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rules are somewhat of an art. The bottom line is that
today’s models are incomplete and certainly not validated.
The lack of adequate analytical models has been noted by
others. Breuhaus pointed out that it is a dubious assumption
that one knows all of the important cues and their
interrelationships (ref. 72). Heffley et al. stated that when
a modeler begins to assemble all of the components that
are believed to influence the pilot-vehicle loop in simulation
that one notices the fragmentary nature of, and the
serious gaps in, the quantification of the component
characteristics (ref. 73). More empirical results from
systematic and realistic investigations are needed before
useful analytical models can be created.
V1
V2
V3
V4
V10
-10 -8 -6 -4 -2 0 2 4 6 8 10
-2
0
2
4
6
8
10
12
Vertical velocity, ft/sec
Altitude, ft
Figure B5. Predicted phase-plane responses.
81
Appendix C—Example of Repeated-
Measures Analysis
A researcher wants to know if the differences among
collected data are due to a manipulated experimental factor,
or if they are due to random effects. If data are taken from
a random sample of individuals, each of whom has
experienced a different combination of the experimental
factors, then experimental error may be attributed to two
effects. The first effect is sampling error and the second
effect is error resulting from differences among the
individuals.
Repeated-measures allows the differences among
individuals to be accounted for in the analysis. This is
accomplished by having each individual experience each
experimental manipulation. It is a technique often used
when subjects are available for a long period of time, such
as in a research institution. Details of repeated-measures
theory may be found in Myers (ref. 54). Only a brief
overview will be given here. An example of the data
processing involved is given next.
The example uses the pilot compensation ratings for
Task 1 in section 3 (15° yaw rotational capture). A plot
of the data is given in figure 15. Table C1 contains the
average compensation rating given by each pilot for all of
the combinations of translational and rotational motion.
The first column gives the pilot number, 1–6. The second
column indicates if translational motion was present. A
1 means translational motion was present, and a zero
means it was not. Column three indicates if rotational
motion was present. Column four gives the average
compensation rating, where the average is taken over the
repeated runs performed by each pilot. Here the values
correspond to 0 = minimal, 1 = moderate, 2 = considerable,
and 3 = maximum tolerable.
The purpose of the statistical analysis is to determine if
pilots provide better compensation ratings for particular
motion configurations. Specifically, it can be determined
if the ratings are influenced by the presence of translational
motion, by the rotational motion, or by a combination
of the two motions. Although figure 15 suggests
that the translational motion is likely to be the dominant
factor, the statistical analysis provides quantitative
information on how often such variations are due to
random effects. So, the analysis indicates how solid the
inferences drawn from the data are.
Table C1. Average pilot compensation ratings for yaw
experiment Task 1.
Pilot (i) Translational
on (j)
Rotational
on (k)
Average
rating (Y)
1 0 0 2.67
1 0 1 2.25
1 1 0 1.75
1 1 1 1.75
2 0 0 2.25
2 0 1 1.75
2 1 0 0.75
2 1 1 0.00
3 0 0 1.25
3 0 1 1.25
3 1 0 1.00
3 1 1 1.00
4 0 0 3.00
4 0 1 3.00
4 1 0 3.00
4 1 1 3.00
5 0 0 2.50
5 0 1 2.50
5 1 0 0.25
5 1 1 0.00
6 0 0 1.75
6 0 1 2.00
6 1 0 1.25
6 1 1 1.00
To determine whether the differences noted owing to
translational motion are statistically significant, the ratio
MStrans / MStrans/pilot is formed. The numerator of this ratio,
MStrans is the between-groups mean square. The denominator
of this ratio, MStrans/pilot, is the population error
variance. The higher this ratio, the more likely that the
differences between the two translational configurations
are due to the effect of translational motion and that they
are not random results. The relations for these terms are:
F
MS
MS
trans
trans pilot
=
/
(C1)
MS
SS
a trans
= trans
( -1)
　
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