Many have been taught that they must remove outliers prior to analysis. This is because much of modern statistics is concerned with creating a mathematical model for the data. Because all these models are created using algorithms, they tend to be severely affected by any unusual or extreme values.

Therefore, to use these mathematical techniques to obtain useful and appropriate models, it’s often necessary to polish up the data by removing the outliers. However, the act of building a model implicitly assumes that the data are homogeneous enough to justify the use of a model.

For example, the histogram in figure 1 has a bell-shaped curve superimposed. This curve is based on the average and standard deviation statistic for all 100 values in the histogram. It’s neither wide enough nor tall enough to provide a good fit to the data. The histogram in figure 2 contains the 93 values left after the seven extreme values (the four lowest and three highest) were deleted. Now the curve based on the average and the standard deviation statistic does a much better job of fitting the data. Thus, it’s true that outliers can undermine our efforts to create a model for our data.

This issue is the first of three consecutive CMSC show-focus issues that highlight the yearly Coordinate Metrology Systems Conference. The CMSC is the largest U.S. trade show focused solely on large-scale 3-D metrology. Attendance has grown each year, with last year reaching nearly 600 attendees. All the key players in large-scale 3-D measurement are there representing every large-scale 3-D measurement technology, including laser scanners, structured-light scanners, laser radar, photogrammetry, theodolites, articulated arms, indoor GPS, and more.

Our CMSC cover story this month focuses on the use of articulated arms (portable coordinate measurement machines) to align collimators at CERN’s Large Hadron Collider in Switzerland. Steering two high-energy beams traveling in opposite directions around a 27 km-circumference accelerator so that they collide head on at a predetermined point requires the most accurate in 3-D metrology equipment. You can read how they did it starting on page 22.

Quality Digest is proud to have been the sole media sponsor for the CMSC show for four years, and we look forward to continuing our coverage of the ever-evolving field of large-scale 3-D metrology.

Eighty-four doctors treated 2,973 patients, and an undesirable incident occurred in 13 of the treatments (11 doctors with one incident and one doctor with two incidents), a rate of 0.437 percent. A p-chart analysis of means (ANOM) for these data is shown in figure 1.

This analysis is dubious. A good rule of thumb: Multiplying the overall average rate by the number of cases for an individual should yield the possibility of at least five cases. Each doctor would need 1,000 cases to even begin to come close to this!

The table in figure 2 uses the technique discussed in last month’s column, “A Handy Technique to Have in Your Back Pocket,” calculating both “uncorrected” and “corrected” chi-square. Similar to the philosophy of ANOM, I take each doctor’s performance out of the aggregate and compare it to those remaining to see whether they are statistically different. For example, in figure 2, during the first doctor’s performance, one patient in the 199 patient treatments had the incident occur. So, I compared his rate of 1/199 to the remaining 12/2,774.