Methods for the Analysis of Choices and Evaluations

 

Relations between an antecedent option, an option modification, and a modified option

 

Generating and measuring option change

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, case-by-case, 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 re-evaluation.

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 counter-intuitive results.

Understanding appeal change

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 inter-relations. 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, non-target 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.

Types of change and relations between parameters

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.

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

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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