The article by Deha Dogan systematically discusses the application of bootstrap resampling methods to compute confidence Intervals for various statistics with R. Confidence Interval measures the precision of the point of estimation. It is the probability that a population parameter appears within a set of values in a sample proportion. The study illustrates stepwise computation of mean, median and Cronbach’s alpha coefficient using the various bootstrapping methods. Dogan seeks to push for use of bootstrapped analysis in social sciences using R language in computing confidence intervals. Using R, researcher can compute confidence intervals for any statistics. This paper conducts a critical analysis of the article on the application of bootstrapping resampling method in computation of confidence interval using R.
Bootstrapping
Refers to resampling methods used to assess uncertainty. It involves drawing a sub-sample from the main sample and running analysis, unlike traditional method where a sample is drawn from the population and analysis carried out. According to Dogan, this method provides robust confidence intervals. It requires use of at least 2000 replications for effective bootstrap resampling. The method has a limitation, unlike other methods where samples can be of a smaller size The main methods are normal interval, percentile interval, basic interval, and bias corrected, and accelerated interval. The author concedes that this powerful statistical tool is not used in analysis in social sciences partly due to the perceived complexity of R language. The author, therefore, offers guidance on bootstrap resampling using R.
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Traditional Versus Bootstrapped Confidence Intervals For Mean
The traditional method used a normally distributed population of 100,000 observations with (µ = 60, σ = 7). Six random samples of 50 observations are taken and confidence interval computed. On the other hand, six bootstraps each with 2000 resamples are used and confidence interval computed. The results are almost similar and minor differences are observed in the first or second decimal places. The bootstrapping methods do not produce significant differences from the traditional mean for normally distributed data. Hence, we can conclude with 95% confidence that the interval has the true mean. However, the analysis does not consider other data distributions. For data that is not normally distributed, the article fails to provide a comparative analysis.
Bootstrapped Confidence Intervals For Median For Normal And Sked Data
The researcher computes confidence interval for both normally distributed and skewed data sets. Population 1 is normally distributed with 1,000,000 while population 2 has 1,000,000 with skewed chi-square distribution. The author uses large data to demonstrate how R can be used in generating large data. The comparative results show that confidence intervals for the normally distributed data are almost similar, while for skewed data confidence intervals are different. Clearly, bootstrapping methods cannot be used for all data set especially where a formula for computing standard errors is unavailable. The study only confirms the efficacy of bootstrapping methods in using normally distributed data. Researchers should therefore pay attention to the distribution of data before using bootstrapping techniques. Non-parametric bootstrapping in calculation of confidence interval is limited, unlike empirical Bayes confidence intervals which are more accurate in non-parametric testing (O’Rourke & MacKinnon, 2015)
Bootstrapped Confidence Intervals For Cronbach’s Alpha Coefficient
This test measures the internal consistency of a scale and ranges between 0 and 1. In calculating Cronbach’s Alpha Coefficient using bootstrapping technique, the study generated 2000 resamples using R syntax. The analysis provided for bias and standard error. The Cronbach’s Alpha was 0.83 and for the item correlations, it was between 0.60 and 0.70. Further, the Cronbach’s Alpha interval was found to be smaller compared to confidence interval for the other item correlations. The findings are inconclusive because the author disclaims that the study was not focused on constructing a scale but rather computing the CI. Whereas the study affirms the use of bootstrapping methods in calculation CI, it does not guide the reliability of the results.
Conclusion
The results show consistency in the various bootstrapping methods under normal data distribution. However, with skewness, the methods show variability in computing confidence interval, especially for median. Undoubtedly, confidence intervals are a good measure of significance and should be adopted. I also agree with the study that researchers need to decide on the bootstrapping method to use depending on the distribution of data. Bootstrapping analysis is efficient in skewed data where a formula for computing standard error is available. Despite the few limitations, the technique can be used to encourage use of confidence intervals in academic studies.
References
Dogan, C. D. (2017). Applying bootstrap resampling to compute confidence intervals for various statistics with R. Eurasian Journal of Educational Research , 17 (68), 1-18.
O’Rourke, H. P., & MacKinnon, D. P. (2015). When the test of mediation is more powerful than the test of the total effect. Behavior research methods , 47 (2), 424-442.
