Help - Correlation of measurable and ordinal data plssss
geetha...@gmail.com
I am need to design an experiment for my research work, which involves
ranking of a product finish(plastic panels).
Each of the Panels has 6 measurable variables associated (say
thickness, shininess, color, gloss, etc., which can be MEASURED by an
instrument) In a group of 100 panels I have selected only 18 panels
which have low, medium and high value of each Variable, but all other
variable have average value of their own [i.e., low,medium, high value
of A1 and Average values of A2,A3,A4,A5,A6(100 panels)]
---------------------------------------------------------
Ex:
Panel No. A1 A2 A3 A4 A5 A6
Panel 1: 2 avgA2 avgA3 avgA4 avgA5 avgA6
Panel 2: 14 avgA2 avgA3 avgA4 avgA5 avgA6
Panel 3: 27 avgA2 avgA3 avgA4 avgA5 avgA6
Panel 4: avgA1 5 avgA3 avgA4 avgA5 avgA6
Panel 5: avgA1 17 avgA3 avgA4 avgA5 avgA6
Panel 6: avgA1 36 avgA3 avgA4 avgA5 avgA6
.
.
.
Panel 18:avgA1 avgA2 avgA3 avgA4 avgA5 35
----------------------------------------------------
The above 18 panels are evaluated i.e, just RANKED by people based on
what they like (Ranking based on the overall Finish ONLY, so they are
not aware of the SIX variables)
The people who are ranking the plastic panel are focusing on the
Product FINISH only. They Rank from 1 to 18 ( 1 = BEST and 18 =
WORST )
Person Panel 1 Panel 2 Panel 3 ...... Panel 18
1. 4 14 7 1
2. 13 10 3 5
3. 9 7 15 11
4.
5.
.
.
.
99.
100.
My aim is to determine which among the six variable is more
influential/ related to RANK and develop a STANDARD for this
instrument.
My problem is how can I do statistical analysis to develop an STANDARD
if I have a RANK DATA and a MEASURABLE DATA ...
The Rank data does not follow a normal distribution even after
transformation.
Of the 6 variables only 3 variables are normally distributed and the
rest 3 are not Normally distributed.
Is it necessary to have each of the data ( rank, A1, A2, A3, A4, A5 ,
A6) to be normally distributed to do regression analysis.
Can you please suggest me some solution for how approach this very
Tricky problem.
Ray Koopman
wrote:
First, there is no one right way to analyse your data. No matter what
you do, there will be places where people can say "yes, but...."
I would treat the average of the 100 rankings as an interval variable
and look its scatterplot with each of the 6 measured variables. If any
plot is obviously nonlinear, then transform the variable to linearize
the relation. If your job is to pick the one best variable, then pick
the one with the highest correlation. I don't know what you mean when
you say that you are to develop a standard for this instrument.
There are many other potentially interesting analyses that could be
done. For starters, look at the standard deviation of the ranks for
each panel. A large SD indicates lack of agreement among the raters.
You may want to incorporate this information into the correlation by
doing a weighted correlation -- weight = 1/variance -- that pays less
attention to the panels about which the raters disagreed more.
People often suggest Kendall's coefficient of concordance for such
sets of rankings, so do it, even though it tends to be noninformative,
because someone may ask about it. However, you'll get more information
from doing a component analysis of the rankings. That will tell you
how many different points of view there were about which panels were
better. If there is not one point of view that is clearly dominant
then looking at the average rankings may not be the best approach.
The correlations of the "points of view" factors from the CA with
the (possibly transformed) measured variables might be enlightening.