Page 392 - Sensing, Intelligence, Motion : How Robots and Humans Move in an Unstructured World

RESULTS—EXPERIMENT ONE 367

MS AB
F = ∼ F [(I−1)(J−1),N−IJ] (7.15)
MS w

where MS AB represents the Interaction Mean Square between factors A and B.
The ratio has an F distribution with (I − 1)(J − 1) degrees of freedom in the
numerator and (N − IJ) degrees of freedom in the denominator.
In the case considered now, the results of F test may show that the effect of
visibility factor on the path length depends on the type of interface utilized in
a given task. In other words, there is an interaction between the visibility factor
and the interface factor. One way to express interactions is by saying that one
effect is modified (qualified) by another effect.
When the data indicate an interaction between factors, the notion of a main
effect has no meaning. In such cases, tests of simple effects can be more useful
than tests of main effects. Simple effect tests are done via one-way analysis
of variance across levels of one factor, performed separately at each level of
the other factor. For example, even if we suspect an interaction between the
visibility factor and the interface factor, we might undertake simple effect tests
for the visibility factor separately at the virtual and physical level, respectively,
and see what kind of conclusions can be made based on the results.

7.4.5 Implementation: Two-Way Analysis for Path Length
We are now ready to perform the analysis of variance on the Experiment One
data. From other tests above, we already know that the direction factor has a
significant effect on the path length. We know, further, that the left-to-right task
is significantly easier for the subjects (it results in shorter paths) than the right-to-
left task. We now want to analyze the combined effect of visibility and interface
factors on the subjects’ performance. Even though the underlying data are not
known to obey the normal distribution, we justify using the ANOVA by the F
test being known to be robust.
The data set has been first separated into the LtoR and RtoL data sets. The
ANOVA variables are:

• Dependent variable: Path length.
• Independent variables:
1. Visibility factor, with two levels: visible and invisible.
2. Interface factor, with two levels: virtual and physical.

In the tables of results that appear here, the following terms are used:

df effect—degrees of freedom for a given effect, including main and interac-
tion effects.
MS effect—Mean Square for an effect, including main and interaction effects.
df error—degrees of freedom for the error variance, or Mean Square Within.