Empirical Investigation on the Effect of the Number of Resamplings on the Distribution of Bootstrap Standard Error Using Response Time Data

Abstract

Aims: To investigate how the number of bootstrapping B affects the values returned by the bootstrap standard error of the arithmetic mean and the α-trimmed mean of response data using bootstrap confidence intervals (CI) at 95% level; carried out to fill up observed gap for study on standard error, the tool generally employed in assessing the long run accuracy of a given statistical estimator of θ. Study Design: This was a parametric, empirical bootstrap simulation study. Place and Duration of the Study: Departments of Computer Science and Statistics, Federal Polytechnic Oko, 2020/2021 session. Methodology: Response time data were generated with student customers of mobile telephone network (mtn) Nigeria and stored in SPSS. A sample n = 51 responses was selected using “Select Cases” command to increase precision and minimize bias. Bootstrap simulation study was carried out using R programming language. Four approaches for estimating bootstrap confidence intervals were used. The interval coverage and the interval lengths were determined and compared for B = 20, 50, 100, 500, 1000, 5000, and 10000. Results: The 95% CI for 0.2266338 (the estimated sample standard error of 10% trimmed mean) returned the best interval for our skewed data set; when B = 20; the CI for  returned (0.2051, 0.2343) for the normal approach, (0.2082, 0.2371) for the basic, (0.2071, 0.2360) for the percentile and (0.2071, 0.2360) for the BCa method. As B increased to 5000, it returned (0.2259, 0.2277) for the normal approach, (0.2259, 0.2277) for the basic, (0.2260, 0.2277) for the percentile and (0.2261, 0.2279) for the BCa showing a shorter interval yet covering the estimate. Conclusion: Thus for our response data study, increasing B in estimating standard error increases the chances of more precise and shorter confidence intervals rather than the chances for coverage.