Information Technology Reference
In-Depth Information
•
The evaluation order for the pieces of music agreed by the group after discussion.
•
The order of preference for another actor as mentor or ally.
To enable us to make ordinal comparisons without the problems of individual scale
choice we used a relative z-score. This is employed differently from the normal use
of a z-score since we consider each individual subject as though they had their own
personal distribution. Thus each subject's personal scale is normalised according to
the following equation.
z
−
score
(
i
)
=
(x
i
−
μ
i
)
/σ
i
where
i
is a particular actor, x
i
is a value given by that subject for a piece of music,
μ
i
is the mean of the subject's values and
σ
i
is the standard deviation of the values
adjusted for a small sample (Moroney
1963
, p. 137) such that
/
√
n where
n
is
σ
i
= σ
4 in this case.
In this way all the scores are normalised such that all their scores are:
•
distributed about a common mean of zero
•
the spread of their evaluations is made equal.
Thus the only significant information is the ordering. However, since all scales are
now normalised the relative ordering (nearer or further from other pieces of music)
information can also be compared. Each subject is represented as a single point in a
four-dimensional music space where each dimension represents one of the pieces of
music they are judging.
Having eliminated personal scaling differences we can see if there are any simi-
larities in choice combinations. We now look to see how independent the four music
dimensions are. We are asking the question, “
Does knowing a person's first choice
make it possible to predict their second choice?
”
However, from the correlation analysis of pairing pieces of music, no significant
correlation is found (Fig.
14.1
). This indicates that there is no pattern of common
approval between items; i.e. approval of Stravinsky does not imply approval of, say,
Stenhammar. (See example in Fig.
14.1
).
The result was also corroborated using the raw (non z-score normalized) analysis
and using optimised principle component analysis (Billinge and Addis
2004
). This
result confirms that we can treat music space as a set of independent dimensions so
that distance calculations in this space conform to normal n-dimensional geometry.
The raw un-normalised values were also used to see if there was any correlation
between the group scaling and the average of all the individuals' scales. We found
that these were positively correlated (see Fig.
14.2
). This result suggests that partic-
ipation within the discussions has some influence on the individual with a statistical
significance
r
0.7584. For 22 experiments, as looked up in statistical tables, an
r
-value of 0.6524 is better than 0.001 probability that a correlation exists, i.e. there
is a 0.1 % chance of this happening accidentally. For the 24 experiments we did this
would be even better, i.e. less likely to occur by chance.
By contrast, and as we have noted in previous findings (Billinge and Addis
2004
)
no information about music experience or content is exchanged during these group
=
