# TWO MULTI-PHASE SURVEYS THAT COMBINE OVERLAPPING SAMPLE CYCLES AT PHASE I

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4 ::::::.:.:... : : : : : : : : : : : : : : : : : : : : : : :::::.: :: : : : : : : : : : : : : : : : : : : : : : : : : :::: :: :::... ::... : : : : : ::::::::::::::::::::::::::::::::::::: To produce CSU expectations on the number of outlets required in oversampling to achieve the desired number of outlets for each formulation, ratios of the formulations were derived using the monthly survey where possible. Where ratios could not be calculated, such as ones involving OPRG, which is not collected separately in the monthly survey, population ratios for the specific attainment status at the state level were used instead. For each CSU, the CSU's total gasoline volume across the three grades was multiplied by the expected proportion of gasoline for each of the four formulations to yield an expected volume by formulation. The CSU's monthly weight was applied to these formulation volumes and divided by the total weighted volumes for the PADD for that formulation and then multiplied by the cell's desired allocation to yield the expected number of outlets to be sampled for each CSU. This was done separately for companies in each of the two monthly respondent cycles and the results of the two cycles added together. These expectations were then divided by their proportion of the CSU volumes. The maximum of these four results, one per formulation, was the global expectation or the size measure that was used for each CSU. Sampling then proceeded as in the diesel fuel sample, using Probability Proportional to Size (PPS) and a sampling interval of 1. Because of the use ofoversampling, second stage sampling was necessary. For each outlet selected, the outlet's adjusted expectation was divided by the maximum adjusted expectation. If this quotient was larger than a selected random number between zero and one, the outlet was retained. If the quotient was smaller, the outlet was dropped. The second phase sampling produced 507 CSUs from 304 companies. Stage 1 resulted in 1,174 outlets, and stage 2 yielded an expectation of 820 outlets as shown in Table 4. Final stage 2 expected and actual allocations by formulation are shown in Table 5. Table 4. GASOLINE FRAME AND SAMPLE ALLOCATIONS (IST STAGE AND 2ND STAGE EXPECTATIONS~, BY CELL i iiit:~i~i~i!~!~:~ i;:~:!~ ~ili i~:! :! i~ ~:!~:~: i~::: : :i ;:;:::i ~. i i : ~!: :ii::::: ~ : i ~ :i i::: i:i::: :i ::i::i!i ::::: ~:::i i~i :::i::::ii: ::i ~ :i i~ :i: i:i ~!: ::.:i:i:i iii:!ii:::!ii~iliiiii:::i!i!:..iiil!iiiii:..i~:::~::~i:ii!:!ii:~i:.:i-~::il i ii:::i : ~ " : i. - :il :~ i!! :i.! : i ~ :i : ::~:~i :: - :i!~:~ ii - I:I:::P~D:... :... ~....B :.i :IC!... :::ii.i... : 111: : IV :!CA: :: OtherV:! TOT~ : :.. :..:::::.:.:...::.-::-:: :::. :.:::::...::..,..:..:.::. :.::.,. :..... :. :.: :...: :: ::...:. :::. :..: : :. :.. :..:. :.. : :... :..... i ~ Pha~ i ii i i! esu '~ ::::: : ': :Ph:~e 2: : ::CSU ::!! i... i::s:ple:i;.:.: :-::... :.:... ::::: ::::::..::..: : :!:i,ph~sei',21:::;::ii il :::~ioufiets ::::i! ::!st Sta :: ::::..:::: :.: :.:::::::::.:: : i!ii :.::oufietsii~!iii

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