Appendix: Cost Analysis for SPARCCS Survey
For this analysis, we apply mathematical modeling to estimate the costs of both a one-contact
strategy (baseline contact only), and a two-contact strategy (baseline and one recontact) – and
then compare these to the four-contact strategy used in SPARCCS. Considering first the twocontact strategy, let ni , ri , and ci be, respectively, the sample size, the response rate, and the
unit cost for Contact i , where i  1, 2 . Then, there will be r1n1 respondents and (1  r1 )n1
nonrespondents from Contact 1 (baseline). From Contact 2 (follow-up), we will obtain
r2 (1  r1 )n1 respondents, and thus the overall respondent sample size is r1n1  r2 (1  r1 )n1 . The total
data collection cost for the two-contact strategy is then CM  c1n1  c2 (1  r1 )n1 . To obtain the
same sample size for the single contact, the initial sample size should be r1n1  r2 (1  r1 )n1 r1 .
Its data collection cost is then given by CS  c1 r1n1  r2 (1  r1 )n1 r1 . Assuming that c1  c2 and
r1  r2 , we compare the two total costs by computing the difference between them as follows:
D  c1n1  c2 (1  r1 )n1  c1 r1n1  r2 (1  r1 )n1 r1
 c1n1  c1 (1  r1 )n1  c1 r1n1  r2 (1  r1 )n1 r1 if c2  c1

c1n1
r1  r12  r2  r1r2 

r1

c1n1
1  r1  r1  r2 
r1
 0 if r1  r2
From the above inequality, we can deduce that the two-contact strategy is more expensive. For
the K-cycle strategy, assuming that c1  ci and r1  ri for i  1, 2,..., K , we obtain the following
cost difference expression:
D
c1n1
1  r1  r1  r2   1  r1 1  r2  r1  r3   ...  1  r1 1  r2   1  rK 1  r1  rK   0
r1
1
Depending on the data collection mode, the data capture cost for respondents should be added to
the total cost (for example, sometimes an incentive is promised and provided only to
respondents). Let c0 be the unit cost for data capture and other expenses applicable to the
respondents only. Then the additional cost for both strategies is CA  c0{r1n1  r2 (1  r1 )n1} when
the two strategies are compared. In general the additional cost is given by C A  c0 m , where m is
the target sample size, which is the same for both strategies. Therefore, the cost comparison does
not change because CA is cancelled out in D . However, the relative cost saving is affected, and
the saving by the one-contact strategy would be diminished when there is an additional cost for
the respondents only.
In the following table we consider a very simple (and conservative) case, where the unit cost -arbitrarily set at $1.00, for convenience-- is the same for all contacts. Based on this analysis, a
one-contact strategy would save 32% compared to the four-contact strategy ($6,291 versus
$9,315). (Note that these are not actual dollar costs, but relative values based on our
establishment of $1.00 as the unit cost.)
One-contact strategy
SPARCCS (four contact
cycle) strategy
First contact
Second contact
Sample Size
Response Rate
Resp Sample Size
Cost
6,291
0.350
2,202
$6,291
Sample Size
Response Rate
Resp Sample Size
Cost
3,574
0.350
1,251
$3,574
2,323
0.217
504
$2,323
Third contact
1,819
0.121
221
$1,819
Fourth contact
1,598
0.141
226
$1,598
2,202
$9,315
Total
Note: Costs listed are not actual survey field cost, but relative values based on setting unit cost
to $1.00 at each contact.
2
However, this calculation does not account for incremental costs associated with respondents
(but not non-respondents) such as data capture and processing. As a more realistic approach, we
recognize that SPARCCS was a mail survey with an incentive provided to all potential
respondents (although only 9 percent of non-respondents cashed the incentive check), so the cost
ratio between the two strategies depends on the cost associated with respondents only. If the
additional unit cost for respondents is again set at $1.00, then the total cost under this scenario is
$8,493 (= $6,291 + $2,202) for the single-contact strategy and $11,517 for the SPARCCS fourcycle strategy. In this case, the cost ratio would be 74 percent, resulting in a cost savings for the
single-contact strategy of 27 percent. If the additional unit cost for respondents is set at $2.00,
then the cost ratio would be 78 percent, and the savings reduced to 22 percent. The overall
savings may even be higher than these figures indicate, because the overhead cost for the multicycle strategy is usually higher. However, we conservatively estimate that a single-contact
strategy for SPARCCS would have resulted in a savings intermediate between the two values
cited above, or (22 + 27)/2 = approximately 25%, relative to the four-cycle strategy that was
implemented.
As an alternative approach, we can also compare a two-contact strategy (initial contact and one
recontact cycle) with the SPARCCS four-cycle strategy. In this case, the equivalent cost
reductions, based on assumptions identical to those above, are estimated at 17 and 14 percent,
respectively, for $1 and $2 respondent unit costs (see the table below). Conservative, we again
take the average of these values and estimate a total savings of 15 percent, relative to the
SPARCCS four-cycle strategy.
3
Unit cost = $1.00 for contact
Two-contact strategy
First contact
Second contact
SPARCCS (4-cycle) strategy
First contact
Second contact
Third contact
Fourth contact
Total
Sample Size Response Rate Resp Sample Size Cost
4,485
0.350
1,570
$4,485
2,915
0.217
632
$2,915
2,202
$7,400
Sample Size Response Rate Resp Sample Size
3,574
0.350
1,251
2,323
0.217
504
1,819
0.121
221
1,598
0.141
226
2,202
Cost
$3,574
$2,323
$1,819
$1,598
$9,315
Respondent cost with unit cost=$1.00
Respondent cost with unit cost=$2.00
$2,202
$4,404
Two-contact total cost with resp unit cost = $1.00
Two-contact total cost with resp unit cost = $2.00
SPARCCS total cost with resp unit cost = $1.00
SPARCCS total cost with resp unit cost = $2.00
Cost ratio with resp unit cost = $1.00
Cost ratio with resp unit cost = $2.00
$9,602
$11,804
$11,517
$13,719
83.4%
86.0%
4