Data and Methods
THE SURVEY
Data was collected through a web survey (for a copy of the full survey instrument see section A7 of the Appendix ). To create a comprehensive list of
manufacturers in Virginia, we used data purchased from Manufacturers’ News, Inc. and augmented those data with VMA membership records. Based
on these sources, a list of 5,863 Virginia manufacturers was compiled. Survey invitations, including a cover letter from Governor Kaine (see section A6
of the Appendix), were mailed to all manufacturers on that list, along with instructions for accessing the web survey. In addition, email invitations were
sent to the approximately 2,900 manufacturers on the list for which an email address was available. Later, two sets of follow-up postcards were sent to manufacturers who had not responded, with additional instructions for obtaining a paper version of the survey, should that option be necessary.
The initial deadline for the survey was set for July 12, 2007 and was later extended to July 27, 2007 in an attempt to encourage a greater number of responses. The final number of completed surveys received was 456. Face-to-face interviews were employed to verify the data received for ten randomly selected survey responses (for a tabulation of the responses from these validation interviews, see section A8 of the Appendix).
EXTRAPOLATION TO THE STATEWIDE LEVEL
Projecting the information received from the survey to the statewide level involved two statistical operations. First, because the distribution of survey
responses was more heavily weighted toward larger manufacturers than is typical of the broader distribution of manufacturers within the state (i.e.,
larger firms were more likely to respond to the survey than smaller firms), it was necessary to adjust the survey sample to bring it into alignment with
the statewide norm. This required stratifying the survey responses according to firm size and re-weighting the findings from each stratum to bring
them into alignment with the proportion of statewide employment accounted for by manufacturers within that size category.21 Second, the results obtained from the survey were projected to the statewide level and standard errors were calculated around each of those statewide estimates.22
21The survey sample was stratified according to nine standard firm size categories. To account for differences in the distribution of different size firms between the sample and the
population of manufacturers within the state as a whole, weights were applied to the survey results obtained for each of the nine stratum. These weights forced the sum of the number
of employees estimated in each sample stratum to that of the statewide population of manufacturers within that firm size category (based on Virginia Employment Commission 4th quarter
2006 data on industry employment). Whereas more typical weighting schemes would adjust the sample strata to match the statewide proportion of firms in each firm size category (as
opposed to the number of employees), this approach proved untenable because the weighted estimate was found to be biased. The source of that bias proved to be the largest stratum
(firms with over 1,000 employees), where the sampling units included outliers that biased the sample for that stratum relative to the statewide population of manufacturers.
22The “survey” library for the statistical package R2.4.1 was employed to estimate the standard errors of the total and mean estimates. This software was developed by Thomas
Lumley at the University of Washington. The Jackknife method of replication was used and each replicate was pos-stratified to produce the standard errors (see Valiant, Richard,
“Post-stratification and Conditional Variance Estimation,” Journal of the American Statistical Association, pp.88:89-96, 1993, for a detailed description of the benefits associated
with using this method to address situations of this nature). The results were verified by hand.