### COMMON MISTEAKS
MISTAKES IN
USING STATISTICS: Spotting and Avoiding Them

# Analyzing Data Without Regard to How They Were Collected

Using
a two-sample t-test when observations are paired is one example of
this. Here is another:

Example:^{1} An
experiment was conducted to study the effect of two factors
(pretreatment and stain) on the water resistance of wood. Two
types of pretreatment and four types of stain were considered. For
reasons of practicality and economy, the experiment was conducted with
a split-plot design as follows:

Six entire boards were the
whole plots. One pretreatment was applied to each board, with the two
pretreatments randomly assigned to the six boards (three boards per
pretreatment). Then each pre-treated board was cut into four smaller
pieces of equal size (these were the split-plots). The four pieces from
each entire board were randomly assigned to the four stains. The water
resistance of each of the 24 smaller pieces was measured; this was the
response variable.

If the correct split-plot analysis is used, the
interaction of
pretreatment and the effect of pretreatment are not statistically
significant, but the effect of stain is statistically significant.

However, if you were to do an analysis of variance incorrectly assuming
that the experiment used a crossed design, with the 6 treatment
combinations randomly assigned to the 24 smaller pieces of wood, the
analysis would indicate that the interaction and effect of stain are not statistically
significant, whereas the effect of pretreatment
is -- a very different conclusion.

Some of the many considerations to take into account in deciding on an
appropriate method of analysis include:

Notes:

1. For details (including data), see Potcner
and Kowalski, How to Analyze a Split-Plot Experiment, Quality Progress,
December 2004, pp. 67 - 74.

Last updated August 28,
2012