Published on March 8, 2014
Prepared by SATYAM ANAND
WHAT IS COMPRATIVE SCALING TECHNIQUES? A comparative scale is an ordinal or rank order scale that can also be referred to as a nonmetric scale. Respondents evaluate two or more objects at one time and objects are directly compared with one another as part of the measuring process. For example you could ask someone if they prefer listening to MP3s through a Zune or an iPod.
We can take step further and add some other MP3 player brands to the comparison. MP3 players would be scaled relative to each other and the scale position of any one player would depend on the scale position of the remaining players.
NAME OF MP3 PERSON A PLAYER SCALING PERSON B SCALING SONY 2 1 PHILIPS 3 4 APPLE 1 3 SAMSUNG 4 2
RANK ORDER SCALE A Rank Order scale gives the respondent a set of items and asks them to put the items in some form of order. The measure of 'order' can include Preference Liking Importance Effectiveness The order is often a simple ordinal structure (A is higher than B).
FOR EXAMPLE:Rank the 4 activities that you would like to do in evening by writing A to D. As ‘A’ is the most preferred and ‘D’ is the least preferred. Staying in and watching television. A Going bowling. D Going to a bar with a friend. C Going out for a meal. B
HOW CAN WE SHORT ORDINAL DATAS? Sorting of ordinal data can be done in several ways:Priority sorting Block sorting Score sorting Pairwise sorting Q-Sorting
SPEARMAN RANK CORRELATION COEFFICIENT The Spearman Rank Correlation Coefficient is a form of the Pearson coefficient with the data converted to rankings (ie. when variables are ordinal). The raw scores are converted to ranks and the differences (di) between the ranks of each observation on the two variables are calculated. ρ = 1 - (6 * SUM(di2)) / (n * (n2 - 1))
EXAMPLE Two groups, x and y, are asked to rank ten items. The correlation between their rankings are then compared as below:-
KENDALL TAU RANK CORRELATION COEFFICIENT The Kendall Tau Rank Correlation Coefficient is used to measure the degree of correspondence between sets of rankings. The Kendall coefficient is denoted with the Greek letter tau (τ). τ = (4P / (n * (n - 1))) - 1
Q. A GROUP OF PEOPLE, DENOTED AS A TO E, HAVE THEIR IQ AND HAT SIZE MEASURED, TO DETERMINE IF A BIGGER BRAIN MAKES YOU BRAINIER. THE PEOPLE ARE RANKED BY BOTH IQ AND HAT SIZE (1 - HIGHEST RANK), AND PUT IN A TABLE, AS BELOW. Now P is the sum of the 'unexpected' rankings, measured as the sum of the number ranked hat sizes to the right (ie. in lower positions than the assessed position). P=2+3+1+0+0=6 τ = (4*6 / (5* (6 - 1))) - 1 = 0.04
PAIRED COMPARISON: Respondents are presented with two objects and asked to select one according to some criterion. For n objects, there are:- n(n-1)/2 comparisons
EXAMPLE:- IF WE HAVE TO COMPARE FIVE ITEMS SAY A,B,C,D,E TOGETHER. THEN WE WILL COMPARE:- A&B B&D A&C A&D A&E B&C B&E C&D C&E D&E Hence total number of comparisons= N(N-1)/2 =5(5-1)/2 =10
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