Sample Size Determination in Test-Retest and Cronbach Alpha Reliability Estimates

Abstract

The estimation of reliability in any research is a very important thing. For us to achieve the goal of the research, we are usually faced with the issue of when the measurements are repeated, are we sure we will get the same result? Reliability is the extent to which an experiment, test, or any measuring procedure yields the same result on repeated trials. If a measure is perfectly reliable, there is no error in measurement, that is, everything we observe is the true score. However, it is the amount/degree of error that indicates how reliable, a measurement is. The issue of sample size determination has been a major problem for researchers and psychometricians in reliability studies. Existing approaches to determining sample size for psychometric studies have been varied and are not straightforward. This has made the psychometric literature contain a wide range of articles that propose a variety of sample sizes. This paper investigated sample sizes in test-retest and Cronbach alpha reliability estimates. The study was specifically concerned with identifying and analyzing differences in test-retest and Cronbach alpha reliability estimate of an instrument using various sample sizes of 20,30,40,50,100,150,200,300, and 400. Four hundred and eight (408) senior secondary school students from thirty-eight (38) public senior secondary schools in Benin metropolis part took in the study. The Open Hemisphere Brain Dominance Scale, by Eric Jorgenson was used for data collection. Data were analyzed using Pearson Product Moment Correlation Coefficient (r) and Cronbach alpha. The findings revealed that the sample sizes of 20 and 30 were not reliable, but the reliability of the instrument became stronger when the sample size was at least 100. The interval estimate (Fisher's confidence interval) gave a better reliability estimate than the point estimate for all samples. Based on the findings, it was, therefore, recommended that for a high-reliability estimate, at least one hundred (100) subjects should be used. Observed or field-tested values should always be used in the estimation of the reliability of any measuring instrument, and reliability should not be reported as a point estimate, but as an interval.