Paired comparison technique is a method for scale construction developed by Thurstone. It involves comparing stimuli in pairs to determine which is perceived as better. Judges' responses are used to construct F, P, and Z matrices to calculate scale values. An example is given of identifying benefits of a dairy development scheme using this technique. The results show economic independence had the highest scale value, followed by sustainable employment, risk reduction, and social acceptability, with supporting others having the lowest value. Internal consistency is checked by calculating the average absolute discrepancy between empirical and expected proportions, with a lower value indicating higher consistency.

1. Paired Comparison Technique of
scale construction
Asif Mohammad
Scientist
Eastern Regional Station, ICAR-National Dairy Research Institute
Kalyani-741235, West Bengal

2. Introduction
The technique of paired comparison for scale construction has been
developed by Louis Leon Thurstone on the basis of comparative
judgement.
The scale helps in ordering stimuli along a continuum.
While formulating scale by using this method, the stimuli are
compared with one another and hence this method of scale
construction is known as ‘Paired Comparison Technique’.
By using this method researcher can also identify the estimates of
distances between each of the stimulus.

3. Step by step method of scale construction by using
Paired Comparison Technique:
1. Grouping of stimuli in to different pairs:
The total number of pair can be formulated by using n number of stimuli can
be calculated by using the following formula: Number of pair= n*(n-1)/2.
For example if the number stimuli is 5, then the possible number of pair will
be = 5 *(5-1)/2= 10.
If the stimuli are coded as a, b, c, d and f, then the possible combination of the
pair will be as follows
a d c b e a b a e d
b c a d c e c d b e

4. 2. Construction of f-matrix:
The F- matrix is constructed by calculating the frequencies corresponding to
the number of times each stimulus is judged as better or more favourable
than the other.
Stimuli Column
Row
1 2 3 . i . n
1
2
3
.
J
.
n
f11
f12
f13
.
f1j
.
f1n
f21
f22
f23
.
f2j
.
f2n
f31
f32
f33
.
f3j
.
f3n
.
.
.
.
.
.
.
fi1
fi2
fi3
.
fij
.
fin
.
.
.
.
.
.
.
fn1
fn2
fn3
.
fnj
.
fnn

5. 3. Construction of P-matrix:
The cell entries in the P- matrix represents the proportion of times the
column stimulus is found to be more favorable or better than the row
stimulus.
Stimuli 1 2 3 . i . n
1
2
3
.
J
.
n
P11
P12
P13
.
P1j
.
P1n
P21
P22
P23
.
P2j
.
P2n
P31
P32
P33
.
P3j
.
P3n
.
.
.
.
.
.
.
Pi1
Pi2
Pi3
.
Pij
.
Pin
.
.
.
.
.
.
.
Pn1
Pn2
Pn3
.
Pnj
.
Pnn
Sums ∑ P1 ∑ P2 ∑ P3 . ∑ Pi
. ∑ Pn

6. 4. Construction of the Z-matrix:
In the next step, the Z-matrix is constructed by taking the normal deviates
corresponding the proportion mentioned in the P-matrix.
Stimuli 1 2 3 . i . n
1
2
3
.
J
.
n
z11
z12
z13
.
z1j
.
z1n
z21
z22
z23
.
z2j
.
z2n
z31
z32
z33
.
z3j
.
z3n
.
.
.
.
.
.
.
zi1
zi2
zi3
.
zij
.
zin
.
.
.
.
.
.
.
zn1
zn2
zn3
.
znj
.
znn
Sums ∑ z1 ∑ z2 ∑ z3 . ∑ zi
. ∑ zn
Means 𝒛 𝟏 𝐳 𝟐 𝐳 𝟑 . 𝐳𝒊
. 𝐳 𝒏

7. Example
• Suppose one researcher want to measure the hierarchy of benefits derived
from ‘Dairy Entrepreneurship Development Scheme’ as perceived by the
beneficiary.
• For the study, he has collected responses from 60 beneficiaries.
• To achieve the objective of the study, he has identified 5 benefits of ‘Dairy
Entrepreneurship Development Scheme’ namely
 Risk reduction(A)
Sustainable employment(B)
Economic independence(C)
High social acceptability(D)
Supporting others(E).

8. F-matrix for benefits generated from ‘Dairy
Entrepreneurship Development Scheme’
Benefits generated
Risk
reduction
Sustainable
employment
Economic
independenc
e
High social
acceptabilit
y
Supportin
g others
(A) (B) (C) (D) (E)
Risk reduction (A) 40 45 20 15
Sustainable employment (B) 20 35 15 12
Economic independence (C) 15 25 14 9
High social acceptability (D) 40 45 46 25
Supporting others (E) 45 48 51 35

9. P- matrix
Benefits generated
Risk
reduction
Sustainable
employmen
t
Economic
independen
ce
High social
acceptabili
ty
Supporti
ng others
(A) (B) (C) (D) (E)
Risk reduction (A) 0.500 0.667 0.750 0.333 0.250
Sustainable employment
(B)
0.333 0.500 0.583 0.250 0.200
Economic independence (C) 0.250 0.417 0.500 0.233 0.150
High social acceptability (D) 0.667 0.750 0.767 0.500 0.417
Supporting others (E) 0.750 0.800 0.850 0.583 0.500
Sums 2.500 3.133 3.450 1.900 1.517

10. Rearranged P- matrix
Benefits generated
Supporting
others
High social
acceptabilit
y
Risk
reduction
Sustainabl
e
employme
nt
Economic
independe
nce
E D A B C
Supporting others(E) 0.500 0.583 0.750 0.800 0.850
High social acceptability(D) 0.417 0.500 0.667 0.750 0.767
Risk reduction(A) 0.250 0.333 0.500 0.667 0.750
Sustainable employment(B) 0.200 0.250 0.333 0.500 0.583
Economic independence(C) 0.150 0.233 0.250 0.417 0.500
Sums 1.517 1.899 2.500 3.134 3.450

11. Z-matrix
Benefits generated Supporting
others
High social
acceptability
Risk
reduction
Sustainable
employmen
t
Economic
independe
nce
E D A B C
Supporting others(E) 0 0.207 0.674 0.842 1.036
High social acceptability(D) -0.210 0 0.432 0.674 0.729
Risk reduction(A) -0.674 -0.432 0 0.432 0.674
Sustainable employment(B) -0.842 -0.674 -0.432 0 0.21
Economic independence(C) -1.036 -0.729 -0.674 -0.21 0
Sum Z -2.762 -1.628 0 1.738 2.649
Mean Z (dividing by 5) -0.552 -0.326 0 0.348 0.530
Addition of largest negative
value
+0.552 +0.552 +0.552 +0.552 +0.552
Rank order (Scale value) R 0 0.226 0.552 0.900 1.082

12. Hierarchy of benefit generated by the Dairy
Entrepreneurship Development Scheme
S
C
A
L
E
V
A
L
U
E
1.082 Economic independence
.900 Sustainable employment
.552 Risk reduction
.226 High social acceptability
.000 Supporting others

13. Checking the internal consistency
• Checking the internal consistency is very important as it shows the
comparison of empirical and expected proportion Pij.
• The smaller difference in empirical and expected proportion
indicate higher level of internal consistency.
• For measuring the same, first of all theoretical Zij’ or theoretical
normal deviates are calculated by subtracting the scale values
written in the left side from the column entry mentioned at the
top of the table

14. Theoretical Zij’ corresponding to scale distance between
the Z-matrix
Statemen
ts
E D A B C
Scale
value
0.000 0.226 0.552 0.900 1.082
E 0
D 0.226 -0.226
A 0.552 -0.552 -0.326
B 0.900 -0.900 -0.674 -0.348
C 1.082 -1.082 -0.856 -0.530 -0.182

15. Theoretical Pij’ corresponding to scale distance between
the Zij’
Statements E D A B C
E
D 0.411
A 0.290 0.372
B 0.184 0.25 0.364
C 0.140 0.196 0.298 0.428

16. Calculation of average absolute discrepancy
Statements E D A B C
E
D 0.006
A -0.040 -0.039
B 0.016 0.000 -0.031
C 0.010 0.037 -0.048 -0.011
I∑I
(Summation is taken by
ignoring the sign)
0.072 0.076 0.079 0.011
=0.238

17. Average absolute discrepancy or AD
𝑨𝑫 =
𝑷𝒊𝒋 − 𝑷𝒊𝒋′
𝒏 𝒏 − 𝟏
𝟐
=
. 𝟐𝟑𝟖
𝟏𝟎
= 𝟎. 𝟎𝟐𝟑𝟖

18. Conclusion
• In the scale constructed by paired comparison technique, stimulus is placed
according to the scale value.
• Stimuli are distributed along the scale and the stimulus having the smallest
scale value has the arbitrary zero value.
• The stimulus are arranged in the continuum with the lowest stimulus having
the zero and subsequently all other stimuli arranged according to high to
low scale values.
• The scale constructed by using this method give accurate estimate of
relative distances among the stimuli.

19. Thank you