests wltose means did not change significantly d u r i n g the lot cllange or the significance o f whose ntean c h a n g e was ambignotis d u r i n g the lot change also showed an increase in one coefficient o f variation when calculated as two coefficients o f variation, one b e f o r e the pool clmnge and a n o t h e r after. This indicates that some o t h e r source o f e r r o r was present that

T A B L E 3. COMI'ARISON OF ~IEAN VALUES BEFORE AND AFTER INSTALLATION OF NEW LOT OF CALIBRATING REFERENCE SERUM ON DAY 2 0 AND POOLED COEFFICIENTS OF VARIATION WITI! BEFORE AND AFTER COEFFICIENTS OF VARIATION

Coefficient of Variation Pool

Mean Before Day 20

Mean After Day 20

Pooled

Before Day 20

Albumin

Normal Abnormal

3.89* 2.8 I*

4.06* 2.93*

3.3 3.6

2.7 2.8

2.3 3.3

Alkaline p h o s p h a t a s e

Normal Abnormal

41.48" 166.42*

44.92* 177.21"

7.0 7.0

6.4 6.5

4.9 5.9

Bilirubin

Normal Abnormal

1.24* '2.76*

1.79* 4.08*

21.3 21.9

10.0 8.6

10.8 10.4

Calcium

Normal Abnormal

10.51 * 12.77*

10.26" 12.43*

2.2 2.4

2.0

1.6

'2.'2

1.7

Cholesterol

Normal Abnormal

164.82 NS 126.95*

162.80 NS 124.05*

4.9 -t .7

4.2 4.6

5.9 4.6

Glucose

Normal Abnormal

84.77 NS 259.39 NS

82.86 NS 269.39 NS

5.1 2.6

5.8 2.1

2.8 !.5

Normal

142.15* 587.30*

150. ! 1" 609.84*

5.4 4.2

3.8 3.6

5.9 4.1

Test Name

Lactic d e h y d r o g e n a s e

Abnornh|l

After Day 20

Phoslflmrus

Normal Abnormal

4.{}4 NS 6.67 NS

4.01 NS 6.64 NS

2.6 2.7

3.0 3.0

1.5 2.0

Total protein

Normal Abnormal

7.43* 5.56*

7.33* 5.48*

1.6 1.7

1.6 1.6

1.3 1.2

Transaminase

Norlnal Abnormal

47.75* 165.15*

55.00" 2{)0.01"

9.4 , 9.9

7.6 3.4

4.3 2.1

Urea n i t r o g e n

Normal Abnormal

15.51" 51.22*

14.88" 50.58*

4.11 1.7

3.3 1.5

3.7 1.6

Uric acid

Normal Abnormal

5.0 4.1

4.1 4.5

6.2 2.7

4.37 NS 9.42*

4.42 NS 9.65*

*Tile asterisks indicate m e a n value pairs whose S t u d e n t t tests o f m e a n s exceed t h e critical values at p = .95 before day 20 a n d f r o m d a y 20. NS indicates not significant. In almost every case, significant differences in m e a n values result f r o m t h e two lots o f calibrating r e f e r e n c e sera with striking increases in pooled coelficients o f variation.

39

HUMAN PATI1OLOGY--VOLUME

4, N U M B E R l - M m r h

may have concealed any significant mean change present for these tests. For the r e m a i n i n g tests s h o w i n g significant changes in m e a n values accomp a n y i n g calibrating s e r u m lot changes, coetficients o f variation fnrther con-

firmed a large source of error in pooled coelficients o f variation. When coefficients o f variation were recalculated for quality control results fl'om each lot, substantially lower coelticients o f variation occurred in each case, i,tdicating segregation o f a significant error source, "between xllanufacturer" el'rOl-.

DISCUSSION T h e s e statistically significant differences in the imrformance of the SMA 12/60 concurrent with a change in lots o f calibrating s e r u m indicate that, at least in the case o f two nmnufacturers, printed values provided by the manufacttlrer c a n n o t be relied u p o n for accuracy in calibrating the S M A 12/60. Further, we have no evidence that calibration o f o n e lot is m o r e accurate than that o f the o t h e r lot. In addition, assessment o f the absolute accuracy o f these sera is impossible, as water standards c a n n o t be used with the S M A 12/60. It would appear that the only way to r e d u c e this major contribution of lot changes to between-day error would be to calibrate each new lot of calibrating s e r u m against the old lot, while nmintaining a carefid c h e c k on deterioration. Outside control s e r u m sources must also be used to evahmte accuracy, such as the

Virginia Regional Quality Control Program. This will require much expensive and redundant analytical work, which might be averted if m a n u f a c t u r e r s o f 12/60 were all required to use the sante g r o u p o f r e f e r e n c e laboratories. This would not solve the p r o b l e m o f accuracy but would go a long way toward providing

unifi)rm clinical laboratory assays across the United States.

4o

1973

REFERENCES 1. llerman, T. S., and Farrell, E. C.: Variation in pellet weights, nonprotein constituents, and enzylne activity within single lots of commercial quality control serum. Clin. Chem., 17: 6 t 6 - 6 t 7 , 1971. '2. Ilchnan, E. A., Reiugold, 1. M., and Glcason, I. O.: Plea for standardization of commercial calibratioll materials for automated instruments. Clin. Chem., 17:1144, 1971. 3. l.evey, S. I.., and Jennings, E. R.: The use of control charts in the clinical laboratory. Amer. J. Clin. l'ath., 20:1059-106fi, 1950. 4. Shcwhart, W. A.: ht Economic Control of Quality of .M,mutactured l'roducts. Van Nostrand, New York, 1931. 5. Page, E. S.: Continuous inspection schelncs. Biometrika, 41:l(i0-115, 1954. 6. l)orsey, I). B.: Qt,ality co,m'ol in hematology. Amcr. J. Clin. Path., 40:457-464, 1963. 7. ttcggcn, I). W., Ncwm:m, !t. A. 1., and Keller, M.D.: A dual quality control systeln for large clinical laboratories. Ame,'. J. Clin. l'ath., 58: 37-42, 1972. 8. Goozen, J. A. t1.: The use of control charts in the eli,ileal laboratory. Clin. Chim. Act,,, 5: 431-438, 1960. 9. Amen,a, J. S.: Analysis of variance, control charts, and the clinical laboratory. Amer. J. Cliq. Path., 49:842-849, 1968. 10. Seligson, D.: Effect of computers on precision and accuracy. In Westlake, (;. E., and Bennington, J. I.. (Editors): Automation and Manageinent in the Clinical I.aboratory. Bahimore, University Park Press, 1972, pp. 235-267. 11. Riddick, J. H., Jr., and Giddings, N. W.: Computerized preparatio,a o f average ct,su.m charts for clinical chemistry. Clin. Biochem., 4:156161, 1971. 12. Riddick, J. H., Jr.: Computerized charts for quality control. Bull. l'ath., 10:406-408, 1969. 13. Riddick, J. H., Jr., and Johnston, C. l.., Jr.: Hematology control using computerized range charts. Lab. Mcd., 3:32-34, 1972. 14. Riddick, J. If., J,.: Automated quality control with an IBM 1800 comlmter. Amcr. J. Clin. l'ath., 53:176-180, 1970. 15. Riddick, J. tt., Jr., Flora, R., and Van Meter, Q. L.: Computerized prel~ar:,tion of two way analysis of variance control dmrts for clinical chemistry. Clin. Chem., 18:250-257, 1972. 16. Ridclick, J. 11., Jr., Sullivan, M. L., Kitchen, E., and Reynolds, R.: Quality control in the clinical laboratory using the remote computer tcrnfinal. Clin. lfiochem., 5:125-132, 1972. 17. SMA-12-60. Tarry,turn. New York. "l'cchnicon Corporation, I tJ67. 18. (;oldstcin, A.: Biostatistics. New York, The Mac,nillan Co., 1964, pp. 51-55. 19. Anderson, R. L., and Bancroft, R. A.: Statistical Theory in Research. New York, McGraw-[lill Book ('ompany, 1952, pp. 80-83. McGuire Veterans Administration I lospital 1201 Broad Rock Road Richmofld, Virginia 23249