A Robust Likelihood Ratio Test for Testing Equal Means in the Presence of Unequal Variance

• Activity Number: 368
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Achut Adhikari*+
• Companies: University of Northern Colorado
• Keywords: Likelihood ratio test ; Type I error rate ; Unequal Variance ; Sampling Distribution

Abstract

In this work, I studied the sampling distribution of the likelihood ratio statistic, denoted ?, within the context of unequal variances. My search for a more general test is in response to the elevated alpha of the F test, in the presence of unequal variances. This work is valuable because the empirical alphas for the F test and the -2log (?) are often higher than the intended a = 0.05, in the presence of unequal variance, especially for small samples. I presented a framework for a robust test which relies on the sampling distribution of ? and not the transformed ?. Hence, we do not have to depend on the chi square distribution for an approximation. Finally, simulations revealed for each value of n, the P05 values are very stable under the effect of different variance patterns. So indeed the 5th percentile values are stable (within a fixed value of n) over the variance patterns we studied. It remains to be seen if these P05 values serve as effective critical values for a test of equal means. This question will be studied in subsequent research.