ACF OPRE: National Study of Child Care of Low-Income Families

Appendix A: Analysis Weights and Nonresponse

Weights were calculated for both the screener analysis sample and the survey analysis sample to account for the probability of selection and nonresponse. The weights are intended to make the screener analysis sample representative of all low-income families with children living in communities with child poverty rates above 14 percent, and to make the survey analysis sample representative of all low-income families with children using nonparental care while the mother works or is in school, living in communities with child poverty rates above 14 percent. The sections below describe how these weights were constructed.

Site Weights

Associated with each of the 25 sites was a probability weight corresponding to its likelihood of selection into the sample, w_i. These weights are shown in Exhibit A.1.

Exhibit A.1

Site Probability Weights
Site	Weight
Mobile, AL	17.572
Los Angeles, CA	1.000
Orange, CA	3.106
Riverside, CA	9.129
Cook, IL	3.342
Madison, IN	56.295
Oachita, LA	44.567
Franklin, MA	146.716
Wayne, MI	1.506
Hennepin, MN	8.819
Itaska, MN	128.023
Alamance, NC	102.024
Johnson, NC	148.026
Mecklenberg, NC	16.713
Union, NJ	18.765
Dona Ana, NM	45.113
Luna, NM	121.904
Orange, NY	23.187
Hamilton, OH	8.979
Hardenman, TN	92.620
Marshall, TN	124.187
Shelby, TN	8.498
Harris, TX	2.370
Arlington, VA	88.657
King, WA	5.475

Basic Analysis Weights

Let n_i be the number of phone numbers dialed in site i, and N_i be the total population of phone numbers in site i, so that a fraction (n_i/N_i) of the population in site i was sampled. Then it may be supposed that the same fraction of low-income families with children under 13 has been sampled, and likewise the same fraction of low-income families using nonparental child care. Hence the basic analysis weight for each respondent in site i on both the screener analysis file and the survey analysis file is:

w_i x N_i / n_i.

Nonresponse Adjustments

The basic weights are imprecise to the extent that response rates vary among the sites. For site i, let R_i be the number of respondents to the screener, NR_i be the number of eligible nonrespondents, I_i be the number of known ineligibles, and U_i be the number with unknown eligibility. Then faute de mieux, we calculate Ê_i, the estimated total number of eligibles in the site, as equal to

{(R_i + NR_i / (R_i + NR_i + I_i)} x (R_i + NR_i + I_i + U_i)

— that is, that the eligibility rate among those of unknown eligibility is assumed to be the same as the rate among those of known eligibility. The response rate in site i is then calculated as

R_i / Ê_i,

and the response-adjusted weight is

(w_i x N_i / n_i) x (Ê_i / R_i).

Note that the weight is the same for all respondents in a site. The survey analysis weights are calculated identically except that different values are used for R_i and Ê_i, corresponding to the numbers of survey respondents and estimated eligibles.

Aggregate Response Rates

A total of 327,855 telephone numbers were released for dialing in the 25 sites. Of these,

129,244 were determined to be ineligible, even without any interviewer contact, because they were not household phone numbers. (They were phone numbers of businesses, FAX numbers, or beepers, or were disconnected).
84,007 were not reached, and hence were eligibility unknown.
The remaining 114,604 were contacted, and fell out as follows:
1. 106,323 were ineligible for the screener analysis (not a household, or no children, or annual income over 200 percent of FPL)
2. 1,897 were eligibility unknown for the screener analysis (because they terminated before responding to the questions about presence of children and income threshold)
3. 6,384 were found to be eligible for the screener analysis, of whom 224 refused the screener questions and 6,160 responded.

For calculating the aggregate screener response rate, therefore, we use:

R = 6,160
NR = 224
I = 129,244 + 106,323 = 235,567
U = 84,007 + 1,897 = 85,904

These numbers yield Ê = 0.0264 327,855 = 8,651, for an estimated response rate of 71.2%.

Of the screener respondents,

3,181 were ineligible for the interview (because they did not use nonparental care);
11 were of unknown eligibility for the interview (because they terminated before providing
information on use of nonparental care); and
2,710 were deemed eligible for the interview, of whom 2,264 responded and 480 refused.

For the survey, therefore, we have:

R = 2,264
NR = 480
I = 129,244 + 106,323 + 3,181 = 238,748
U = 84,007 + 1,897 + 224 + 11 = 86,139

so that Ê = 0.0123 327,855 = 4,026, for an estimated response rate of 61.8%.

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