Power Analysis of the I,ikelihood Ratio Tests for Exponential Populations

Abstract

Abstract The statistical power of the likelihood ratio (LR) test for testing the parameter (7) of the exponential distribution under different puameter , considerations and sample sizes was- inuestigated. Up tiil now, , considerations hud only been on the effect and sample sizeswhile determining the power of statistical hypothesis tests, especially those that involve the parameters of exponential distribations of the form Hq: 7 = 7o vs, Hr: A = 7r Thus, literature is apparently silent on the impact of the siies of the parameterpair (7s,7) being tested on the power of the test. This was investigated in this stady in addition to some other situqtions considered for determining power of LR test for exponential distribations through detail Monte Carlo studies. Part of the novel resultsobtainedfrom this study showed that the power of the test is highly sensitive to the sizes of parameter pair (7s,\) being tested irrespective the effict sizeA: lls - 71l.In other words, at any given sample size, small values of the parameter pair (7s,7) yielded appreciable power than the large values of the parameter pair (70,71 of the bxponential distibutions being tested even under equal effect sizes. Therefore, increasing the sample size at any point may only be desirsble as a corrective me&sure to increase the power of the LR test whenever the power provided by the test is considered small, the situation that can possibly occur when the parameter pair (As,A) of tlte exponential distributions being tested is relatively large. The implication oJ' these results is thut fewer samples would be reqaired to attain an appreciuble power with small vulues of the parameter pair (7o,7) while large samples would be needed to attsin u similar feat of power size under large values of the parameter pair (7s,7) even if the effect size is the same under the tw,o test problems. Further results from this study indicated that fewer samples would be required by the LR test to ach,ieve appreciable power as the chosen size a level of the test increases. Empirical illustrations are provided to validate the results from Monte Carlo experiments. It is therefore recommended tlrat more attention should be given to the size of the parameters being tested in any statisticul significant test if the prime interest is to achieve appreciable power.