I
ALFRED
P.
SLOAN SCHOOL OF MANAGEMEJ
Measurement of Priority Schedules in the
Acquisition of Durable Appliances
161-66
Jagdish
N.
Sheth
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS 02139
Measurement of Priority Schedules in the
Acquisition of Durable Appliances
161-66
Jagdish
N.
Sheth
Preliminary Report
The present paper attempts to substantiate the hypothesis that there exists
a
continuum on which most of the existing and known durable products can be
placed in some fashion of
a
priority system both at the aggregate and at life
cycle subgroup levels.
The notion of a product continuum is not a new one; it has been expressed
by the essence of economic behavior namely satisfying unlimited wants with
limited resources.
However, such notion though expressed, has not been system-
atically tested and analyzed, at least with respect to durable goods.
Theoretical Analysis
As stated above,
:
a household,
holding changes in income, education, dwelling,
members of the family etc. constant, attempts to make the best use of the limited resources at its disposal in satisfying unlimited wants;
and in doing so,
it encounters the problem of scheduling the purchases of various durable products
by the criterion that most urgently needed must be acquired first.
fact is that a household
is not
The plain
within a short-time interval of say one year or less,
in a position to acquire all the appliances it may need;
some acquisitions
have to be deferred to a later time in order that more urgent may be acquired
now.
The yearly savings of a household (Disposable Personal Income less annual
living expenses including repayments of loans, etc. in agreed upon terms)
is
not
sufficient for the immediate investment needed in buying the existing and needed
number of appliances.
Besides, other expenditures compete for the savings like
the life and medical insurances,
recreation and vacationing, etc.
Hence,
the
emergence of a product acquisition scheduling over a period of years on the part
of the household.
Page
2.
The acquisition schedule or continuum of durable goods is dictated largely
by the strengths of different unsatisfied needs.
To the extent that some durable
goods act complementarily and are very much like joint products in the sense that
their simultaneous acquisition alone can satisfy one common and general need, the
scheduling distance between such products may be very short almost amounting to
an overlap.
A good example is Range and Refrigerator, but not the washer and dryer.
In the latter case, dryer acquisition is conditional upon prior acquisition of the
washer, whereas washer is independent of the prior or even joint acquisition of a
dryer.
(Data reveal that, at the aggregate level, the conditional probability of
acquiring a dryer given prior possession of a washer i.e. P(D/W) is .97 whereas
the vice versa [P(W/D)] is only .28.
But in the case of refrigerator and Range,
the conditional probability of acquiring a refrigerator given the possession of
a
range [P(Ref. /Range)
]
is
.94 and the vice versa [P(Range/Ref
.
) ]
is
.92.)
It seems also that a variety of needs for different durable products with
their individual strengths does exist for a household given that it belongs to
a
particular socioeconomic class.
Such needs are largely dictated by exogenous
variables like class, culture and economic standing.
A household would,
go along the schedule of acquisition in a systematic way.
therefore,
The acquisition of a
product later on the continuum will not be planned until all the earlier products
For example, a household may not buy a dish-
are acquired or made available.
washer before it can get a refrigerator since the latter is likely to be more
urgent.
One point must be clear.
The product continuum hypothesis is not related to
past ownership and future purchases
ability and future acquisitions
.
;
rather,
it shows relation between past avail -
Such availability may have been made by the
.
Page
3.
rented facilities or by a gift from someone, or it may even have been a prize in
a drawing.
So must be the case with future acquisitions;
from sources other than purchase.
level,
However,
they also can result
it will be attempted,
at
the aggregate
to find out whether acquisitions other than by purchases are radically
affecting the acquisition schedule, and if so how to predict future purchases.
Marketing strategies available to
company knowing first, that a scheduling
a
process does exist and second, that there is a particular product continuum are
immense.
Methodology
:
The procedure chosen to measure a product continuum is the establishment of
ordinal continuum scales in terms, of past joint availability (PJA) and the current
acquisition frequency or rate (A).
As stated before,
a
household, on the average
will not buy say the 6th product on the continuum unless it has jointly availably
to it the first five products.
The relevance of past joint availability becomes
apparent because of the continuum and the dependency of
a
product on past all the
products prior on such continuum.
The following equation gives past joint availability scores for each durable
appliance under consideration.
(l)
PJ Ai
=
j^x..
i
=
1,
-
2,
(y
+
ij
3,
.
2ij )J
.
.
,
-a.
n and i 4
j
where
PJA.
=
Past joint availability score of
n
=
number of durable appliances in consideration
.
=
the percentage joint possession of
x.
possession of the
probability)
i
appliance,
i
j
appliance given the
appliance (conditional percentage
,
Page 4.
y ij
=
the percentage acquisition of the
j
appliance during the
past one year or less given the possession of i
=
the percentage availability of
ij
t~
acquisition of
=
i
j
appliance
appliance given the
Vi
appliance for one year or less.
percentage acquisition rate among sampled households of
i
appliance during past one year or less.
In order to simplify the understanding of the equations, the following
schematic may be useful:
.th
J
th
Available
1
appliance
Acquired
1
appliance
Page 5.
The products when analyzed in terras of individual PJA
placed on an ordinal continuum of PJA. score strengths.
scale will be reverse in order, the lowest PJA.
the continuum.
scores then can be
However, the ordinal
score getting the first rank on
This reversal of PJA. scores is easy to understand.
A product
earlier on the continuum will have fewer prior products to account for than a
product near the end of the continuum.
For example,
it may be
assumed that a
household prefers radio much more than a canopener so much so that the former is
3rd on the continuum and the latter is 20th on the continuum.
Under this hypo-
thetical situation, the only joint availability to be accounted for in case of
radio is the satisfaction by prior possession of needs pertaining to the first
two products which may, again for example, be refrigerator and range.
But in
the case of canopener the joint availability to be accounted for is with respect
to 19 prior products including radio.
However, if one can use Bayesian statistics, one need not reverse the ordinal scale.
The condition on which the acquisition of a product rests is that of
joint probabilities of the prior product availabilities and, of course, the more
the prior products, the smaller the probability because of multiplication rule.
But in order to use Bayesian conditional probability theorem,
condition is the knowledge of the product continuum itself:
the necessary
what products stand
where on the continuum, and this is not available.
Coming back to the methodology, the one year or less time period used to
define acquisition and purchase is largely the outcome of the data.
available do not give information on a shorter interval base.
The data
If the analysis
of acquisition were by quarters it would improve the whole study.
However, for
,
Page 6
durable appliances, it is generally felt that one year is not too long a time
period.
If the product continuum hypothesis is true then there must exist positively
high correlation between past joint availability (PJA.) and acquisition rate (A.)
for the appliances under consideration.
The rank correlation between the two
ordinal scalings can be obtained by
Rank
(2)
=
1
-
6ZD
N(N
2
2
-
1)
D
=
Difference of rank position for an appliance
N
=
Number of ranked appliances.
where
Also, the obtained correlations can be tested for reliability at specified
levels of significance by
=
t
(3)
y.,\/(N
-
2)
1(1 -7,
where
N
7
=
number of ranked appliances
=
rank correlation
=
degrees of freedom
7
and
df
Analysis of Data
=
N
-
2
:
A sample of 14,348 households is analyzed to substantiate the hypothesis,
both at the aggregate and life cycle levels.
sample of the U.S. population in 1962.
The sample is a true probability
The data gathered related, among other
things, to 22 durable appliances in all the three categories
major and minor appliances.
—
electronics,
However, electric toothbrush was discarded from the
analysis because it was then just introduced in the market.
Only 117 households
acquired an electric toothbrush out of the 14,348 households sampled, and no
Page
7.
household had available to it prior to one year because it was only introduced
during the past one year from the date of the sample.
The PJA. scores both at the aggregate and life cycle levels were tabulated
on IBM 7090/94 unit of the Columbia University Computer Center.
size of the sample, the total analysis took more than
7
and an output of approximately 100,000 printed lines.
Owning to large
hours of computer time
Using cross-tabulation
program, a total of 3780 tables was produced with approximately 1200 control cards.
Each table, among other things, gave one conditional percentage availability score
for each cell entry of nine 21 x 21 matrices (one matrix for the aggregate level
and eight for eight life cycle levels), the diagonals of each matrix remaining
blank because of the condition in Equation
reproduced as Tables
1
through 9.
(1)
that
i
4 j.
The
9
matrices are
As can be seen from the titles to these tables,
.- (y..+
each cell entry
of the final PJA. scores,' namely
z..)l.
L
VJ
/J
j is only
j one part
r
J [x
x
ij
ij
ij
Aggregate Level
:
Using raw scores of Table
the final PJA. score for each
1
i
and Equation (1), Table 10 is created which gives
appliance of the aggregate level.
Table 11
then ranks the products in terms of PJA. scores and A. scores (see Table 36).
l
l
At the bottom of Table 11, using equation (2), a rank correlation is obtained
(7
=
.91).
This when tested for reliability using equation (3) is found to be
significant at least at .0001 level.
If two appliances are removed from the analysis (hair dryer and toaster) for
no reason other than being most deviant,
is again,
the correlation goes up to .95 and,
significant at least at .0001 level.
Page 8.
Life Cycle Levels
:
The total aggregate sample was divided in terms of the life cycle position
of a household in the sample.
The following are the eight categories of life
cycles.
Life Cycle
1
=
Head under 45, not living with spouse, no children under 18
Life Cycle
2
=
Head under 45, living with spouse, no children under 18
Life Cycle
3
=
Head under 45, living with spouse, one or more children under
18 with youngest child under 6.
Life Cycle 4
=
Head under 45, living with spouse, one or more children under
18 but none under 6
Life Cycle 5
=
Head 45, or over, living with spouse, one or more children
under 18
Life Cycle
6
=
Head 45 or over, living with soouse, no children under 18
Life Cycle
7
=
Head 45 or over, not living with spouse, no children under 18
Life. Cycle 8
=
Others.
Research on household decision-making has suggested with good evidence that
life cycle as a single variable takes into account the effects of differences
in income, education,
age,
dwelling unit and duration, region, occupation, etc.
To replicate such evidence and to see that it does reflect in the present sample,
Tables 12
-
19 show the
contingency analysis of these variables with the life cycle.
Non-parametric tests reveal that each analysis is significant at .005 level (onetail test) and therefore, strengthens the hypothesis that differences in the var-
iables are reflected in classification of life cycle groups.
Thus,
the choice
of life cycle as one variable which will reflect the effects of some of the major
Page 9.
variables in household decision-making seems both relevant and adequate.
a.
Life Cycle
(1).
1
b.
The rank correlation is .97 which is significant at least
2
scores using Table
3
and Equation
Table 23 ranks the appliances in terms of PJA. scores and
A.
scores
The rank correlation is .78 which is significant at least
.0001 level.
Life Cycle
(1).
Table 24 gives the PJA. scores using Table 4 and equation
3:
Table 25 ranks the appliances in terms of PJA. scores and A. scores
The rank correlation is .91 which is significant at least
(Table 36).
d.
Table 22 gives the PJA
:
(Table 36).
at
scores
i
.0001 level.
(1).
c.
and Equation
l
Life Cycle
at
2
Table 21 ranks the appliances in terms of PJA. scores and A
(Table 36).
at
Table 20 gives the PJA. scores using Table
:
.0001 level.
Life Cycle 4
(1).
Table 26 gives the PJA. scores using Table 5 and equation
;
Table 27 ranks the appliances in terms of PJA. scores and
A.
scores
The rank correlation is .80 which is significant at least
(Table 36).
at .0001 level.
e.
Life Cycle
(1).
5
Table 29 ranks the appliances in terms of PJA. scores and
(Table 36).
at
f.
A,
scores
The rank correlation is .87 which is significant at least
.0001 level.
Life Cycle
(1).
6
Table 30 gives the PJA. scores using Table
:
Table 31 ranks the appliances in terms of PJA.
(Table 36).
at
Table 28 gives the PJA. scores using Table 6 and equation
:
7
and equation
scores and A. scores
The rank correlation is .78 which is significant at least
.0001 level.
Page
g.
Life Cycle
(1).
7
h.
and equation
A.
scores
The rank correlation is .91 which is significant at least
.0001 level,
Life Cycle 8
(1).
Table 34 gives the PJA. scores using Table
:
Table 35 ranks the appliances in terms of PJA
(Table 36).
at
8
Table 33 ranks the appliances in terms of PJA. scores and
(Table 36).
at
Table 32 gives the PJA. scores using Table
:
10.
9
and equation
scores and A. scores
The rank correlation is .92 which is significant at least
.0001 level.
Thus rank correlations at life cycle levels range from .78 to .97 onlyj
the variation is not too high.
It is interesting to note that any changes brought about by the life cycle
in the placings of products on a continuum are all in the direction reasonably
considered correct.
1
For example, washing machine is quite low in life cycles
and 2 as compared to life cycles
be available:
3,
4,
households in life cycles
5,
1
and
and
6
2
for which some explanation may
are young, only rent rather
than own as compared to households in other life cycles.
the effect of life cycles can be found.
Many such instances of
However, if we compare the product con-
tinuum of the 8 life cycles with the aggregate continuum, one is surprised at
high correlations ranging from .84 to .97 (see Table 37).
This suggests that
product continuum hypothesis is not only substantiated but is sort of universal
to American households.
Cls.
Dry.
Table 10
Aggregate
Scores
PJA.
Table 11
Aggregate
Rank Correlation Between PJA, and A.
i
Product Rank
in terms of
PJA. scores
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m
rg
f
c
m
m
oq
If
c
a
a
*
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er.
—
in
in rv
co cr
•
cr-
o
rg
rg
C
3
rg
>r rv
o
cr <\
r»
LT
rg
in
ro
«\
f
*
oo
r-
<4
N
r\
oo
c
r-
O
r-
o
ii
ir(
a
«
in
fVJ \T\
rvi
rg ^i
u-
<\
m
C_
1-
-J
=J
OX
in
oc
Table 20
Life Cycle 1
PJA. Scores
1
Table 21
Life Cycle 1
Rank Correlation between PJA. and A.
1
Product Rank in Terms
of
PJA.
X
Scores
i
Table 22
Life Cycle 2
PJA. Scores
1
Table 23
Life Cycle 2
Rank Correlation Between PJA. and A.
1
Product Rank in Terms
of
PJA.
i
Scores
l
Table 24
Life Cycle 3
PJA. Scores
l
4=2-3
Product
1.
Z[x.
.-
ij
(y.
ij
.
+
z. .)]
ij
PJA.
i
Table 25
Life Cycle 3
Rank Correlation Between PJA. and A.
1
Product Rank in Terms
of
Scores
PJA
i
Product Rank in Terms
l
Table 26
Life Cycle 4
PJA. Scores
1
1
Table 27
Life Cycle 4
Rank Correlation Between PJA. and A.
1
Product Rank in Terras
of
PJA
Scores
i
l
Table 28
Life Cycle 5
PJA Scores
i
4=2-3
Product
Z[x.
.-
ij
1.
(y.
ij
.
+
z. .)]
ij
PJA.
Table 29
Life Cycle 5
Rank Correlation Between PJA. and A.
i
Product Rank in Terms
of
Scores
PJA
i
1
Table 30
Life Cycle 6
PJA Scores
Table 31
Life Cycle 6
Rank Correlation Between PJA. and A.
1
Product Rank in Terms
of
PJA.
i
Scores
i
Table 32
Life Cycle 7
PJA. Scores
1
1
Table 33
Life Cycle 7
Rank Correlation Between PJA. and A.
1
Product Rank in Terms
of
Scores
PJA
l
i
Table 34
Life Cycle 8
PJA. Scores
i
Table 35
Life Cycle 8
Rank Correlation Between PJA. and A.
1
Product Rank in Terms
of
PJA.
l
Scores
x
Table 36
Table 37
Rank Correlations of Product Continua at Different Life Cycle Levels
with Aggregate Product Continuum
3 AH
3 '69