498 Statistical Methods
As you can see from Figure 12-7, no mean score falls outside the con-
trol limits. The lower control limit is 77.462, the mean subgroup average is
84.17, and the upper control limit is 90.878. There is no evident trend to the
data or nonrandom pattern. You conclude that there is no reason to believe
the teaching process is out of control.
Because we conclude that the process is in control, in contrast to what
the typical student might conclude from the data, there is no evidence that
this professor’s performance was better or worse in one semester than in
another. The raw scores from the last three semesters are misleading. A
student might claim that using a historical value for s is also misleading,
because a smaller value for s could lead one to conclude that the scores
were not in control after all. The exercises at the end of this chapter will ex-
amine this issue by redoing the control chart with an unknown value for s.
One corollary to the preceding analysis should be stated: Because even
one professor experiences wide fluctuations in student evaluations over
time, apparent differences among various faculty members can also be
deceptive. You should use all such statistics with caution.
You can close the Teacher Control Chart workbook now, saving your changes.Calculating Control Limits When s Is Unknown
In many instances, the value of s is not known. You learned in Chapter 6
that the normal distribution does not strictly apply for analysis when s is un-
known and must be estimated. In that chapter, the t distribution was used in-
stead of the standard normal distribution. Because SPC is often implementedvalues
are in
controlFigure 12-7
Control chart
of teacher
scores