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| In general, for a given confidence level, there are seemingly infinite confidence intervals that may have such a confidence level, thus the question is which one to choose? Evaluation of the shortest length method provides a robust approach in this regard as it localizes the best, or rather true value of the parameter. To this end, in this study, a systematic comparison of the length of confidence interval (c.i) is conducted. The approach adopted involves the equal-tail method based on splitting equally and the shortest confidence method which involves a problem minimization concept. Results obtained from the analysis show the ratio of variance if the sample size not large (n <30) , the length computed by equal-tail method and the shortest method are different. But as the sample size increases, it was found that the lengths approximate each other. But it’s noticeable to add that for the ratio of two variance, if the two degrees of freedom r1 and r2 are different there exist always difference between the two length computed by the two methods. If r1 is less than r2, the difference between the both length is small than if r1 is great than r2.
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| Keywords:Pivotal Quantity, Confidence Interval, Confidence LevelContinuity, Bijection, Minimization, Equal-tail, Shortest Length. |
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