中  華  心  理  學  刊
民93，46卷，1期, 029-047

Pei-Chen Wu（Department of Elementary Education, National Ping- Tung Teachers College）

Abstract

T his study examines five measures of location (means, 10% and 20% trimmed means, one step M-estimators based on Huber's 111 and modified one step M-estima- tors) in terms of t heir Type I error rates, standard errors and significance levels in 24 empirical data sets. Twenty-four empirical data sets can be categorized into eig ht kinds of distributions w hic h frequently arise in ed- ucational and psyc hological researc h--- dis- crete mass at zero, mass at zero, extreme positive skew, extreme negative skew, bi- modality, multi-modality and lumpy, digit preference, and smoot h symmetric. T he re- sults s how t hat t he 20% trimmed mean, one step M-estimator and modified one step M-estimator, are good alternatives for com- paring two groups based on comparing mea- sure of location. Student's t is t he least sat- isfactory statistic. Also, t his study indicates t hat comparing measures of location pro- vides information only on t he typical value of t he groups. T his limitation is apparent in some situations considered here w here none of t he five measures of locations are completely satisfactory. T hus, t he study rec- ommends comparing quantiles of two groups to obtain an overall picture of t he re- lations hip between two groups.

Keywords: measure of location, means, trimmed means, one step M-estimators, modified one step M-estimators