In
Example 1.1: Designing and Analyzing a 2^{(7-4)} Fractional Factorial Design,
we studied the effect of 7 different factors on the speed with which a
bicyclist can climb a hill (see also, Box, Hunter, and Hunter, 1978).
Let's suppose that on one of the runs for this hypothetical experiment,
the gear was incorrectly adjusted to the second level rather than the
first (lowest) level so that the run was no longer consistent with the
original design. Such imprecise settings will alter the properties (confounding,
resolution) of the experiment; however, unless the experimental runs are
grossly mismatched (different from the desired values), valid and meaningful
analyses can still be conducted. These so-called botched designs can still
be analyzed correctly in *STATISTICA Experimental Design*

**Botching the Experiment.** To begin, open the example
data file *Cycling.sta.*

*R*ibbon
bar. Select the Home tab.
In the File group, on the Open menu, select Open
Examples to display the Open
a STATISTICA Data File dialog box. Double-click the Datasets
folder, and then open the data set.

Classic
menus. On the __ File__ menu, click

Shown
here are the original settings for the factors; note that text values
(e.g., *Up*, *Down*) were also entered to identify the respective
settings. You can toggle between text and numeric values in the data file
by clicking the __ Show/hide text labels__ button.

Let's
assume that for the second run, the gear was not actually shifted to the
low position; instead, it was shifted to the second lowest position. To
make this modification, enter a -0.8 in the second case of the variable
*GEAR*. The data will now look as shown below.

**Specifying
the design**. Select the __ Experimental
Design (DOE)__ analysis.

Ribbon
bar. Select the Statistics tab,
and in the Industrial Statistics
group, click DOE to display the
__ Design
& Analysis of Experiments__ Startup Panel.

Classic menus. From
the *Statistics** - Industrial Statistics & Six Sigma* submenu, select
Experimental Design (DOE) to
display the __ Design & Analysis of Experiments__ Startup Panel.

Then
select *2**(k-p) standard designs* *(Box, Hunter, and Hunter)*
from the Startup Panel and click the *OK* button. In the __ Design
& Analysis of Experiments with Two-Level Factors__
dialog, click on the

**Reviewing results**. Now, click the *OK*
button, and the __ Analysis of an Experiment with Two-Level Factors__
dialog will be displayed.

Note that the DESIGN SUMMARY statement now indicates that this is a botched design.

**Main effects**. Now click on the __ ANOVA/Effects
tab__ and click the

As with Example 1.1, *STATISTICA*
will fit a simple main effects model, without interactions. Remember that
our initial design is of __resolution__ III (3); hence, the two-way interactions are confounded with the
main effects, and they cannot be estimated from this design. The first
numeric column of the __spreadsheet__ shown above contains the *Effect*
estimates. These parameter estimates can be interpreted as deviations
of the mean of the negative settings from the mean of the positive settings
for the respective factors. Recall that even though our design is botched
(i.e., for one run, the seat setting was at -.8 instead of -1, the scaling
was still for a minimum of -1 and a maximum of 1. So, for example, the
Effect column gives us the estimate of what happens when the factor goes
from its low value to its high value. When the seat position went from
down (-1) to up (+1), the time to climb the hill increased by an average
of 2.92 seconds. The second numeric column contains the effect *Coefficients*.
These are the coefficients that could be used for the prediction of climb-time
for new factor settings, via the linear equation:

*y*_{pred.} = b_{0} + b_{1}*x_{1} + ... + b_{7}*x_{7}

where
*y*_{pred.} stands for the predicted
climb-time, *x _{1}* through

See
also, __Experimental Design Index__.