Interpreting a Joint Space Map - Session 4 HW help

Hi all,

I received some pretty pointed Qs on how exactly one should interpret a Joint Space map. Here's my attempt at a simplified answer.

A perceptual map positions multiple brands against multiple attributes. Each one of you evaluated 4 course offerings along 5 attributes (4 regular + 1 preference atribute). So we should be able to make p-maps for each one you, individually, right? Below is the rating set one of you (let's call him/her SK) gave:

Courses GSB INVA MGTO SAIT
Conceptual Value 3 4 5 4
Practical Relevance 4 5 5 5
Interest Stimulated 4.8 4.9 5.2 5.1
Difficulty 3 6 3 3
Preference 1 4 5 6

Note: The third row of ratings was '5' for all courses. A constant row or column is problematic as the matrix would be singular. So I had to introduce small variation there, hence the '4.8' type numbers you see.

The ratings clearly say that SK perceives SAIT, INVA & MGTO to be high on the first 3 attributes, INVA high on difficulty, SAIT high on preference and GSB low on all attributes. Any perceptual map (henceforth, p-map) must faithfully capture and depict at least this much information. Let us see how well our p-map does:

What if all courses are rated the same on an attribute?
Notice that when all courses are rated the same (score was '5') on 'Interest', that attribute is no longer informative in the p-map. Apart from Interest, seems like the map pretty much captures the basic ordering of SK's perceptions. Would you agree?

How does SK's preference vector - the meroon line - enter the picture?
Well, SK's given his/her preferences for each of the 4 courses. And each course has its position on the map already marked in trms of (x,y) co-ordinates. So, we weight each course's (x,y) co-ordinates with SK's preference score. The weighted averages of the x- and y- values become SK's preference vector co-ordinates. Simple, no?

Look closely and you can see that SK's preference ordering is borne out on SK's p-map. SAIT has the highest pref and is closest (perpendicular distance) to the higher side of the meroon line, followed closely by MGTO. INVA is exactly at the mean preference score ('4' for SK) and so is almost on the origin w.r.t. the meroon line. GSB is well below the mean level and so appears on the opposite side.

That was one student's p-map. To see how p-maps vary when attribute evaluations change, consider another student HS's ratings set followed by his/her Joint Space map.

Courses GSB INVA MGTO SAIT
Conceptual Value 7 1 3 5
Practical Relevance 5 3 3 7
Interest Stimulated 7 6 1 5
Difficulty 1 5 1 4
Preference 7 1 3 5

Compare this map with SK's map. What would happen if I take an *average* of these students' scores and draw a *third* map? Would it adequately represent the perceptions of either, neither or both students? How better to find out than to simply perform the experiment, eh? Below is the attribute table of the average of SK's and HS' ratings. The preferences are not averaged, instead we'll get two pref lines - 1 per student.

Courses GSB INVA MGTO SAIT
Conceptual Value 5 2.5 4 4.5
Practical Relevance 4.5 4 4 6
Interest Stimulated 5.9 5.45 3.1 5.05
Difficulty 2 5.5 2 3.5
preference SK 1 4 5 6
preference HC 7 1 3 5

Compare the three p-maps. Look at student 1's preference vector in the combined map. Where it was clearly favoring MGTO and SAIT on one side and slightly away from INVA on the other, now it is showing a weird position away from all 3. Think of the potential for how distorted preference vector locations became when we averaged over just 2 people.

Now imagine averaging over a group of 71 respondents. Would the distortions cancel out or get aggravated? Segmentation procedures try to find groups of people with similar perceptions. Based on what we have just seen, is the case for segmentation prior to p-mapping strengthened? I'll leave you with these Qs as you interpret and get the final answers to your homeworks for session 4.

Sudhir