Estimating the Reliability Index Using Confidence Interval: A Comperism of the Fisher Z and the Bootstrap Confidence Interval Method

Abstract

The study focused on estimating the reliability index using confidence interval by comparing the Fishers Z and the bootstrap confidence interval methods. The rational for the study was to examine the bootstrap and the Fisher –Z methods and finding out the better of the two. The population of the study consists of the senior secondary school students in Egor local government area, Edo State. There are a total of 12 school with 8,207 students. A sample size of 410 representing 5% of the total population of students were randomly selected from the 12 schools. The instrument for data collection was the Open Hemisphere Brain Dominance Scale 1.0 (OHBDS) a personality scale designed by Eric Jorgenson (2015). It was adapted for the study. The instrument was validated. The reliability was part of the issues raised in the study. The data were analyzed using the Pearson Product-Moment Correlation Coefficient to determine the reliability. The Fishers Z 95% and the Bootstrap (percentile and bias corrected and accelerated) confidence interval were also used. The findings revealed that as the sample size became large, the length of the interval became narrower; the three methods utilized in this study yielded the same length of the interval (width) when the same size was 100 and 150; and as the sample size increases, the bias corrected and accelerated bootstrap gave a shorter interval length, thereby becoming the best of the three method considered in the study. It was therefore recommended that reporting reliability should be based on interval estimation as against the point estimate, the sample size should be at least 100 and the bootstrap confidence interval should be adopted as it is not liable to the normality condition associated with the classical statistics.