The size of the nonresponse bias depends on the amount of nonresponse and the difference between the respondent and nonrespondent mean values of the study variables. For example, in an equal probability sample (a description of an unequal probability sample is provided in the section on base weights) of size n selected from a population of N families, let n1stand for the number of respondents and let n2 stand for the nonrespondents where n2(= n - n1 ). Let y be the study variable (e.g., family income) with as the respondent mean and as the mean for nonrespondents (whereis unknown). The sample mean for the total sample can be expressed as (see, for example, Groves, 1989)
Becauseis unknown, analysts useto estimate for the target population. When no nonresponse adjustments are made, the bias can be estimated as
Therefore, the extent of bias is a function of both the nonresponse rate (n2 /n ) and the difference between the respondent and nonrespondent means .
For example, assume that a survey of 820 low-income families has been carried out and that the variable of interest is the average monthly family income. Table 5-3 provides examples of the amount of bias in the estimate of variable of interest (i.e., average monthly family income) for various levels of nonresponse and average incomes for respondents and nonrespondents.
The level of bias in Table 5-3 is a function of both the variable response rates and the difference in the mean income for respondents and nonrespondents.
|Example 1||Example 2||Example 3|
|Sample Size||Average Income||Sample Size||Average Income||Sample Size||Average Income|
|Survey estimate with no nonresponse adjustment||$1,500||$1,500||$2,000|
|Estimated population value||$1,393||$1,300||$1,759|
|Bias||$ 107||$ 200||$ 241|
|NOTES: The data used for the Family Income Survey(FIS) example is hypothetical.|
Some part of differences in average income between respondents and nonrespondents is usually due to differences in their demographic composition (e.g., race, age, as in the States A and B examples) and the fact that income tends to vary among these demographic groups. The bias resulting from this distortion of the respondent sample can be reduced considerably by devising adjustment factors and applying them to the responding units data. Adjustment factors typically vary among demographic groups, and their purpose is to establish a data set whose sample representation has been adjusted to compensate for the missing nonrespondent data. (We used the term ''demographic groups" because race, age, gender, and other factors, are most frequently known for the population of interest. However, sometimes additional information such as income in a recent time period or employment status also is available for both respondents and nonrespondents. Adjustment factors can, of course, be developed for these variables as well as the demographic variables.) The underlying assumption for these adjustments is that respondents are similar to nonrespondents within the adjustment subgroups (or classes); that is, the data are missing at random (MAR)(4) and nonresponse is ignorable within the nonresponse adjustment group (Little and Rubin, 1987). Because respondents are not fully representative of nonrespondents (the MAR assumption does not hold perfectly), some unknown bias remains, even after conducting weighting adjustments.
The adjustments for nonresponse described in this report are designed to eliminate the part of the bias arising from the distortion in the respondent sample, but they have little effect on other causes of bias, which are usually independent of the sample composition. (Among possible reasons are that many persons who cannot be located have obtained jobs outside the area and have moved and that nonrespondents are in some ways psychologically different from the general population and the differences affect their ability to find employment.) Unfortunately, the extent to which these causes affect the result of a particular survey are, in most cases, not known, and consequently there is the possibility of significant bias when high nonresponse rates exist. Although we strongly recommend the adjustment procedures, they should not be considered replacements for a vigorous effort to achieve the highest response rate possible. They are an adjunct to such an effort.
A later section provides a summary of the general-purpose nonresponse adjustment methods currently used in many social surveys. The nonresponse adjustment factors are incorporated into the survey weights. The next section reviews the properties of sampling weights in preparation for the discussion of nonresponse adjustment procedures.
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