Quality Progress - American Society for Quality

of why you would want to (or need to) include blocks within designs. It also pointed out
clearly that you need to understand the experiment before applying statistical tools that
may not be appropriate. In an effort to practice DOE data analysis, I decided to look at
the data for Example C (a full factorial study of the strengths of plastics). After exploring
the data, I feel some additional analysis sheds further light on the results. From the data
set presented one might infer that the data itself is questionable, so any analysis based on
it is also questionable. The first 16 runs constitute a full factorial experiment, while the
next 16 runs replicate all of the measurements. However, the replicate set is quite
different from the first set, as revealed by a simple two-sample t-Test. Block 1 (runs 1-8)
and Block 4 (replicates in runs 25-32) are fine. These were both done at the high
temperature setting and the mean strength of the plastic is the same for the two blocks.
Two-sample T for Block1 vs Block4
N Mean StDev SE Mean
Block1 8 62.94 6.26 2.2
Block4 8 64.34 4.78 1.7
Estimate for difference: -1.40000
95% CI for difference: (-7.41544, 4.61544)
T-Test of difference = 0 (vs not =): T-Value = -0.50 P-Value = 0.624
However, Block 2 and Block 3, done at the low temperature setting, are problematic. The
means are quite different, well outside the 95% confidence interval. In a nutshell, the
replicate experiment didn't produce replicate data.
Two-sample T for Block2 vs Block3
N Mean StDev SE Mean
Block2 8 57.81 3.05 1.1
Block3 8 62.96 3.06 1.1
Estimate for difference: -5.15000
95% CI for difference: (-8.45230, -1.84770)
T-Test of difference = 0 (vs not =): T-Value = -3.37 P-Value = 0.005
This implies a few things. First, it isn't surprising that it is difficult to determine which of
the factors - particularly temperature - are significant, since the blocks aren't behaving as
expected. Second, the data is most likely suspect, as evidenced by the lack of
repeatability. Possible explanations might be: 1) There is a significant, uncontrolled
factor at play here. 2) A mistake was made with the preparation and/or handling of the
samples. 3) An error was made in the data entry.
In any case, the data strongly suggests rechecking at least part of the experiment,
especially the parts at the low temperature setting. These problems cast doubts on what
was otherwise a valuable article.
Tim Folkerts
CRE
FolkertsT@bartonccc.edu
17256 Handling the Human Side of Change
Cyndy Berrones
Nov-12-03