Appendix

Sample Design

The sample design can be described as a customized multistage stratified area probability sample encompassing the universe of all private households in the conterminous United States.

National Analysts' basic sample design consists of three levels of stratification. This was accomplished by grouping all housing units in the United States, as given in the 1970 Census of Population and Housing and the corrections therein, into a two-way model. This stratification contains two levels - type of population (urbanization), and geographic divisions. Three types of population and nine geographic divisions were defined. The third level of stratification was carried out within each of the 3x 9 strata cells formed by the two-way model.

In setting up the strata, the 3,103 counties and independent cities which comprise the total land area of the United States were stratified by "type" of population, either metropolitan or non-metropolitan areas. Each of the resulting 243 metropolitan areas of the United States was then divided into two parts, central cities and the remainder of the metropolitan area. The non-metropolitan population was put into a third class. The three types of populations (zones) follow definitions from the 1970 Census of Population and Housing, and are:

Zone I: The area comprised of the central city(ies) in metropolitan areas (a central city is a city named in the metropolitan area title).

Zone II: Suburban - that area in standard metropolitan statistical areas (SMSA) outside Zone I [central city(ies)].

Zone III: Non-metropolitan areas.

The level of stratification that is based on Census geographic divisions and regions was accomplished by classifying every private household in the conterminous United States into one of the nine Census divisions. Within each division, parts of the metropolitan areas, central cities or "suburbia" were ordered geographically and/or by size. In the nonmetropolitan zone, states were ordered geographically and, within each state, groups of state economic areas were ordered. This array provided the sampling frame such that 114 strata of approximately equal size could be identified by legal or Census boundaries. The average stratum size is approximately 600,000 housing

units.

Stratification and Selection

of the Metropolitan Primary Sampling Units

That part of metropolitan areas defined as central cities were formed into 38 strata. This was accomplished by grouping together within strata central cities which are alike in either size or geographical proximity. Some strata contain only one central city.

Primary sampling units (central cities) were given measures of size based on the 1970 Census housing counts. One city sampling unit was selected from each stratum with the chance of selection of any city unit being proportional to its 1970 housing units.

48

A book of random numbers was used to select a number between "one" and the stratum number of housing units. This gives each number between "one" and the stratum total number of housing units an equal chance of being selected. This same procedure was followed for each stratum. The probability of any central city within the stratum being selected is the quotient of its 1970 housing units and the total of the 1970 housing units within the strata. In the stratum where Worcester, Mass., was selected, for example, the size of the city of Worcester is 58,589 housing units. The stratum size is 574,259 housing units. If we divide this into 58,589 the result is a probability of selection of .10202.

In Zone II the remaining portions of each of the 243 metropolitan areas (“suburbia" - that area outside of central cities) were grouped into 39 strata. This grouping was done by placing in the same strata, counties that are in the same geographic area. A primary sampling unit in Zone II is a metropolitan county or that part of a metropolitan county less the central city if it contains only one county. The size of the primary sampling unit is the number of 1970 housing units in the county, or the county less the central city if it contains one county. The size of each of the 39 strata is the sum of the housing units of all the primary sampling units it contains. Again, the book of random numbers was used to select one primary sampling unit from each stratum.

Stratification and Selection

of the non-Metropolitan Areas

In Zone III, the counties of the United States defined as non-metropolitan in the 1970 Census were grouped into 37 strata, following the Census divisions and states within. State economic areas were used to form these 37 strata.

A Primary Sampling Unit in Zone III is one or more counties. The reason for having more than one county in some PSU's is that a minimum county size of 10,000 housing units was established for each PSU. We believe that any county of less than 10,000 housing units is quite homogeneous. All counties with less than 10,000 1970 housing units were combined with an adjacent county to form a PSU of two or more counties. This was done before any selection of PSU's was made.

The size of each of the 37 strata is the total of all the counties it contains. A book of random numbers was used to select 37 primary sampling units proportional to the 1970 housing units in the primary sampling unit.

Sample Size

The sample design was drawn to yield a disproportionate sample with fixed sample sizes in each of 48 cells (12 age cells, 2 sex cells, and 2 race cells: black and non-black) in 1977, and 96 cells (8 age cells, 2 sex cells, 2 race cells and 3 buying cells) in 1980.

In 1977 a total of 8, 145 households were drawn into the sample and in 1980 a total of 8,766 households were drawn into the sample and by sub-sampling certain age, sex and race cells, the sample yielded the number of interviews shown in Attachment A and Attachment B by the domains of interest. The elimination of certain eligible households was necessary to yield a specified number of interviews in each of the 48 cells in 1977 and 96 cells in 1980.

In 1977, 452 area segments and in 1980, 458 area segments were selected into the sample. Disproportionate sampling of segments was incorporated to oversample black households in the population.

Weighting Model

Since the sample design was disproportionate in nature, statistical weighting was necessary to attain a threefold objective. The weighting process served:

• To put the sample back in balance due to disproportionate sampling of segments.

• To adjust for non-response within each segment area.

• To present meaningful estimates to known U.S. Census data.

The weighting was accomplished in three stages utilizing both the screening data for all households contacted and the interview data.

A. First Stage

The first stage of the weighting model is an adjustment in each segment area for both disproportionate selection of households and non-response. From the data on completed household screenings, an estimate was made for each segment area of the number of households that should have been screened in each segment with a balance or self-weighting sample of segments. This was done by adjusting the number of sample households for vacant dwelling units and the increase or decrease in households since the 1970 model. The screened households were then weighted up to the estimate of total occupied sample households in each segment. At the end result of this stage was an adjustment in each segment area for non-response.

This same first stage weighting procedure was utilized for the number of completed interviews in each segment area. This was achieved by adjusting the number of interview households for vacant dwelling units and non-response and then weighting the interview households up to the estimate of total occupied sample households in each segment.

B. Second Stage

The second stage of the weighting model is based upon the record and tape buying status of all individuals screened in the study, regardless of whether or not they were interviewed. The procedure was to tabulate the weighted screening form data by buying status in each of the 48 age, sex and race cells. In 1977 this resulted in a 192 cell matrix (12 age cells x 2 sex cells x 2 race cells x 4 buying status cells - never buyer, bought within the past year, bought between 1 and 5 years ago, and bought more than 5 years ago). In 1980 this resulted in a 144 cell matrix (12 age cells x 2 sex cells x 2 race cells x 3 buying status cells - buyers, nonbuyers/ tapers, and nonbuyers).

Census estimates were obtained for each of the age, sex and race cells. The buying status in both 1977 and 1980 within each of the 48 cells was used to make a ratio estimate to the Census estimate for each of the 192 cells in 1977 and 144 cells in 1980. This yielded the buying status estimate within each of the 192 cells and 144 cells as representing totals to the U.S. population.

This total derived for each of the age, sex, race and buying status cells was used as a weighting model for the 3,385 interviews in 1977 and the 2,370 interviews in 1980.

Each interview was put into one of these 192 cells in 1977 and 144 cells in 1980 as reported for that respondent on the screening form. C. Third Stage

The first stage weight was cumulated for all interviews within a cell. A constant weight was given each interview within a cell so that the product of both weights, summed for all interviews, within a cell, equaled the previous developed cell total as outlined in second stage weighting.