Nordheim Statistics 411 Spring 2015 Notation For finite populations: [[used for design-based/randomization approach]] Population size is N: sample size is n. I will try to use Greek letters to represent population parameters or values. (One exception will be for binary data where we will use a Roman letter for population proportion.) General: The following 4 symbols refer to the entire population and are independent of sampling approach. Population notation: Population mean: µF (text uses yU) Population total: τ (text uses t) Population variance: σF2 (text uses S2) Population proportion: pF (text uses p) Sample notation: Sample mean: ˆµF (text uses different symbols, depending on sampling scheme --- we will also) Sample total: ˆτ (text uses ˆt) Sample variance: ˆσF2 (text uses s2--- for SRS) Sample proportion: ˆpF (text uses ˆp) SRS Notation for estimation: ˆµF= ySRS ˆτ=ˆτSRS ˆσF2= sSRS2= s2 (If there is no subscript, it will almost always be clear from the context that this refers to SRS.) ˆpF=ˆpSRSStratified Sampling: There are H strata. There is some specific notation beyond the general noted above. yhj value of jth unit in stratum h Population notation: Nh population size for stratum h τh population total for stratum h µhF population mean for stratum h σhF2 population variance for stratum h Sample notation: nh sample size for stratum h yh sample mean for stratum h sh2 sample variance for stratum h Notation for estimation (of population parameters): ˆτh ˆµF= ySTR
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