A necessary part of the option change process is determining the kinds of
modification that will deliver increased share, improved advantage or reduced
disadvantage.
This will obviously invoke a review of attributes, supporting processes,
etc. likely to change appeal. The changes sought are those able to deliver a
change distribution that will appropriately modify an antecedent option appeal
distribution. This will enable achievement of the change objectives through a
modified or "new" option.
An "antecedent option" for the purposes of research is a
reference option to which variations may be added or subtracted to obtain
further appeal evaluations. It may describe a past or currently existing
option, a baseline scenario for a proposed future option, or simply one
possible scenario on its own or amongst others. Similarly, "option
changes" may be currently existing attributes of an option or possible
variations. A "new option" simply refers to the appeal distribution
of the antecedent option modified by the option change.
A recommended methodology for evaluating potential change is:
1.
Rating
the appeal of an antecedent option.
2.
Rating
the appeal of the same option
with modification
.
3.
Analysing
each in the context of the relevant selection set.
4.
Measuring
the net effects as the differences between the
antecedent and modified results on appeal, advantage,
disadvantage, and share.
This provides the required answer in a direct and readily appreciated
manner. Some idea of the distributional dynamics involved can be obtained by
subtracting, casebycase, antecedent from the modified appeal to yield the
"change" distribution. You can analyse this in relation to the prior
distribution to assess the relative distribution "weights" which
yield the given results.
These are the relationships being
intuitively guessed when option modifications are being selected. Clearly,
there is considerable underlying complexity and this is a major factor
contributing to the rather mixed results achieved in practice from
"improvements". Without applying the above evaluation methodology,
or, without a clear understanding of the underlying relationships, the results
for any modified option are somewhat unpredictable. Effective development of
new options will usually be an iterative process involving a range of possible
modifications, evaluation and reevaluation.
While commonly not essential, some appreciation of these complex
underlying relationships may be helpful in considering possible avenues for
option modification, point to likely limitations, or, provide a basis for
reviewing
counterintuitive results.
Option modification changes the appeal of an option to an individual
depending on the prior option appeal, the appeal of the change, and the
respective weights to be assigned to each source of appeal.
When concern moves from individual change to changing groups, obtaining
the desired results may be quite challenging. The focus moves from changing a
point on a scale to changing appeal distributions. The difficulty is that
option modification may increase appeal for some individuals while decreasing
appeal for others, and amongst all to varying degrees. The end result is that
changes amongst the parameters of appeal for the option modification, with
respect to the prior option, can yield results requiring a convoluted
understanding of parameter interrelations. Differential weighting of the two
sources of change may enhance or inhibit the outcome.
Distribution outcomes for modified options, and thereby their share, advantage
and disadvantage, are not the result of random relationships between ratings
for the prior option and the option modification. Rather the modified
distribution is the result of parameter entanglement displaying varying degrees
of obscurity.
While attention is bound to concentrate on factors known or thought to
be associated with target parameters, nontarget parameters are unavoidably
involved. It is quite possible for intuitively promising changes to end up
being counterproductive. An important reason for creating and gathering
data on a wide range of possible changes and change variants is the difficulty
of anticipating these outcomes. Indeed, some of the most valued changes may
involve synergistic or "missing link" relationships. These are as
likely
to emerge from intuitive or creative thinking as from structured analysis.
Further compounding this complexity is the need to translate
relationships between the prior option, the option modification and the
modified option, out of and into the context of the casewise adjusted data
relationships between the options in the appropriate selection set.
To appreciate possible avenues for
change and to interpret obtained change results, there is a need to obtain at
least a theoretical feel for how particular change distributions, together with
antecedent options, generate outcomes for modified options.
The full character of the impact of the combined antecedent and change
appeal distributions will not be obvious. Nevertheless, it is possible to
provide some indications on outcomes based on known parameter by parameter
relationships.
The tables below set out the most important relations between antecedent
option appeal, modification appeal, and the modified appeal for each
parameter. The comments indicate the outcome status relative to the antecedent
option i.e. how the option has been changed.
The role of correlation is given a special place as it has the ability
to reverse the effects of each of remaining parameters (other than the mean).
Only by putting together the results for the full range of parameters
can one obtain a picture of the final likely result or interpret an obtained
result.
Appeal for the antecedent option and option change are treated as having
about equal weight in determining the outcomes listed in the table. (In more
realistic examples the antecedent option is likely to have greater weight than
a change.)
When parameters for antecedent appeal and change appeal are directly
compared they are assumed to be of about equal size unless otherwise indicated.
Positive and negative correlations between antecedent option and option
change are, say, about 0.7. Positive and negative skewness and kurtosis assumed
to be +1 and –1, respectively.
It is important that the tables be seen as providing some "rules of
thumb" for 'middle or the road" data and a feel for the kinds of
relations likely to emerge under the given circumstances. They are not a
substitute for simulation or gathering data to confirm actual relationships.
RELATIONS BETWEEN APPEAL
DISTRIBUTION MEANS


PARAMETER FOR ANTECEDENT OPTION

PARAMETER FOR OPTION CHANGE

PARAMETER OUTCOME FOR CHANGED OPTION


(relative to antecedent)

CORRELATION BETWEEN ANTECEDENT OPTION AND OPTION
CHANGE



POSITIVE

NEGATIVE


Given

Higher 
Weighted average increase in mean appeal


Same

No change


Lower

Weighted average decrease in mean appeal

RELATIONS BETWEEN APPEAL
DISTRIBUTION STANDARD DEVIATIONS


PARAMETER FOR ANTECEDENT OPTION

PARAMETER FOR OPTION CHANGE

PARAMETER OUTCOME FOR CHANGED OPTION


CORRELATION BETWEEN ANTECEDENT OPTION AND OPTION
CHANGE


POSITIVE

NEGATIVE


General

The lower the correlation the smaller the standard deviation i.e. +1
highest, –1 lowest.


Similar

Similar

Modest reduction in standard deviation.

Major reduction in standard deviation.

Wider

Narrower

Somewhat below a weighted average standard deviation.

Very major reduction in standard deviation approaching the narrower
standard deviation.

Narrower

Wider

Somewhat below a weighted average standard deviation.

Somewhat moderated major reduction in standard deviation.

RELATIONS BETWEEN APPEAL
DISTRIBUTION SKEWNESS


PARAMETER FOR ANTECEDENT OPTION

PARAMETER FOR OPTION CHANGE

PARAMETER OUTCOME FOR CHANGED OPTION


CORRELATION BETWEEN ANTECEDENT OPTION AND OPTION
CHANGE


POSITIVE

NEGATIVE


Zero

Positive

A weighted
average positive skewness.

Reduction in positive skewness and large reduction in standard
deviation.

Negative

A weighted
average negative skewness.

Reduction in negative skewness and large reduction in standard
deviation.


Positive

Positive

A weighted
average positive skewness.

A neutralising of skewness but watch for negative kurtosis and large
reduction in standard deviation.

Negative

A neutralising
of skewness but watch for negative kurtosis.

A neutralising of skewness but watch for positive kurtosis and large
reduction in standard deviation.


Negative

Positive

A neutralising
of skewness but watch for negative kurtosis.

A neutralising of skewness but watch for positive kurtosis and large
reduction in standard deviation.

Negative

A weighted
average negative skewness.

A neutralising of skewness but watch for negative kurtosis and large
reduction in standard deviation.

Zero skewness involves a
symmetrical distribution of scores about the mean i.e. equal number of cases
above and below with a similar spread of ratings.
Positive skewness refers to
an asymmetric distribution where scores for cases are more closely packed at
the bottom and stretched apart at the top.
Negative skewness refers to
an asymmetric distribution where scores for cases are more closely packed at
the top and stretched apart at the bottom.
RELATIONS BETWEEN APPEAL
DISTRIBUTION KURTOSIS


PARAMETER FOR ANTECEDENT OPTION

PARAMETER FOR OPTION CHANGE

PARAMETER OUTCOME FOR CHANGED OPTION


CORRELATION BETWEEN ANTECEDENT OPTION AND OPTION
CHANGE


POSITIVE

NEGATIVE


Zero

Positive

A weighted
average positive kurtosis.

Large reduction in positive kurtosis and standard deviation.

Negative

A weighted average
negative kurtosis.

Neutralised kurtosis and large reduction in standard deviation.


Positive

Positive

A moderated
weighted average positive kurtosis.


Negative

A neutralising
of kurtosis.

A neutralising of kurtosis but watch for large reduction in standard
deviation.


Negative

Positive

A neutralising
of kurtosis.

A neutralising of kurtosis but watch for large reduction in standard
deviation.

Negative

A moderated
weighted average negative kurtosis.

A more strongly moderated positive kurtosis but watch for large
reduction in standard deviation.

Zero kurtosis involves a distribution of
ratings the same shape as a normal distribution i.e. 68% of ratings within one
SD of the mean and 95% within two.
Positive kurtosis refers to a
distribution where there are disproportionately more case ratings in the centre
and tails of the distribution.
Negative kurtosis refers to a
distribution where the shape is flatter than normal and the cases are spread
relatively more evenly across the scale.
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