by W. J. Youden National Bureau of Standards
I
STATISTICAL DESIGN A
W O R K B O O K
F E A T U R E
E C
Presentation for Action Dual reference program for cement industry illustrates value of a vivid presentation of the results of an investigation
MANY workers feel disappoint ment at the small amount of interest aroused by their findings. Nat urally enough, these workers would like to see some action taken on the basis of the results they obtain. Often the trouble lies in the way the evidence is presented to those who have either the opportunity or responsibility for putting the i n formation to work. Statistical Design and Presentation Technique
The importance of statistical de sign in the efficient conduct of an investigation has been the thesis of many of these columns. I t must be admitted that one of the drawbacks of some of the more complex sta tistical designs is the amount of statistical background required to follow the chain of computations upon which the experimental con clusions are based. The fact that considerable statistical skill is often required to extract any meaning from the data, has often acted either as a barrier to the adoption of sta tistical design or as a deterrent to action. M e n who have to make decisions are more apt to have confidence if the data "speak for themselves." M u c h of the impact of the statistical quality control chart depends upon its presentation. A n operator can see at a glance just how he is doing and in consequence he does a better job. Coordination of Test Procedures
M a n y companies have plants scat tered in widely separated areas. Test procedures are used to ensure that the same product produced i n different plants meets a common standard. Test procedures themselves vary i n different hands and locations. Co-
ordination of test procedures is necessary to ensure that results are truly comparable wherever tests are carried out. Devising and policing test pro cedures is a continuing task, partic ularly i n an era of new product development. The sum total of effort expended i n this endeavor to maintain production standards must be very large. Many A S T M com mittees are involved in the conduct of interlaboratory tests. Invariably these programs reveal that different laboratories do not agree with each other nearly as well as would be desirable. A l l this effort runs afoul of the deep-seated conviction that when another laboratory does not check your results the other labora tory is probably at fault. O r both laboratories may preserve their mor ale by maintaining that the sam ples were different. Little improve ment can be expected as long as each one takes the attitude that it is the other fellow who needs to i m prove his testing. Dual Reference Test Program
Use of two different reference mate rials, A and B, sent simultaneously to each of a number of laboratories, has important advantages. Data can be presented i n a form that sharply exhibits shortcomings i n the test procedure as well as difficulties of individual laboratories. The pres entation suggests the nature of the difficulties and in a convincing manner. Also the performance of different test procedures can be com pared visually without recourse to statistical arithmetic. The presentation is graphical and consists of drawing the familiar χ and y axes at the bottom and left of a piece of graph paper. O n the I/EC
W
χ axis a scale is laid off that covers the range of results reported for material A. A similar scale for material Β is laid off on the y axis. The pair of results, one for material A and one for material B, from each laboratory determines a point which is plotted on the graph paper. Such a plot is shown i n the graphs for two different tests recently per formed by 32 cement laboratories. (The laboratories were selected by lot from a larger study.) After the points have been plotted, a line is drawn vertically so that half the points lie to the left and half to the right of the line. This line inter sects the χ axis at the median value for the results reported for material A. A similar line drawn horizon tally for Β has equal numbers of points above and below the line. The two lines so drawn divide the paper into four quadrants. I t is interesting to speculate (in ad vance) about the distribution of these points among the four quad rants under different sets of cir cumstances. I f all the laboratories, by some miracle, are without any bias, the results being subject to the random errors of precision only, the four quadrants should be nearly equally populated w i t h points. O n the other hand, if some of the labora tories are afflicted w i t h constant errors so that some tend to obtain high results and others low results, the points will be concentrated in the upper right and lower left quadrants at the expense of the other two quadrants. I f the graph shows this to be the case, an undesirable state of affairs is revealed without point ing the finger at any particular laboratory. I t might be argued that half the laboratories are all right, even if all the points reside in these two quadrants. This is falORKBOOK
FEATURES
83A
I/EC
STATISTICAL DESIGN
•
lacious because, if there are lab oratories without biases, half of their points should lie in the upper left and lower right quadrants. No, i f an overwhelming majority of the points lie in the lower left—upper right pair of quadrants the procedure itself requires revision or more care ful specifications. One cannot fairly criticize the laboratories in this event. Consider the reaction of the in dividual laboratories when each, i n privacy, has circled its point in this anonymous report. (There may be very good reasons for not identifying the individual points i n the cir culated report.) A laboratory far out i n either quadrant stands out dramatically. I f a single test ma terial, A, has been used, the results might have been shown graphically by projecting all the points on to the χ axis. This point then appears as an extreme point at either the left or right end of the axis and the analyst may believe that he got a bad sample. The analyst will be shaken with the point plotted from two materials, because then he has to maintain that he got high (or low) samples for both materials. I n point of fact the sampling argument can be disposed of pretty quickly. I f inhomogeneity of the stock used for the samples really dominated the situation, then there should be samples that are i n fact high and i n fact low i n about equal numbers. I n assigning samples, pairings high i n A and high i n B, high i n A and low in B, low i n A and high i n B, and low in A and low in Β should occur equally often and 84 A
A Workbook Feature
the points should be evenly spread over the four quadrants. Conse quently i f the points are clustered in the two quadrants, the outermost points should prompt the correspond ing laboratories to seek for a pro nounced bias i n their results. Any investigation w i l l turn up isolated points far out i n either the upper left or lower right quadrants. These quadrants correspond to be ing high on one material and low on the other. This immediately sug gests a typographical error i n re porting, a mistake i n calculation, or some mishap i n the conduct of the test. N o laboratory can afford to ignore such a location for its point. A little consideration shows that a test procedure that is excessively vulnerable to individual laboratory bias will give a long narrow ellipse running from lower left to upper right. Improvements i n the test procedure should be reflected by a broadening of the oval until it be gins to approach the ideal circular distribution. Experience shows that even the very best procedures fall short of the ideal. I f dispersion is the same for both materials, the long axis of the ellipse will be 45° to both axes. Departures from this angle indicate more scatter with one mate rial than the other. When the distribution is more equitable among the quadrants, there is still the question as to whether a perhaps undesirably large scatter reflects imprecise technique or sampling limitations. A graphi cal device can be used here to dif ferentiate between sampling and measurement sources of variation. I f there are k laboratories, k/2 samples of double size are pre pared for each test material. Each of these double size samples is carefully quartered into two samples that should be as identical as pos sible. The two halves for each sample are assigned to laboratories paired at random. I f sampling is the trouble, the points when plotted should tend to appear in k/2 doublets like double stars i n the heavens. Although it is clear that even as few as one third of these points (picked at random) would throw light on the state of affairs, the larger number of points makes a more substantial impression. I f the
INDUSTRIAL AND ENGINEERING CHEMISTRY
number of laboratories is limited, more points can be obtained by send ing around a second pair of ma terials (both different from the first pair). A second graph is prepared and the two graph papers are su perimposed, so that the axes coincide. The two sets of points can then be represented on one sheet using the coincident axes to determine the quadrants. I f the two points for each laboratory are i n reasonable proximity, there will be a verification of good (or poor) work. Such a verification could not be lightly brushed aside. The intent of this approach has been to reveal concisely to all con cerned the performance of a test procedure. The chart carries the sort of conviction that hopefully might lead individual laboratories to take steps to improve the testing. I t also protects the laboratories from unjustified criticism when all of them are having trouble with the proce dure. I n the discussion of this dual sample technique no space has been left to comment upon the two test procedures illustrated. Readers can form their own opinions.
Our authors like to hear from readers. If you have questions or comments, or both, send them via The Editor, l/EC, 1155 16th Street N.W., Washington 6, D C . Letters will be forwarded and answered promptly.
