Der Nicht-Stichprobenfehler und seine Zerlegung in die beiden Komponenten „glatter Wert“ – wahrer Wert plus systematischer Fehler- und „Zufallsfehler“ / The Non-Sampling Error and its Decomposition into the Two Components “Permanent Value” – True Value plus Systematic Error- and “Random Error”: Schätzung mit Hilfe der Variate Difference-Methode und Analyse der horizontalen Aggregation individueller Zufallsfehler / Estimation by Means of the Variate Difference Method and Analysis of the Horizontal Aggregation of Individual Random Errors

In order to judge the quality of survey data it is necessary above all to estimate the size of the individual error components, i. e. the systematic and the random errors in the responses (survey data) of the surveyed units and, if feasible, to determinate their true value. This paper develops an estimation procedure by which the individual random errors included in individual response values can be ascertained as well as the total random error of a survey. As costumary in statistical surveys an additive linear error model is assumed: Individual response value = true value + systematic error + random error. The true value of a characteristic together with its systematic error are referred to as the permanent (smooth) component of the survey value. To assess the value of the permanent component the variate difference method is suggested in analogy to time series analysis, and the difference between response and estimated permanent component is the estimated random error. The permanent component is being estimated for each unit in a first stochastic approximation by means of an average of responses in three (re-)enumerations. With more than three (re-)enumarations further individual random errors and their average could be computed, this meaning a horizontal aggregation of individual estimates. This procedure is demonstrated for a simulated case.