Applying Bootstrap Resampling to Compute Confidence Intervals for Various Statistics with R

Ankara University, Faculty of Educational Science, Department of Measurement and Evaluation,
DOI: 10.14689/ejer.2017.68.1


Background: Most of the studies in academic journals use p values to represent statistical significance. However, this is not a good indicator of practical significance. Although confidence intervals provide information about the precision of point estimation, they are, unfortunately, rarely used. The infrequent use of confidence intervals might be due to estimation difficulties for some statistics. The bootstrap method enables researchers to calculate confidence intervals for any statistics. Bootstrap resampling is an effective method of computing confidence intervals for nearly any estimate, but it is not very commonly used. This may be because this method is not well known or people may think that it is complex to calculate. On the other hand, researchers may not be familiar with R and be unable to write proper codes.

Purpose: The purpose of this study is to present the steps in the bootstrap resampling method to calculate confidence intervals using R. It is aimed toward guiding graduate students and researchers who wish to implement this method. Computations of bootstrapped confidence interval for mean, median and Cronbach’s alpha coefficients were explained with the R syntax step-by-step. Moreover, traditional and bootstrapped confidence intervals and bootstrapped methods were compared in order to guide researchers.

Main Argument and Conclusions: With the help of statistical software today it is easy to compute confidence intervals for almost any statistics of interest. In this study R syntax were used as an example so that beginners can use R to compute confidence intervals. Results showed that traditional and bootstrapped confidence intervals have very similar results for normally distributed data sets. Moreover different bootstrapped methods produce different results with skewed data sets. This is because bias corrected and accelerated interval methods are suggested for use with skewed data sets.

Implications for Research and Practice: R codes presented in this study guide researchers and graduate students while computing bootstrap confidence intervals. Furthermore findings about the comparison of bootstrap methods help researchers choose the most appropriate bootstrap methods. Results and the main argument of this study may encourage researchers to compute bootstrap confidence intervals in their studies.

Keywords: Confidence Interval P value Bootstrapped resampling Methods of bootstrapping R software.