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A Simple Alternative to Student's T
Author(s) -
Prescott P.
Publication year - 1975
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.2307/2346569
Subject(s) - simple (philosophy) , mathematics , statistics , mathematics education , computer science , philosophy , epistemology
Summary An easily computed t ‐statistic is defined in terms of a trimmed mean and a highly efficient linear estimator of scale. It is shown that the statistic is satisfactorily approximated by a multiple of a Student's t variable with slightly reduced degrees of freedom. Alternatively the statistic may be referred to a table of percentage points produced by an efficient Monte Carlo technique. The procedure requires only a partial ordering of the data into three groups and the calculation of the averages of the observations in these three groups. No sums of squares are involved. For observations from a normal distribution the procedure is shown to have power only slightly lower than that of t whereas for certain long‐tailed non‐normal situations it is demonstrated that the alternative has greater power than t to detect moderate to large shifts in population mean.

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