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Objectifying Information About Dance
Dr. Don Herbison-Evans
Technical Report 322
Basser Department of Computer Science
University of Sydney
(updated 1 March 1999)
INTRODUCTION
Dance by its nature is about people, emotions and aesthetics. Any data about dance
is, in the first instance, bound to be subjective.
A variety of techniques have been evolved in science for the assessment of information
which enhance the objectivity of the results. These can be applied to data from dance.
They include: the design of sampling methods, the design of data collection methods,
statistical analysis, and pilot studies. These techniques can enhance the reliability
and accuracy, and hence the objectivity, of the results.
SAMPLING METHODS
The data for study must be obtained from some group or population of subjects. Depending
on the study, the population may be everyone in the world, or the students in some
particular class, or any appropriate group of people. If that group is small enough,
all of the subjects can be studied; but sometimes the group is too large, or the
time available too short, and then a subset of the population must be selected for
study.(Barr, 1953, 158).
A difficulty then arises: choosing subjects who are representative of the population.
There may easily be overlooked indirect relationships between the selection procedure
of the subjects and the information being sought.
To avoid this, two techniques may be useful.
One is to select the subjects from a complete list of the population by a random
procedure. This can be done using tables of random numbers (Abramowitz, 1965, 991).
Alternatively, a pseudo-random number generator can be used (Pollard, 1979, 236).
The other technique is systematic selection. If the size of the population is 'n',
and 'm' subjects are required for study, then every 'p'th member of the complete
list is chosen, where p = n/m (Barr, 1953, 163)
A further problem arises when some chosen subject cannot be reached. Leaving incomplete
coverage or choosing a replacement are both particularly likely to lead to bias (Barr,
1953, 163).
DATA COLLECTION
Four basic methods are available for obtaining data:
(1) literature survey
(2) questionnaires
(3) interviews
(4) observation
(1) The learned and critical literature can provide valuable data for research on
dance; indeed for studies extending back beyond living memory, there is little alternative.
Any study attempting to provide a baseline of more than a few decades will need to
use the literature.
(2) Questionnaires can be useful if the subjects can read and write (Burroughs, 1975,
106). The preparation of questionnaires has many traps for the unwary. One problem
is simply that of persuading the subjects to answer and return them. The likelihood
of this can be improved by making the questionnaire short, by personal contact with
the subjects, by using a suitable covering letter, by making the questionnaire look
attractive, and by enclosing a return paid envelope (Burroughs, 1975, 106).
The questions themselves need careful wording. It is important to avoid complexity,
ambiguity, bias, and causing offence (Barr, 1953, 67).
(3) Interviews have similar problems to questionnaires: The wording of questions
must again avoid complexity, ambiguity, bias and causing offence. The personal contact
in an interview can encourage subjects to be more forthcoming than when using a questionnaire,
but interviews are more time consuming. The interviewer can also clarify questions
if they are not understood, but care must be taken not to invalidate comparison of
answers between the different subjects (Burroughs, 1971, 105).
(4) Observation can derive data from either controlled or natural situations. Data
from experiments in controlled situations may appear to give the more objective data,
as this most closely approaches the techniques in those most objective of sciences:
physics and chemistry. However in dance, where both the subjects and the observer
are people, complex interactions can occur, which can distort the results. Even if
the observer is obscured by for example a one-way mirror, the results can be distorted
by the nervousness or other emotional reactions of the subjects.
This effect on the subjects of the fact that they are being observed can be reduced
by using natural situations for the observations. This however carries the ethical
question of how right it is to observe people without informing them of the fact
that their privacy is being invaded (Burroughs, 1971, 99).
ANALYSIS
Four different types of data are obtained by any of the above methods of data collection:-
(a) continuous eg., height
(b) ranked but discrete eg, number of siblings
(c) unraked and discrete eg., hair colour
(d) free eg. why began dancing
Data of type (d) must be converted into one of the other types for analysis. This
is done by summarising it into categories, which must be exhaustive, mutually exclusive,
and independent (Burroughs, 1975,44).
Data of types (a) and (b) may often be treated the same way, in which case it may
be described as ordered.
Measured data is typically affected by a number of parameters, only a few of which
are themselves available for measurement. The effects of the unmeasured parameters
is conveniently assumed to be random and is called noise. Statistical analysis consists
of trying to discern relationships between measured parameters despite the noise.
The four basic methods used for statistical analysis are:
(i) significance tests
(ii) regression coefficients
(iii) correlation coefficients
(iv) analysis of variance
(i) Significance tests are useful when an unranked but accurate parameter 'q' affects
the population on q. The dependence of the population can be judged by a chi-squared
test (Burroughs, 1975, 266). Its interdependence on another parameter 'p' that is
ranked but noisy can be judged using the means and standard errors of 'p' for each
value of 'q'. These can be compared by 't' and 'F' tests, which give the likelihood
that the null hypothesis is true ie., that 'q' is irrelevant (Burroughs, 1975, 167).
(ii) Regression coefficients are useful when one or more ordered but noisy parameters
(dependent variables) are to be correlated with one or more ordered but accurate
parameters (independent variables) (Barr, 1953, 257). The regression does not have
to be linear in terms of the independent variable(s), but does have to be linear
in the coefficients. The procedure depends on fitting a mathematical form to the
data which minimises the sum of square deviations of the noisy values from the curve.
(iii) Correlation coefficients are useful when there are two parameters which are
both ordered and noisy affecting the population (Barr, 1953, 283). The coefficient
is a measure of the angle between regression lines obtained by assuming each parameter
in turn is noise free. A coefficient near 1.0 between two parameters typically means
that they are either a cause and effect pair, or that both have a common cause. The
decision about which is cause and which is effect requires the elucidation of the
mechanisms of dependence, which is quite a different study. With noisy data, this
can be impossible to determine objectively.
(iv) Analysis of variance is a generalisation of the correlation coefficient to the
case where more than two ordered noisy parameters are measured. (Burroughs, 1975,
168). It studies how combinations of parameters interact with the population.
PILOT STUDIES
When some issue needs to be investigated, and the methods of sampling, data collection
and analysis have all been tentatively decided upon, it is still desirable to perform
a pilot study. This can reveal unexpected problems, and allow redesign of the investigation
to overcome them. For example in one study of how students rate teachers versus how
fast students advanced, a correlation coefficient of 0.05 was obtained (Barr, 1953,321).
This was unexpected.
Another advantage of doing a pilot study is that by appropriate scaling, the amount
of effort required for the full study can be more accurately assessed. A comparison
between available effort and this assessed effort may indicate a need for the re-design
of the study.
REFERENCES
Abramowitz M, and Stegun, I.A., Handbook of Mathematical Functions, Dover, New
York, 1965.
Barr, A.S., Davis, R.A, and Johnson, P.O., Educational Research and Appraisal, Lippicott,
Chicago, 1953.
Burroughs, G.E.R., Design and Analysis in Educational Research, Educational Review,
Birmingham 2nd Edn: 1975.
Pollard, J. H., A Handbook of Numerical and Statistical Technique, Cambridge University
Press, 1979.
About Don Herbison-Evans
Don's parents were dance teachers who could not
afford baby sitters, so he was taken along to their
classes, so has been dancing ever since he could walk.
Later on he obtained several degrees, including a
doctorate from Oxford University in Physical Chemistry,
and has pursued careers in Microwave Engineering,
Astronomy, and Computer Graphics. He brings an unusual
perspective to the study of dance. He and his partner Anna have been competitive
Latin-American dancers for approximately 14 years.
Home page > > Don Herbison-Evans email > > don@socs.uts.edu.au
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