COLOR MATCHING THROUGHOUT THE WORK WEEK: AN INDUSTRIAL APPLICATION OF THE SWALLOWTAIL- DIFFERENCE EQUATION

by Stephen J. Guastello Marquette University

This article considers a multilevel system problem involving color perception of individual human beings, man-machine interactions, and changing social factors. Pre- vious research on the same system found critical differences in color matching perform- ance over a 24-hour period, modeled by a cusp catastrophe. The hypothesis now tested is whether critical differences in group performance occur in a regular weekly cycle. Subjects were 13 color matchers and 30 printers who worked rotating shifts. Data were drawn from production records for 27 pairs of multicolor jobs performed over three four-week periods. The swallowtail hypothesis was upheld for three criteria: color matching time (R' = .55), printing press time (R' = .55). and printing paper conserved or wasted (R' = .83). Job length (difficulty), time period (dengting organi- zational dynamics taking place), and whether the job pair occurred in the Monday- Wednesday, or Thursday-Saturday part of the week (semicycle) served as control variables.

KEY WORDS: group, organization, information processing, man-machine system, catastrophe theory, color matching, weekly trend.

Eu

This paper investigates weekly trends in color matching efficiency in an industrial setting. In an earlier investigation on the same group-produced data, a diurnal cycle was found which was empirically described by a cusp catastrophe (Guastello, 1982a). The present effort considered what appears to be a socially-induced cycle, the weekly trend, as a swallowtail catastrophe model. Taken together, the primarily physiological process of color matching and perception, man-machine interactions, ambient orga- nizational change, and mathematical mod- eling compose a multilevel systems prob- lem.

Small color differences Wandell (1982) reviewed a number of

geometric and stochastic theories pertain- ing to the measurement of small color dif- ferences. While the work that follows does not proceed from any particular one, it does address some general attributes of them all. Besides the basic scientific objective of de- termining the best depiction of a phenom- enon, one objective of the theories is to determine standards for manufacturing and governfnent use for what are the allow-

able variations in color specificity for a manufactured product. A true color match seldom exists, as error is introduced in the manufacturing process. The problem be- comes psychological when the question is asked: How much physical difference in color constitutes a psychological differ- ence?

Additional variance in similarity judg- ment is introduced when color decisions are made under stress. Time pressure to com- plete a match, concern for cost of materials, and the need to match several colors at once in a design are forms of stress that industrial color matchers often experience. Types of color vision fatigue include desen- sitivity to brightness and intensity, color desaturation, target disappearance, and background fade (Bartley, 1976). Stress in- troduced by shift work has been reported to affect color decisions for individuals (Hartley & Shirley, 1976), and a manufac- turing group of color matchers (Guastello, 1982a). In the latter example, matching efficiency (time to complete a criterion match relative to time and color standards) was empirically described by a cusp catas- trophe with job length (bifurcation) and a

213

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214 STEPHEN J. GUASTELLO

time variable (asymmetry) as controls. Job length was an index of matching difficulty; the difficulty was attributed to color drift induced by printing cylinder wear. The time measure indicates which one of three four- week periods the work was performed in, during which some organizational changes were introduced The organizational status of the printing and color matching depart- ment was equalized and supervisors reas- signed; the changes were directed at human relations improvement. A similar cusp was found for another criterion, paper con- served or wasted. A fold catastrophe for circadian variation in printing press time was also discovered.

Weekly trend in industrial perform- ance Weekly trends in industrial performance

or accidents have received far less attention than the circadian effect. Two somewhat related effects may be gleaned from existing

Sunday

findings. Risk is high during the first half of the week compared to the second half, with sometimes an upturn just before a weekend or other nonwork period. (“Don’t buy a car built on Friday afternoon.”) Risk is also higher on booking-up day, on which weekly production scheduling begins or in which the deluge of new job orders comes in (Colquhoun, 1971).

Popular folklore offers the piece of (re- touched) office graffiti in Figure 1. The pattern of attitude change expressed by the dog may well be responsible for perform- ance fluctuations where they have been noted. It is possible that attitude variations may only affect performance when aggre- vated by appropriate environmental con- ditions.

Catastrophe hypothesis It is hypothesized that critical (discon-

tinuous) fluctuations in performance in the course of the week follow the swallowtail

Work Week

Monday Tuesday A

Wednesday Thursday Friday FIG. 1.

Sat u r d ay

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COLOR MATCHING 215

FIG. 2.

catastrophe rule depicted in Figure 2. The model is evaluated using the swallowtail- difference equation (Guastello, 1982b):

(1) Az = PO + P1.21~ + P2z13 + P3cz12 + &a,

where

(2) such that y is the criterion at one or the other point in time, X is its lower limit, and O its standard deviation. Control variables are similarly normalized. Three dependent measures are investigated color-matching time expressed in positive and negative de- viations from production standard, the amount of paper saved or wasted (measured in feet), and printing press time which was also expressed in deviations from standard. The swallowtail or bias factor c, was whether the job occurred in the first or second half of the work week (semicycle). Bifurcation factor, b, was job length, and asymmetry factor, a, was accounting pe- riod, denoting which one of three consecu- tive four-week periods the job was executed.

2 = (y - X ) O

METHOD

Subjects Personnel for the study consisted of 13

color matchers and 30 rotogravure printers from a Midwestern firm. Specifics of the

setting remained the same as in the pre- vious color matching study.

Measures The job order was the unit of analysis.

Production records from a finite set of jobs contained all data for variables listed above. All jobs were woodgrain designs in usually three, but sometimes four or five colors. Job runs were sorted into 27 pairs in which they were matched by job length within accounting period. The value of b used in the analysis was the average of the two job lengths. The following differences were assembled, Monday vs. Tuesday jobs, Wednesday-Tuesday (different) jobs, Thursday-Friday, and Saturday-Friday.

Analyses Swallowtail models were tested using Eq.

1, plus skew and lag variables after the primary variables were entered into the equation. Since the subjects to variables ratio was low (about 4 to l ) , models were tested first with lag without skew, then with skew without lag. Also, since power against the null hypothesis was low given the num- ber of cases, a p-value of .25 was accepted as “significant but possibly speculative,” as opposed to the usual type of acceptance given to lower p-values (cf., Schmidt, Hunter, & Urry, 1976). A forward selection procedure with hierarchical inclusion was used.

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216 STEPHEN J. GUASTELLO

As an additional check on the semicycle effect, swallowtail models were calculated again with job length replacing semicycle in the c position; the comparison would tell if the semicycle effect was merely a product of anomolous distribution of high risk jobs throughout the week.

For comparison, swallowtail models were compared against the next closest alterna- tive, the explicit difference model:

(3) AY = Po + P I ~ + Pzb + P3c

in which no special normalization proce- dure was used.

RESULTS

Swallowtail models for the three de- pendent measures with skew terms and semicycle in the c position appear in Table 1.

The swallowtail model accounted for 55% of the variance in the color match time criterion ( F ( 7 , 19) = 3.29, p < .05). Weights for all terms were significant except for c.2. Quintic terms were not entered for any

TABLE 1 SWALLOWTAIL MODELS-c = SEMICYCLE.

R* F F Simple Multiple Predictor Overall ~ e t s r R'

Color Matching Time

zI' 9.11d -.I2 .02 ZIS 8.fiSd -.09 . I1 Accounting period 5.7W -.40 .31

dependent measure due to insufficient tol- erance or F-to-enter. Thus, only models with skew terms are reported.

The swallowtail model also accounted for 55% of the printing press time variance ( F ( 7 , 19) = 3.24, p < .05). Significant weights were obtained for the two power potentials, bifurcation, and job length as an asymmetry term (skew).

The swallowtail model accounted for 77% of the paper variance (F(7,19) = 9.33, p < .001). It was noticed that on the second step the two power potentials accounted for 69% of criterion variance, both with sig- nificant weights. When all variables were entered the F-ratios for power weights dropped below 1.0, indicating that variance accounted for by those terms was redun- dant with variance accounted for by job length and accounting period.

Swallowtail models with job length in the c position appear in Table 2. Models did not improve the prediction of color-match time or press time, with R2 = .55 and 5 4 , respectively, and fewer significant weights resulting. An improvement was noted for paper consumption ( R 2 = .83, F(7, 19) = 13.35, p < .001), in which both power po-

TABLE 2 SWALLOWTAIL MODELS-c = b = JOB LENGTH.

RZ' F F Simple Multiple Overall Beta r nZ Predictor

Color Matrhinn Time Ziz.Semicycle 0.87 -.01 .31

4.91' -.I2 .02 5.61' -.09 . I 1

4.64' .I0 .31 z14 Zi2.Joh length

Semicycle Job length 5.922 .38 .49 ZI3

Zlz.Joh length n.tx5 .04 . I I 0.04 .lo .IS

3.29 2.27' -.06 5 5 .38 ZI*Job length Printing Press Time

~ Accounting period 6 . 7 9 -.40 .36 Z? 3.3ob -61

z13 5.19 -63 Zi2&micycle 0.44 -.33 ZI-Job length 2.84. -25

Job length 4.3C .03 Semicycle 3.34" 0.26 -.I3

Accounting period 0.02 -.38

Paper Coneerved/Wasted-Step 2

2: 13.91 -.63 213 26.47. 22.88 -.71

Pawr Conserved/Wasted-Final S t e ~

.37

.40

.41

.41

.42

.55

.55 .38

.39 6 9 .66

ZI' 0.73 -.63 .39 ,

ZIS 0.57 -.71 .69 ZI'.Semicycle 0.36 -.33 .69 ZI.Job length 5.922 - 2 6 6 9 Accounting period 0.03 .M .69 Job length 6 .47 .31 .77 Semicvcle 9.33. 0.25 -.06 .77 6 9

Op < .26; b p < .lo; " p c .OX d p < .01;'p < .W1: ' Adjusted Rz using Wherry's formula.

. . 5.W .38 5 1 .Job length

Semicycle 3.2R 1.70' -.OK 3.5 38 Printine Press Time

~

2 1 4 2.5.5. - 3 1 .37 zi3 4.922 - 6 3 .40 ZIZ.Joh length 0.22 - 2 5 .40 ZI*Job length 0.00 -.31 .46 Accounting period 0.02 -.38 .46

3.1fib .03 5 4 .Job length Semicycle :3.20' 0.0s -.I3 .54 3 7

Paper Conserved/Wasted

ZI' 4.2gb -59 .39 z13 2.00. -.71 .69 ZI2.doh length 6.RIc -.46 6 9 Z,.Joh length 4.03' -.26 .R1 Accountina perird n.oi -.os .RI doh length 0.19 3 1 .R2 Semicycle 13.35. 1.69 -.06 .tx? 3 7

.p < 25; ' p < .IO;'p< .05: dp < .Ol; ' p 4 ,001;' Adjusted HZuslnK Wherw's formula.

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COLOR MATCHING 217

TABLE 3 EXPLICIT DIFFERENCE MODELS.

8s Overall Beta Simple Multiple r R' Predictor

-~ ~ ~ ~~

Printing Press Time Accounting period 4 . 4 6 -.38 .I5 Job length 0.05 -.03 .I5 Semicycle 1.64. 0.83 -.I3 .18 .Ol

Pawr ConservedNested

Accounting period 0.01 -.05 .00 Job length 2.31. .31 .I0 Semicycle 0.83 0.00 -.06 .I0 .00

Color Matching Time

Accounting period 4.Mb -.40 .16 Job length 3.2& .38 21 Semicycle 2.87b 0.05 -.06 21 .I1

. p < .25; b p < . 1 0 : ' p < .05: d p < .01; * p < .001; 'Adjusted R z using Wherry'n formula.

tentials, bias and bifurcation were signifi- cant; semicycle contributed significantly to asymmetry.

Swallowtail models performed consider- ably better than explicit difference models, the latter accounted for 27%, 18%, and 10% of color matching, press time, and paper variance, respectively, (Table 3).

DISCUSSION

It appears safe to conclude that weekly trends in color matching and other indus- trial activities do exist. The trend found in this study followed the swallowtail model in Figure 1, with Tuesday and Friday as high risk days, Monday and Thursday rel- atively low risk; Wednesday and Saturday could go either way. While prior research found a weekly cycle to be more true than false at the individual level, it is now con- cluded to be true at the group level when aggrevated by task and social conditions. The social conditions captured by the ac- counting period variance emanated from the organizational level of the system.

While circadian variations in human per- formance have links to concommitant physiological changes, the weekly trend ap- pears to be social in origin. Its first known report may be traced to the Book of Genesis, obviously predating the industrial revolu- tion, which, in turn, suggests that booking- up in an of itself is not a primary cause of the cycle. Rather, the cycle has an impact that predisposes commercial behavior. Booking-up with high risk work, on the other hand, has a more dynamic link to

behavior fluctuations. In the present appli- cation, high risk (longer) jobs were begun as early in the week as possible in order to be finished by the end of the week.

The weekly cycle for color matching was not as strong as the circadian effect for the same group and conditions using different job pairs, possibly on account of the re- duced sample size. The same was true for paper conservation; the bifurcation term, job length, has a positive effect on color matching, but a negative one of paper con- servation, as in the circadian rhythm prob- lem. The weekly trend on press time, how- ever, appears stronger than the circadian trend, which was just a fold catastrophe.

The organizational changes captured by the a parameter have an interesting impact on the circadian and weekly trends. In the circadian cusp, low values of a result in negative-to-negative performance differ- ences, middle values result in positive-to- negative differences, and high values result in positive-to-positive changes. In the weekly swallowtail, low values of a have the same effect as in the cusp, middle and higher values have the same effect as the middle values in the cusp. When the polar- ity of a reversed as in the present situation, high a has positive-to-positive changes re- sulting. The central lesson is that a well- chosen organizational development strat- egy can compensate losses which have been incurred by the circadian or weekly cycles. The semicycle effect had only a speculative impact in the swallowtail model, and a t that only in the a position. It would be more likely to have an effect in the swallowtail position if in the latter part of the week the high-low risk cycle inverted in some con- ditions, but not in others; in that event it would be more worthwhile to identify the conditions under which inversion takes place. The latter is a condition similar to booking-up with high risk work in the latter half of the week.

Suppressor variables are those which have nonsignificant simple correlations with the criterion, but significant weights in the regression equations, or negative simple correlations but positive weights (or vice versa). Suppression effects of all vari- eties were noted in the swallowtail models,

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218 STEPHEN J. GUASTELLO

and accounted for the accounting period variable entering the equation for color matching time in the third step instead of the fifth. Suppression effects of the former variety were found in the circadian rhythm example. Suppresssors are considered rare, and tend not to hold up on cross-validation; those that do tend to gain special notoriety (Cohen & Cohen, 1975). While it may be premature to speculate, suppressor effects may be regularly expected in empirical ca- tastrophes.

The two color matching catastrophes of- fer a number of new research directions. It is presently unknown how many vision functions are affected by the swallowtail or cusp cycles; nor is it known how many types of stress may act as bifurcation factors. The same questions may be asked of audio and other sensory abilities, and complex infor- mation processing behaviors. Other psy- chological or biological effects already known to show circadian variation may be studied as catastrophes as well. Other work inputs and outputs and hospital intake and census trends are likely to show swallowtail effect; such information may be useful in staffing decisions. Finally, while there is much work to be done yet on the measure- ment of small color differences, it is hoped that legal or manufacturing recommenda- tions will take into consideration cyclic var- iations in color work efficiency, as it ap-

pears than man-machine system attributes that are not specifically related to the colors themselves influence the matching process.

REFERENCES Bartley, S. H. Visual fatigue. In E. Simonson & P. C.

Weiser (Eds.), Psychological aspects and physi- ological correlates of work and fatigue. Spring- field, Illinois: Thomas, 1976.

Cobb, L. Multimodal exponential families of statistical catastrophe theory. In C. Taillie, G. P. Patil, & B. Baldessari (Eds.), Statistical distributions in scientific work. Holland Reidel, 1981.

Cohen, J., & Cohen, P. Applied multiple regression/ correlation analysis for the behavioral sciences. Hillsdale, New Jersey: Lawrence Erlbaum As- sociates, 1975.

Colquhoun, W. P. Biological rhythms and human per- formance. London: Academic Press, 1971.

Guastello, S. J. Color matching and shift work: An industrial application of the cusp-difference equation. Behavioral Science, 1982,27, 131-139 (a).

Guastello, S. J. Moderator regression and the cusp catastrophe: Application to two-stage personnel selection, training, therapy and policy evalua- tion. Behavioral Science, 1982,27, 259-272 (b).

Hartley, 1. R., & Shirley, E. Color name interference a t different times of the day. Journal of Applied

Schmidt, F. L., Hunter, J. E., & Urry, V. W. Statistical power in criterion-related validity studies. Journal of Applied Psychology, 1976, 61, 473- 485.

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(Manuscript received September 10, 1982)

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