Question 19.4: TESTING FOR SHARPNESS IN INKJET PRINTERS A computer magazine......
TESTING FOR SHARPNESS IN INKJET PRINTERS
A computer magazine company regularly tests products from different manufacturers for differences in various aspects of quality. For its next issue, it would like to test sharpness of printed images across three popular brands of inkjet printers. It purchases one printer of each brand, prints several pages on each printer, and measures the sharpness of image on a 0–100 scale for each page. A subset of the data and the analysis appear in Figures 19.27 and 19.28. (See the file Printers.xlsx.) They indicate that printer A is best on average and C is worst. Why might these results be misleading?
Objective To use randomization of paper types to see whether differences in sharpness are really due to different brands of printers.
This is a single-factor design, where the single factor, brand of printer, is varied at three levels. Suppose, however, that there is another factor, type of paper, that is not the primary focus of the study but might affect the sharpness of image. For the sake of discussion, suppose further that all type 1 paper is used in printer A, all type 2 paper is used in printer B, and all type 3 paper is used in printer C. Then it is very possible that the apparent effect of printer is really an effect of paper type. Specifically, it is possible that type 1 paper tends to produce the sharpest image, regardless of the printer used. We can’t know this for sure, but it is certainly possible given our (flawed) experimental design. The solution is to randomize over paper type. For each sheet of paper to be printed by any printer, we randomly select a paper type. This will tend to even out the paper types across the printers. Then if the average sharpness of image from printer A is still higher than the averages from the other two brands, we will have more confidence that this is due to differences in printers, not types of paper. Note that it is not necessary to use equal numbers of sheets of each paper type in the experiment. For example, if paper type 1 is the most used paper type by actual users, then we might use more of it in the experiment. The important point is that no printer is fed a much higher proportion of any paper type than any other printer.
We illustrate how this might be implemented with random numbers in Figure 19.29. Based on actual usage, suppose that approximately 50% of the paper used in the experiment is of type 1, 35% is of type 2, and 15% is of type 3. This information is entered in columns F and G. Then to randomize paper types across printers, we enter random numbers in column B with the RAND() function, enter the formula
=IF(B2<=$G$3,1,IF(B2<=$G$3+$G$4,2,3))
in cell C2, and copy down column C. Of course, Figure 19.29 shows only the experimental design. Now it is up to the company to run the experiment with the printers and paper types shown (one piece of paper per row), measure the sharpness levels, and perform the same statistical analysis as described in Section 19-2. That is, after we randomize and collect the data, the analysis is the usual one-way ANOVA. This time, however, because we have randomized over paper types, we can be more confident that any observed differences across printers are indeed due to the printers themselves and not differences in paper.
