Abstract:
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Inference with extremely limited available data is a challenge. We consider the case when the only available data from each of k normally distributed populations are sample size and two sample percentiles, where the samples sizes and available percentiles differ across samples. We propose a statistic for testing the equality of the k population means based on the available percentiles. This work includes the case of unequal sample sizes, different percentile pairs across samples, and unequal variances. The proposed test statistic has an approximate F distribution. The power of the proposed test is investigated using simulation.
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