The forecasts are constructed essentially in two different ways:
For responses obtained from the Biggest group, a composite index for growth CI is obtained by aggregating the predicted filings and then dividing by the number of known filings from the same applicants in the previous year to the survey year (base year).
Where n is the number of respondents in the Biggest group and summation is taken over this group i = 1, ..., n.
xi is the intended number of filings for the year of interest reported by the ith responding applicant .
Ai is the number of applications made by the ith sampled applicant in the base year
For responses obtained from the Random group, individual growth indices are calculated and a Q index for growth is obtained as a weighted average after logarithmic transformation of these indices. The weights qi (aka Poisson weights) reflect the numbers of filings previously made by each respondent i and their probability of inclusion of that respondent in the sample. This probability differs for applicants depending on their numbers of applications in the base year, because the random sampling is itself done over all applications rather than applicants.
Where Ii = xi / Ai.,
n is the number of respondents in the Random group and summation is taken over this group i = 1, ..., n.
n+ is the number of randomly selected applications that led to the selection of applicants for the Random group (n+ > n, because some applicants make more than one application)
A is the total number of filings by the population of applicants in the base year.