Sample Weighting

The characteristics of a perfectly drawn sample of a population will vary from true population characteristics only within certain limits of sample variability (i.e., sampling error). Unfortunately, social surveys do not permit perfect samples. The sampling frames available to survey research are less than perfect. The absence of perfect cooperation from sampled units means that the completed sample will differ from the drawn sample. In order to correct these known problems of sample bias, the achieved sample is weighted to certain characteristics of the total population. Each of the survey samples was weighted separately.

The weighting plan for the survey was a multi-stage sequential process of weighting the achieved sample to correct for sampling and non-sampling biases in the final sample. The first stage in the sample weighting procedures was designed to correct the cases in the completed sample for known selection biases in the sampling procedures. At the household selection stage, a random digit dialing process will give households with more than one telephone number an unequal likelihood of selection. Nationally, about 18% of households selected by random digit dialing will have more than one telephone number. This selection bias was corrected by giving each household a first stage weight equal to the inverse of the number of different telephone numbers in the household, up to a maximum of three phone numbers.

The second step in the weighting process was to correct for selection procedures that yielded unequal probability of selection within sampled households. Although the survey was designed as a population survey, only one eligible person per household could be interviewed (because multiple interviews per household are burdensome and introduce additional design effects into the survey estimates). A respondent's probability for selection is inverse to the size (number of other eligible adults) of the household. Hence, the second stage weight was equal to the number of eligible respondents within the household.

The next step in the weighting process was to correct the study design for deliberate disproportionate selection of younger population subsets in the sample design. The survey included both a cross-sectional sample of 4,500 respondents, aged 16 and older, and an over-sample of 1,500 persons, aged 16 to 39 years old. Hence, the total achieved sample yielded a disproportionate sample distribution by age. A third stage weight was used to correct the achieved sample for disproportionate sampling by dividing the expected population distribution, based on Census projections, by the achieved sample distribution on the stratification variables. Specifically, the third stage weight corrected the sample to the cell distribution of the population for five cohorts (16-20, 21-29, 30-39, 40-64 and 65 or older) by gender, using the Census Population Projections for Age, Sex and Race for 1998.

FIGURE 5A
SPSS Program for Assigning Weights

VERSION 1

compute numtel=q110a.
recode numtel (sysmis=1)(4 thru 10=3)(11 thru highest=1).
compute nadults=(q100).
recode nadults (7 thru 98=7)(99=1).
compute weight1=(1/numtel).
compute weight2=nadults.
COMPUTE WEIGHT3=(WEIGHT1*WEIGHT2).

*age by gender weight.
compute catage=q99.
recode catage (16 thru 20=1)(21 thru 29=2)(30 thru 39=3)
               (40 thru 64=4)(65 thru 97=5)(99=6).
value labels catage 1 '16-20' 2 '21-29' 3 '30-39'
              4 '40-64' 5 '65+' 6 'Refused'.
compute gender=q111.
value labels gender 1 'Male' 2 'Female'.
compute weight4=1.
if (gender eq 1 and catage eq 1) weight4=0.749.
if (gender eq 1 and catage eq 2) weight4=0.764.
if (gender eq 1 and catage eq 3) weight4=0.769.
if (gender eq 1 and catage eq 4) weight4=1.221.
if (gender eq 1 and catage eq 5) weight4=1.588.
if (gender eq 2 and catage eq 1) weight4=0.809.
if (gender eq 2 and catage eq 2) weight4=0.768.
if (gender eq 2 and catage eq 3) weight4=0.698.
if (gender eq 2 and catage eq 4) weight4=1.236.
if (gender eq 2 and catage eq 5) weight4=1.671.
compute weight5=(weight3*weight4).
compute weight6=(weight5*.5440619).
recode weight6 (0=1).


FIGURE 5B
SPSS Program for Assigning Weights

VERSION 2

compute numtel=q136a.
recode numtel (sysmis=1)(4 thru 10=3)(11 thru highest=1).
compute nadults=(q129).
recode nadults (7 thru 98=7)(99=1).
compute weight1=(1/numtel).
compute weight2=nadults.
COMPUTE WEIGHT3=(WEIGHT1*WEIGHT2).

*age by gender weight.
compute catage=q128.
recode catage (16 thru 20=1)(21 thru 29=2)(30 thru 39=3)
             (40 thru 64=4)(65 thru 97=5)(99=6).
value labels catage 1 '16-20' 2 '21-29' 3 '30-39'
                 4 '40-64' 5 '65+' 6 'Refused'.
compute gender=q138.
value labels gender 1 'Male' 2 'Female'.
compute weight4=1.
if (gender eq 1 and catage eq 1) weight4=0.7954.
if (gender eq 1 and catage eq 2) weight4=0.8366.
if (gender eq 1 and catage eq 3) weight4=0.7552.
if (gender eq 1 and catage eq 4) weight4=1.2393.
if (gender eq 1 and catage eq 5) weight4=1.2831.
if (gender eq 2 and catage eq 1) weight4=0.8450.
if (gender eq 2 and catage eq 2) weight4=0.7698.
if (gender eq 2 and catage eq 3) weight4=0.7242.
if (gender eq 2 and catage eq 4) weight4=1.2163.
if (gender eq 2 and catage eq 5) weight4=1.4871.
compute weight5=(weight3*weight4).
weight by weight5.
freq gender.
compute weight6=(weight5*.5482615).
weight by weight6.
recode weight6 (0=1).


The final step in the weighting process was designed to correct for the fact that the total number of cases in the weighted sample was larger than the unweighted sample size because of the use of the number of eligibles weight. In order to avoid misinterpretation of sample size, the total number of cases in the unweighted sample was divided by the total number of cases in the weighted sample to yield a sample size weight. When this weight is applied, the size of the weighted sample is identical to the size of the unweighted sample.

The final weight (WEIGHT6) incorporates all of the intermediate weighting steps described above. The final weight adjusts the total completed interviews in the achieved sample to correct for known sampling and participation biases, while maintaining the unweighted sample size.

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