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Verification of Hypotheses Concerning Parameters of the Regression Model for Complex Samples

100%
Domański C., University of Łódź C. o. S. M.
Acta Universitatis Lodziensis. Folia Oeconomica
|
2007
|
vol. 206
EN
The paper considers the linear regression function y = βx + ε, where β is a vector of unknown parameters and ε is a rest component. In case of complex samples some modifications of test statistics should be made. Results of simulation study revealed that the verification of the hypothesis H₀:β = β₀ should be conducted by means of modified test F.
PL
Problem szacowania parametrów funkcji regresji na podstawie prób nieprostych jest badany z górą od dwudziestu pięciu lat. Przedmiotem badania będzie liniowa funkcja regresji postaci macierzowej: y = βx + ε, gdzie β jest wektorem nieznanych parametrów, natomiast ε jest składnikiem resztowym. W przypadku prób nieprostych należy dokonać modyfikacji statystyki testowej, uwzględniając tzw. efekt schematu losowania. W pracy prezentowane są wyniki badań symulacyjnych, które wskazują na konieczność weryfikacji hipotezy H₀:β = β₀ za pomocą zmodyfikowanego testu F.
2
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How (Not) to Estimate the Design Effect of a Complex Sampling Scheme: A Case Study of the Polish Section of the European Social Survey, Round 5

86%
Jabkowski P.
ASK. Research and Methods
|
2013
|
vol. 22
55-77
EN
Design effect (DEFF) is a measure used to assess the effectiveness of a particular sampling scheme. Even though its definition is remarkably simple (cf. Kish 1965: 258), its practical implementation turns out to be problematic. Researchers therefore usually simplify the estimation of DEFF by independently determining the values of three components, namely, the clustering effect (DEFFc), the stratification effect (DEFFs) and the effect of unequal sampling probabilities (DEFFp) and by multiplying these partial measures to obtain a measure of overall effect. However, the validity of such a simplified version depends on strict formal requirements which are met only in a few sampling schemes. The subject of the analysis presented here is the sampling scheme in the Polish section of round 5of the European Social Survey (ESS). It will be shown that the method of DEFF estimation applied by the Polish coordinators of the project, which is compatible with the methodological recommendations of ESS (cf. Lynn et al. 2007: 114),does not satisfy the formal criteria that would validate its use. The author proposes two other ways of estimating the size of DEFF (cf. Gabler et al. 2006: 116-117) appropriate for the sampling scheme in ESS5-PL. Empirical analyses indicate that the use of the simplified procedure of DEFF prediction leads to significant underestimation of variance inflation in the sample design of ESS5-PL and, in turn, to overestimation of effective sample size.
3

Intracluster Homogeneity Selection Problem in a Business Survey

72%
Žmuk B.
Business Systems Research Journal
|
2016
|
vol. 7
|
issue 2
91-103
EN
Background: In the cluster sampling approach many parameters have influence on lowering the survey costs and one of the most important is the intracluster homogeneity. Objectives: The goal of the paper is to find the most optimal value of intracluster homogeneity in case when two or more questions or variables have a key role in the research. Methods/Approach: Five key variables have been selected from a business survey conducted in Croatia and results for the two-stage cluster sampling design approach were simulated. The calculated intracluster homogeneity values were compared among all the five observed questions and survey costs and precision levels were inspected. Results: In the new cluster sampling design, for the fixed precision level, the lowest survey costs would be achieved by using the intracluster homogeneity value which is the closest to the average intracluster homogeneity value among all the key questions. Similar results were obtained when survey costs were held fixed. Conclusions: If there is more than one key question in the survey, then the best solution would be to use an average intracluster homogeneity value. However, one should notice that in that case minimum survey costs would not be reached, but the precision levels would increase at all key questions.
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