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signi cant, then, closer examination of the distribution of the DV is in order If it is markedly skewed, the sphericity test should be repeated after a normalizing transformation of the DV If the test is now nonsigni cant, the problem with the data set is probably nonnormality rather than failure of sphericity If the test is still signi cant, there is probably nonsphericity The Mauchly test also has low power for small samples and is overly sensitive with very large samples Thus, with large samples it is sometimes signi cant when departure from sphericity is slight It is always worthwhile, then, to consider the magnitude of the epsilon factor, even when the test of sphericity is explicitly provided.

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The basic purpose of the study was to discover qualities related to managerial success and advancement in the company Results revealed that test and inventory scores as well as staff judgments on several dimensions predicted salaries and advancement to middle management over several years (Howard & Bray, 1988) This research effort by Bray and his colleagues stands out as one of the most carefully designed and comprehensive longitudinal studies ever conducted (Dunnette, 1998, p 140) Flagging productivity in the 1960s and 1970s forced companies to look at new ways of managing They examined their foreign competitors successes and consequently changed from individualistic, authoritarian systems to structures emphasizing groups, teamwork, employee participation, and total quality management (1986 1987 SIOP past president Sheldon Zedeck, personal communication, July 6, 2000).

There are ve options when the assumption of sphericity is not tenable: (a) use comparisons on the IV in question (usually trend analysis) instead of the omnibus test; (b) use an adjusted F test; (c) use a multivariate test of the within-subjects effects; (d) use a maximum likelihood procedure that lets you specify that the structure of the variance-covariance matrix is other than compound symmetry; or (e) use a multilevel modeling approach in which the multiple responses over time are the lowest level of analyses and are nested with subjects, the next higher level of analysis The rst option comparisons takes advantage of the fact that sphericity is not required when there is only one df for the within-subjects IV.

With the advent of organization development (OD) as an attempt to better understand the process of group dynamics, the assumption that developing people would create healthier and more effective organizations changed to the assumption that developing organizations would create healthier and more effective people (Mirvis, 1988) In the 1980s, stagnant productivity, threats to economic well-being, and American companies failure to adapt to economic circumstances raised concerns about productivity, utility, and quality Although the foundations for utility analyses had been offered earlier (eg, Brogden, 1946), it was not until the 1980s that serious attention to utility analysis surfaced (Cascio, 1991) In addition, a renewed interest in OD reestablished the relationship between employees and organizations (Muchinsky, 2000) Some I-O psychologists view OD as a symbiosis of scientists and practitioners (eg, Lowenberg & Conrad, 1998)..

This option, in the form of trend analysis, is often a good one because questions about trends in the DV over time are usually the ones that researchers want answered anyway, and the assumption of sphericity is most likely to be violated when the IV is time related Trend analysis asks, Does the DV increase (or decrease) steadily over time Does the DV rst increase and then decrease (or the reverse) Are both patterns present, superimposed on each other and Are there other, more complicated, patterns in the data Before the sophisticated software was available for other options, trend analysis (or other comparisons) was preferred on strictly computational grounds It is still preferred if the researcher has questions about the shape of the patterns in the DV over time.

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However, a disadvantage of trend analysis (or any set of comparisons) in within-subjects design is that each comparison develops its own error term This reduces the number of df for error and consequently the power available for the test of the comparison The second option is to use a more stringent F test of the IV in question Both Greenhouse-Geisser (1959) and Huynh-Feldt (1976) adjustments are offered by all three software packages that recognize within-subjects designs Both compute an adjustment factor, epsilon ( ), that is used to reduce df associated with both numerator and denominator of the F test Reducing df makes the F test more conservative Both Greenhouse-Geisser and Huynh-Feldt compute.

Ward, Hudson, & Keenan (2001)