Equations for Calculating Response Rates

Field Crops Production

(OMB # 0535-0002)

Calculations for:

Total responses,

Average response rates, and

Coverage of commodity rates.

October 15, 2015

To calculate the average response rate, OMB Guideline 3.2.2 is used (see below). However, if there is more than one wave of data collection, then the completed cases and in-scope sample cases are summed across the waves. This is shown in the ‘Average Response Rate’ column in the table.

Where C_k = number of completed cases or sufficient partials in k^th data collection wave

R_k = number of refused cases in k^th data collection wave

NC_k = number of non-contacted sample units known to be eligible in k^th data collection wave

O_k = number of eligible sample units not responding for reasons other than refusal in k^th data collection wave

U_k = number of sample units of unknown eligibility, not completed in k^th data collection wave and

E_k = estimated proportion of sample units of unknown eligibility that are eligible in k^th data collection wave.

The ‘Total Responses’ column in table represents the numerator of the response rate above or the sum of completed cases or sufficient partials over all data collection waves.

The ‘Coverage of Commodity Rate’ is a weighted item response rate as described in OMB Guideline 3.2.3 (see below). It can also be described as the proportion of a key survey estimate that was reported by respondents who completed the survey. The formula used to calculate the ‘Coverage of Commodity Rate’ in the table is:

Where w_j = the inverse probability of selection (or initial sampling weight) for the j^th completed report

y_i = reported data for key survey item from j^th completed report

a_i = non-response adjustment for the j^th completed report

The units of survey estimate used to calculate the Coverage of Commodity Rate varies by survey. They are specified in the table below:

Survey	Units of Coverage Rate
Sweet Potato Price	Cwt
Sugarbeets	Tons
Sugar Production Survey	Tons
Tobacco Price Inquiry	Lbs.
All other surveys listed	Acres