Look at any one of the individual Vectors and take note of its row and its grid lined column.

1. The Vector represents the Alternative whose name is at the far left of the Vector's row.

2. The Vector also represents the Criteria whose name is at the top of the Vector's (grid lined) column.

3. Each Vector has a (hidden) horizontal length Vx and a (hidden) vertical height Vy.

4. Each Vector's horizontal length Vx, represents the score of how well its Alternative met the requirements of its Criteria.

5. Each Vector's angle, caused by its positive or negative vertical height Vy, shows the importance or lack of importance of its Criteria.

6. The order of the Criteria subcomponents of the Node have been sorted, left to right, from least important to most important based on the strengths of their Weights of Importance. The result is a VectorString that starts pointing down and then finishes pointing up.

7. The sum of the horizontal lengths of each of the Vectors in an Alternative's VectorString is the weighted score of that Alternative for the current Vectorgram's Node.

8. A vector displayed in red indicates its Alternative’s weighted score is the best for meeting the requirements of its corresponding Criteria.

9. A vector displayed in blue indicates its Alternative’s weighted score is tied with one or more of the other Alternatives’ weighted score, for meeting the requirements of its corresponding Criteria.

10. Picture a line beginning at the leftmost point of a VectorString and connects the rightmost arrow head of the VectorString. If that line has a positive angle, then the Alternative's weighted score is greater than its original unweighted score.

The following figure is the complete Vectorgram for the Cost Node in the first Case History, "Comparison of Three Vacation Home Prospects".

Each Vectorgram has two Benchmark VectorStrings one above, and the other below, whatever number of Alternative VectorStrings there are. The Benchmarks provide additional information about the Alternatives' performances.

The top VectorString represents a hypothetical Alternative called, "The Best in Class" (BestnClass) benchmark. Each one of the BestnClass vectors represents the best score of all the Alternatives for their particular Criteria subcomponent.

The Node score for this benchmark represents the best possible score that can be obtained by using the best of the scores of the Alternatives. Another way of expressing this is to say, the Best in Class Benchmark represents the State of the Art that these Alternatives bring to the table.

The bottom VectorString represents another hypothetical Alternative benchmark whose scores are equal to the weights of each one of the Criteria subcomponents.

Its name is either the "Weights" or "Standards" or "Acceptable" benchmark.
When the Title "Standards" is used, the assumption is, that if the Alternative's score for a Criteria is the same value as the Criteria's Weight of Importance, then that Alternative has met a standard requirement sought by those who assigned the Weights of Importance for that Criteria.

The weights are applied as though they were the acceptable standards for each Criteria. e.g. a Criteria whose requirements are far from necessary would have a low required standard and a low importance rating. Those Criteria whose requirements are extremely necessary would have a high standard and importance rating. It is important that those who are responsible for making the decision are comfortable with this approach and concur with the assigned "Standard" or "Acceptable" assignments.

The result of observing the two benchmarks enables the viewer to see:
. . . how well each Alternative performed versus the Best in Class and
. . . how close each Alternative met the expectations of those who set the Criteria Standards.

5.2 The Structure of the Vectorgram

The following Vectorgrams are a sequence of Vectorgram examples for the same “Cost” Vectorgram above. These contain script formatted explanations for every part of the Vectorgram.

The first Vectorgram displays the critical parts of a Vectorgram and scripted explanations.

The second shows a complete Vectorgram plus additional scripted comments not present in the latter.

The third is a repeat of the standard Vectorgram above as a convenience to see it without scrolling back.

And the fourth Vectorgram is what is called, the "Slide Vectorgram" which came about from clients' requests to produce a simplified version of a Vectorgram for slide presentations. V(ma) provides a table of options for modifying a standard Vectorgram including one option which calls for the VectorStrings to be redisplayed using only the horizontal components of the vectors. The result is a horizontal "Histogram-like" VectorString with slightly thicker vectors for use when presenting to a non oriented V(ma) VectorString audience.

However, there should be many situations where the Slide is used for trimming some of the more detailed information but still show the original VectorStrings in their original format.

A few comments should be made prior to viewing the Vectorgrams. First, the comments were prepared using the drawing capabilities of V(ma) and Excel.

This is significant because the same Excel and V(ma) drawing tools to create text boxes for comments with pointers etc. can be used by observers to pass their observations on to other colleagues participating in the Vectorgram reviews.

This is particularly effective if one is reviewing a Vectorgram database located on a server.

V(ma) provides cosmetic options as well. For example, the background color of a Vectorgram can be assigned any color. The default background is white. Fonts can be altered as well as the Vectors’ thickness using standard Excel procedures. Changing the color of red or blue Vectors should be discouraged because of V(ma)’s use of red and blue.

Toolbar Buttons:
V(ma) also provides viewers with toolbuttons that enable them to toggle various statistics about individual Vectors and Criteria.

For example, the default for a Vectorgram is to display the rank of each Vector by a red W (indicating that the Vector's Alternative is the winner of the Criteria at the top of the Vector's column), a blue T (indicates a tie for first with one or more other Alternatives) or a numeral indicating the rank position of 2nd, 3rd, etc. Those alphanumeric ranks can be toggled on or off using the rank toolbutton.

Other toggle toolbuttons provide toggling for the Vectors’:
Unweighted scores,
Weighted scores,
Standard deviations,
and
Concealing the names and scores of Alternatives.

The latter came about when a client wanted to show an unhappy Alternative why they had lost, without showing any of the other Alternative names or scores. The Alternative was told which row in the top Vectorgram, contained their VectorString. It was significantly weaker than that of the winner’s and left no need for any further discussion. Another use is to show an Alternative their VectorString in order to negotiate a better price or schedule assuming that was allowed.

That situation is only possible if the Criteria is soft, i.e. capable of adjusting the Criteria requirements. e.g. prices, schedules, variable numbers etc.) However, it is worthy to note that those situations are ones that managers should carefully examine because it is they who must initiate negotiations.

All of the toggle functions can be displayed simultaneously at the whim of the observer. e.g displaying the unweighted and weighted scores together is convenient because the observer can see how significant the weighting process changed the unweighted vectors. The toggling is very quick because the statistics have all been calculated and concealed behind the Vectorgram's background sheet.




5.3 Some Comments Regarding Standard Deviation of VectorStrings and "Soft Criteria"

One of the toolbar toggle buttons is used to provide the observer with a Standard Deviation value of the unweighted Criteria scores. For those unfamiliar with the Standard Deviation, a number is generated (after a series of values have been examined) whose value denotes how consistent those values are with one another. A very small number conveys great consistency and conversely a large number shows little of no consistency.

For example, if the unweighted Criteria scores of an Alternative are consistently close to one another then no weighted profile can alter the unweighted Node Score for that Alternative, be it good or bad. . . However, if the unweighted Criteria scores of the Alternative are inconsistent, then that Alternative’s Node score is completely dependent on the Criteria weightings. If the Weights of Importance are in harmony with the unweighted scores then the Alternative is in luck; if not bad luck.

Another insight worth noting is, if the winning Alternative has won because of excellent scores for Criteria of medium or minor importance’s while the Alternative runner-ups’ scores for those same Criteria are weak but whose scores in the more important Criteria are significantly stronger, then it would be wise to look at those less important Criteria to see whether they are cast in concrete or “soft” and capable of negotiation.

In other words, it is most desirable that the winning Alternative be strongest in the more important Criteria. Reviewers should be alert for Criteria that are arbitrary. If practical, an Excel Comment flag would be an excellent way to alert an observer of a soft Criteria.

5.4 The Role of the Vector in the Vectorgram

Each vector in an alternative’s VectorString represents how well an Alternative scored for each of the corresponding Criteria subcomponents of the Node.
And the horizontal length of the VectorString represents the Alternative’s overall weighted score for the Node.

Let’s examine one of the vectors and see what happens to it during the weighting process.
Let the black vector represent the vector before the weighting process with an unweighted score = f

CVA has defined, “A Square Vector" to be one with orthogonal equal components. And we use it here to represent the “Weight of Importance Force” as a "Square Vector" whose horizontal and vertical components are equal to either the dividend or debit value obtained as a result of the weighted averaging process. And that dividend or debit value is represented as, "df".

1. If the df is positive (i.e. a dividend) then adding the green vector to the black vector will produce a red resultant vector, called the “Weighted Vector” whose horizontal length will be f + df i.e. df longer than the black vector f.

Since the vertical component of the red vector is a positive df, then it will be pointing upward indicating an “above average” importance.
How much “above average” is reflected by the height of df.

2. If the df is negative (i.e. a debit) then adding the green vector to the black vector will produce a red resultant vector, called the “Weighted Vector” whose horizontal length will be f – df. i.e. df shorter than the black vector f.

Since the vertical component of the red vector is a negative df, then it will be pointing downward indicating a “below average” importance.
How much “below average” is reflected by the depth of df.

The following five vector examples should shed some light on what a vector in this V(ma) environment can convey. For simplicity's sake we will use the product/customer profile scenario but the same interpretation will be true for all scenarios.

1. A large vector pointing upward at a strong angle

This is the best shape. The vector is rich in score and very much ABOVE average in importance. If the Vector is representing a product’s feature, then it is obvious that the company knew ahead of time that this Criteria feature was important to the customer, and therefore had seriously invested in the development of that feature.

2. A large vector pointing downward at a strong angle

This is the saddest shape. The vector is rich in score and very much BELOW average in importance. Again, if the Vector is representing a product’s feature, one could guess that the company thought this Criteria feature was going to be important to the customer profile and therefore had invested in the development of a strong and attractive feature, only to find out that the effort was a waste of time and money. The research on the customer profile's was wrong. The feature was of little interest.

3. A short vector pointing upward at a strong angle

This is also a sad sign. The vector is weak in score and very much ABOVE average in importance. Again, if the Vector is representing a product’s feature, it is obvious that the company was not aware of the need for this feature by the customer profile, and as such, had NOT invested in developing a strong and attractive feature. This kind of vector usually puts its Alternative into the list of “Also Rans".

4. A short vector pointing downward at a strong angle

This is a wise sign. The vector is weak in score and very much below average in importance. Again, if the Vector is representing a product’s feature, it is obvious that the company was aware that the customer had very little interest in this feature and therefore had NOT invested in developing a strong and attractive feature. Remember, the debits and dividends generated by the weighting process are percentages of the original score. Thus, if your going to have any weak scores then pray that those are of little importance.

The very small unimportant score begets a small debit which will not impact the Alternative’s total score very much. However, the very large unimportant score begets a very large debit and that means trouble.

5. Any size vector pointing downward at a perpendicular angle

This Vector is screaming that its Criteria feature is not needed by this customer profile at all. It is so BELOW average that the Weight of Importance is ZERO. i.e. the vector has NO horizontal component at all. Any significant length in the vector shows extremely poor planning. (Weights of zero are useful if one wants to eliminate certain Criteria from the exercise for some reason.)

In summary, the Vector is an intelligent object which means than when it is selected by being clicked, the V(ma) software has access to the vectors attributes, one of them being which nth vector it is in the VectorString and which Alternative it is representing. From that, V(ma) has what it needs to perform the tasks requested by the various toolbuttons and pulldown menu selections described earlier.

5.5 The Mathematical Explanation of the V(ma) Use of Vectors The following is a paper in PDF format which describes in more detail the mathematical weighted average process and the use of Vector Analysis by CVA.

Why Scoring Vectors



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