Data Research, Vol. 1, Issue 1, Dec  2017, Pages 10-18; DOI: 10.31058/j.data.2017.11002 10.31058/j.data.2017.11002

Bootstrapping Normal Distribution with Different Group Proficiency Forms

Data Research, Vol. 1, Issue 1, Dec  2017, Pages 10-18.

DOI: 10.31058/j.data.2017.11002

Acha Chigozie Kelechi 1*

1 Department of Statistics, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria

Received: 30 November 2017; Accepted: 22 December 2017; Published: 13 January 2018

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Abstract

The objective of this paper is to ascertain which group proficiency form (GPF-models) provide more reliable statistical inference by applying nonparametric bootstrap on a normal distribution and define the performance of the GPF-models estimator for forecasting and predicting. The group proficiency forms (ability levels) are very important in a identifying a more reliable statistical model(s) for forecasting and predicting. This objective was achieved by considering seventeen assessment conditions which includes group proficiency forms-upper and lower quartiles of the variance, test lengths, bootstrap levels, sample sizes and the root mean square error. The result as indicated in Table 1 and 2, GPF4 model was associated with the smallest RMSE; 0.0000 in Test 1, followed by GPF6, GPF1, GPF2, GPF5 & GPF3, GPF7 and 0.0001, 0.0002, 0.0004, 0.0009, 0.0017 & 0.0067 respectively under the same assessment conditions. Moreover, the smallest RMSE in all the models is GPF4; 0.0000 while GPF7; 0.0996 gives the largest RMSE in Test 2.GPF4 and GPF7 produced the same RMSE value (0.0130) at B=99, N(0,0.25), n=50000 assessment conditions. The results of the nonparametric bootstrap RMSE with respect to their group proficiency forms showed that the GPF4 model provides more reliable statistical inference among all other models and can be used for forecasting and predicting, though, the effects of the group proficiency forms were quite small compared to sample sizes and bootstrap levels.

Keywords

Group Proficiency Forms, Test Length, Models, Quartiles, Nonparametric Bootstrap

Copyright

© 2017 by the authors. Licensee International Technology and Science Press Limited. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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