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**APPENDIX 4**

**SURVEY
WEIGHTING PROCEDURES**

OMB No. 0910-xxxx

Expiration Date: xx/xx/xxxx

This appendix describes the survey weighting procedures. Survey weights will be computed in three steps:

1. Compute initial sampling weights by stratum (Establishment size small: 1–19 employees; medium: 20–499 employees; large: 500 or more employees; and tattoo ink manufacturers).

2. Adjust the initial sampling weights for unknown eligibility.

3. Use the WTADJUST procedure within SUDAAN 11 to adjust the weights for nonresponse to the survey (RTI International, 2012).

Each step in the weighting procedures is described below.

**Initial Sampling
Weights.** Each establishment in the sample (i.e., sample point)
will be assigned an initial sampling weight. The initial sampling
weight (W_{0}) is equal to the inverse of the selection
probability, where the selection probability is equal to the sample
size (n) divided by the population (N). Thus, the initial sampling
weight for each stratum is calculated as follows:

W_{0}
= .

For the Large and Tattoo Ink stratum in which a census is being taken, the initial sampling weight is equal to 1. For each stratum, the sum of the initial sampling weights across all sampled establishments is equal to the population.

**Adjustment for
Unknown Eligibility. **Adjustment factors will be calculated within
each stratum to adjust for sample points for which the eligibility
status is unknown.^{1}
The adjustment factor for establishments with unknown eligibility is
calculated as follows:

F_{1}
= .

The adjustment
factor for establishments with known eligibility is equal to 1 (i.e.,
F_{1} = 1).

The adjusted weight for each establishment in a stratum is equal to

W_{1}
= W_{0} x F_{1}

**Nonresponse
Adjustment. **Nonresponse may cause bias in survey estimates if
establishments choosing not to respond would have provided answers to
questions that differ systematically from answers provided by
establishments that choose to respond. If a response rate of 80% is
not achieved, a nonresponse bias analysis will be conducted to
examine the characteristics of respondents and nonrespondents to
determine if they are statistically different. The results of this
analysis will inform us of characteristics we should include in our
nonresponse bias adjustments. Characteristics included in the
nonresponse bias analysis are those found on our sampling frame as we
have information available for both respondents and nonrespondents.
Potential characteristics include establishment size (stratification
variable), census region, and establishment
type (manufacture cosmetics only; manufacture multiple lines of
business including cosmetics, drug and medical; manufacture multiple
lines of business including cosmetics, but no drug and medical
manufacturing; manufacture tattoo ink).

The nonresponse
adjustment factor will be calculated using the SUDAAN procedure
WTADJUST (RTI International, 2012). This procedure uses a
constrained logistic model to predict the likelihood of responding as
a function of a set of explanatory variables (establishment size,
census region, and establishment type for the Cosmetics Survey) and
calculate a nonresponse adjustment factor. This adjustment factor
will be applied to the unknown eligibility adjusted weight, W_{1,
}to create the final weights.

The final weights will vary by the variables included in the WTADJUST procedure. We will review these weights and identify unusually large weights and determine if any additional weight adjustments are needed. If any are found we will use the SUDAAN WTADJUST procedure to calculate a weight trimming adjustment factor that will reduce the size of the large weights.

All results will be weighted using the final adjusted weights. For each stratum, the sum of the final adjusted weights across all respondents to the survey is equal to the population of eligible establishments.

1 It is anticipated that the eligibility status for some establishments will be unknown if we are not able to reach the manufacturer during the survey administration period.

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