1d:T748,# Estimation of the Population Total under Single Stage Simple Random Sampling Without Replacement This function computes the Horvitz-Thompson estimator of the population total according to a single stage sampling design. ```r E.1SI(NI, nI, y, PSU) ``` ## Arguments - `NI`: Population size of Primary Sampling Units. - `nI`: Sample size of Primary Sampling Units. - `y`: Vector, matrix or data frame containig the recollected information of the variables of interest for every unit in the selected sample. - `PSU`: Vector identifying the membership to the strata of each unit in the population. ## Returns This function returns the estimation of the population total of every single variable of interest, its estimated standard error and its estimated coefficient of variation. ## Details The function returns a data matrix whose columns correspond to the estimated parameters of the variables of interest. ## Examples ```r data('BigCity') Households <- BigCity %>% group_by(HHID) %>% summarise(Stratum = unique(Stratum), PSU = unique(PSU), Persons = n(), Income = sum(Income), Expenditure = sum(Expenditure)) attach(Households) UI <- levels(as.factor(Households$PSU)) NI <- length(UI) nI <- 100 samI <- S.SI(NI, nI) sampleI <- UI[samI] CityI <- Households[which(Households$PSU %in% sampleI), ] attach(CityI) area <- as.factor(CityI$PSU) estima <- data.frame(CityI$Persons, CityI$Income, CityI$Expenditure) E.1SI(NI, nI, estima, area) ``` ## References Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), **Model Assisted Survey Sampling**. Springer. Gutierrez, H. A. (2009), **Estrategias de muestreo: Diseno de encuestas y estimacion de parametros**. Editorial Universidad Santo Tomas ## See Also `E.2SI` ## Author(s) Hugo Andres Gutierrez Rojas

E.1SI function