Suggestion of confidence interval methods for the Cronbach alpha in application to complex survey data
Section 5. Concluding remarks
We explained how to obtain the confidence intervals of in survey sampling through the linearization and coverage-corrected bootstrap methods. Through the simulation study in the setting of multi-stage cluster sampling and unequal probability sampling, the linearization method showed the workable property in terms of the coverage rate in the case of the multi-normal distribution or correlated ordinal data. When dealing with some problematic continuous data such as the multi-lognormal distribution, the coverage-corrected bootstrap method showed better performance than the linearization method in terms of the coverage rates. The discussed interval estimation methods were applied to the NCS-R data set. The application demonstrated that both the interval estimation methods provide workable options to carry out an inference of incorporating the survey design.
We conclude this section by noting the following recommendations. First, in the case of an unknown continuous and skewed distribution, the coverage-corrected confidence interval is a safe way to provide a confidence interval whose actual confidence level may be close to the nominal confidence level. Second, if the data are discrete with a large sample size, the normal approximation using the linearization method may provide satisfactory coverage rates and be preferred because of the easiness of computation.
Acknowledgements
The authors are grateful to the Associate Editor and two reviewers for comments and suggestions that led to a substantial improvement in this paper.
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