Page 380 - Sensing, Intelligence, Motion : How Robots and Humans Move in an Unstructured World

RESULTS—EXPERIMENT ONE 355

age group have a noticeable effect on the subjects’ performance in motion
planning tasks.
• The second, more pointed analysis addresses separate effects of individual
factors on subjects’ performance—the effect of interface (virtual versus
physical), scene visibility, and the direction of motion. This study makes
use of tools of nonparametric analysis and univariate analysis of variance.
Only brief summaries of the techniques used are presented below. For more
details on the techniques the reader should refer to the sources cited in the
text below; for details related to this specific study see Ref. 121.

7.4.1 Principal Components Analysis
We attempt to answer the following questions:

1. To what extent are the factors used—interface (virtual or physical), scene
visibility, and direction of motion—indicative of human performance?
2. Can these factors be replaced by some “hidden” factors that describe the
same data in a clearer and more compact way?
3. Which factor or which part of the factor’s variance is most indicative of
one’s performance in a motion planning task?
4. Do the patterns of subjects’ performance differ as a function of their gender,
college specialization, and age group?
5. Can we predict one’s performance in one task based on their performance
in another task?

Principal Components Analysis (PCA) addresses these questions based on
analysis of the covariance matrix of the original set of independent variables
[122, 123]. In our case this would be the covariance matrix of a set of two-
level tasks. The analysis seeks to identify “hidden” factors—called the principal
components—which turn out to be eigenvectors of the sample covariance matrix.
The matrix’s eigenvalues represent variation of the principal components; the sum
of eigenvalues is the total variance of the original sample data and is equal to
the sum of variances of the original variables.
With the principal components (eigenvectors) conveniently ordered from the
largest to the smallest, the first component accounts for most of the total variance
in the sample data, the second component accounts for the next biggest part
of the total variance, and so on. The first component can thus be called the
“most important hidden factor,” and so on. This ordering sometimes allows the
researcher to (a) drop the last few components if they account for too small a
part of the total variance and (b) claim that the data can be adequately described
via a smaller set of variables. Often attempts are made to interpret the “hidden
factors” in physical terms, arguing that if the hidden factors could be measured
directly they would allow a significantly better description of the phenomenon
under discussion.