GB532 Unit 5 Sampling Plan Example

8,160 Automatic Accounts, Two Strata and the Households No Draw Can Reach: A Unit 5 Sampling Plan

[Student Name]

Purdue University Global

GB532: Marketing Research

Unit 5 Sampling Plan

[Instructor Name]

[Date]

The propane distributor, its account counts and every figure are composite and illustrative; the methods and sources cited are real.

Population and Frame

Target population: residential households that heat with Otter Creek Propane's propane.

Sampling frame: the billing list of automatic-delivery accounts active through last winter, about 8,160 accounts.

Groves et al. (2009) distinguish the target population, the group about which conclusions are wanted, from the frame, the actual list names are drawn from, and warn that differences between the two create coverage error. Here the frame excludes about 1,240 will-call customers, who order fuel themselves when they need it.

Table 1: The Strata

Stratum A, flagged accounts: about 1,140 accounts flagged in the secondary data review because their fuel use for the same cold dropped by 20 percent or more year over year.

Stratum B, other automatic accounts: about 7,020.

Stratifying makes sense because the two groups are expected to differ sharply on the main measure: most hybrid homes should fall in stratum A. Lohr (2021) explains that stratified sampling improves precision when strata differ on the variable of interest, and it allows separate estimates for each stratum.

Formula Box

For estimating a proportion, the initial sample size is:

n0 = z² · p(1 − p) / e², with z = 1.96 for 95 percent confidence, p the proportion expected and e the margin of error wanted.

When the stratum is small relative to the sample, the finite population correction reduces the required size:

n = n0 / [1 + (n0 − 1) / N], with N the number of accounts in the stratum.

Table 2: Sample Sizes

Stratum A. The heat pump share is uncertain, so p is set at 0.5, the most conservative value, with a margin of 5 percentage points. Then n0 is about 384, and with N of 1,140 the corrected size is about 287 completed surveys. At an expected response rate of about 30 percent, that requires about 960 invitations.

Stratum B. A planning value of p of 0.20 and a margin of 4 percentage points give n0 of about 384; with N of 7,020, the corrected size is about 364 completed surveys. At about 30 percent response, that requires about 1,217 invitations.

Total invitations: about 2,177.

Stratum A is sampled at nearly one account in every 1.2, while stratum B is sampled at about one in six, because the small stratum holds most of the households the decision is about.

Weighting and Overall Precision

Because the strata are sampled at different rates, estimates for the whole frame must weight each stratum by its share: about 14 percent for stratum A and 86 percent for stratum B. If the heat pump share turned out to be about 70 percent in stratum A and about 15 percent in stratum B, the weighted estimate across the frame would be about 23 percent, give or take about 3.4 points, within the 4.5-point objective in the problem definition memo.

Selection Within Strata

Within each stratum, accounts will be sorted by town and drawn systematically from a random start, which spreads the sample across the service area. Accounts with more than one tank at the same address will be treated as one household.

The Households No Draw Can Reach

Will-call customers. About 1,240 residential accounts order propane themselves and are not on the frame. They cannot be flagged by K-factor, and some may have installed heat pumps and reduced orders. The study's estimates apply only to automatic-delivery customers, and the report must say so.

Households that left. Former customers who switched entirely to heat pumps or to another supplier are not on the active list. A separate short survey of accounts closed in the last two years would be needed to learn why they left.

Tenants. In rented homes, the account holder may be a landlord who does not live there and cannot describe how the home is heated day to day.

Dillman et al. (2014) note that coverage gaps cannot be fixed by larger samples, only by better frames or by stating the limit clearly. The plan does the latter.

Why Not a Simple Random Sample

A simple random sample of 2,177 from all 8,160 automatic accounts would include only about 300 flagged accounts at the same response rate, and only about 90 completed surveys from them. That would leave too few hybrid households to describe their propane use or compare their interest in a backup plan with confidence. Stratifying concentrates the sample where the decision's key group is, at the cost of needing weights for frame-wide estimates, which is a small price for the added precision.

Nonresponse

Response may differ by stratum and by age. The plan will compare respondents with the frame on fuel use and town, and adjust weights if respondents differ substantially from the accounts they represent.

References

Dillman, D. A., Smyth, J. D., & Christian, L. M. (2014). Internet, phone, mail, and mixed-mode surveys: The tailored design method (4th ed.). Wiley.

Groves, R. M., Fowler, F. J., Jr., Couper, M. P., Lepkowski, J. M., Singer, E., & Tourangeau, R. (2009). Survey methodology (2nd ed.). Wiley.

Lohr, S. L. (2021). Sampling: Design and analysis (3rd ed.). CRC Press.