%0 Journal Article
%T Bias and Mean Square Error of Reliability Estimators under the One and Two Random Effects Models: The Effect of Non-Normality
%A Mohamed M. Shoukri
%A Tusneem Al-Hassan
%A Michael DeNiro
%A Abdelmoneim El Dali
%A Futwan Al-Mohanna
%J Open Journal of Statistics
%P 254-273
%@ 2161-7198
%D 2016
%I Scientific Research Publishing
%R 10.4236/ojs.2016.62022
%X The coefficient of reliability is often estimated from a sample
that includes few subjects. It is therefore expected that the precision of this
estimate would be low. Measures of precision such as bias and variance depend
heavily on the assumption of normality, which may not be tenable in practice.
Expressions for the bias and variance of the reliability coefficient in the one
and two way random effects models using the multivariate TaylorĄ¯s expansion
have been obtained under the assumption of normality of the score (Atenafu et
al. [1]). In the present paper we derive analytic expressions for the bias and
variance, hence the mean square error when the measured responses are not
normal under the one-way data layout. Similar expressions are derived in the
case of the two-way data layout. We assess the effect of departure from normality
on the sample size requirements and on the power of WaldĄ¯s test on specified
hypotheses. We analyze two data sets, and draw comparisons with results
obtained via the Bootstrap methods. It was found that the estimated bias and
variance based on the bootstrap method are quite close to those obtained by the
first order approximation using the TaylorĄ¯s expansion. This is an indication
that for the given data sets the approximations are quite adequate.
%K RaterĄ¯s Reliability
%K Random Effects Models
%K Multivariate TaylorĄ¯s Expansion
%K WaldĄ¯s Confidence  Interval
%K Bootstrap Methods
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=65865