Page 397 - Sensing, Intelligence, Motion : How Robots and Humans Move in an Unstructured World

372 HUMAN PERFORMANCE IN MOTION PLANNING

objective of data analysis is to test whether the training and/or visibility fac-
tor improves the overall human performance in motion planning. If in terms of
both dependent variables the improvement in subjects’ performance turns out
to be significant, follow-up tests on the separate effects on human performance
should be conducted, to explain which specific aspects of human performance
are responsible for such effects. Multivariate analysis of variance (MANOVA) is
a good technique for data analysis of overall effects [128].
Multivariate analysis of variance is conceptually a straightforward extension
of the univariate ANOVA technique described above. Their major distinction is
that if in ANOVA one evaluates mean differences on a single dependent vari-
able, in MANOVA one evaluates mean vector differences simultaneously on two
or more dependent variables. In addition, the MANOVA design accounts for
the fact that dependent variables may be correlated. For instance, two depen-
dent variables in Experiment Two, the path length and completion time, are
indeed relatively highly correlated, with the correlation coefficient 0.79. In this
case, MANOVA should provide a distinct advantage over separate ANOVAs.
In fact, performing separate ANOVA tests carries an implicit assumption that
either the dependent variables are uncorrelated or such correlations are of no
importance.

7.5.1 The Technique
Assumptions. The first and partly second of the three following assumptions
are required by MANOVA (and are the same for the statistical tests considered
above):
1. Observation scores are randomly sampled from the population of interest.
Observations are statistically independent of one another.
2. Dependent variables have a multivariate normal distribution within each
group of interest. This means that (a) each dependent variable is dis-
tributed normally, (b) any linear combination of the dependent variables
are distributed normally as well; (c) all subsets of the variables have a
multivariate normal distribution. In practice, it is unlikely that this and
the next assumption are met precisely. Fortunately, similar to ANOVA,
MANOVA is relatively robust to violations of these assumptions. In prac-
tice, MANOVA tends to perform well regardless of whether or not the data
violate these assumptions.
3. Homogeneity of covariance matrices. That is, all groups of data are assumed
to have a common within-group population covariance matrix. This can be
likened to the assumption in ANOVA of homogeneity of variance for each
dependent variable, or the assumption that correlation between any two
dependent variables must be the same in all groups. If the number of sub-
jects is approximately the same in the experimental groups, a violation of
the assumption of covariance matrix homogeneity leads to a slight reduction
in statistical power [128–130].