No abstract

cluster analysis, hierarchical, stopping rule, cluster distances, population overlap,

Heterogeneity of variance produces serious bias in conventional analysis of variance tests of significance when cell frequencies are unequal. Welch in 1938 and 1947 proposed an adjusted t test for the difference between two means when cell frequencies and population variances are both unequal. This article describes two ways to use the Welch t to evaluate the significance of the main effect for two treatments across k levels of a concomitant factor in a two-way design. Monte Carlo results document the bias in conventional analysis of variance tests and the stable and appropriately conservative results from applications of the Welch t to evaluation of treatment effects in the two-way design.

The power of computers has increased so much over the past few years that even personal computers are now practical platforms for training methods using graphics, sound, and animation. The use of multimedia in training has widespread applicability. However, in this chapter we focus on the use of multimedia to train people how to use software.Changes in available hardware have made multi-media-based training practical at a time when changes in software have made it a p pear necessary. Graphical user interfaces (GUIs; e.g., the Macintosh o p erating system, Microsoft Windows, and related software) are typically easier for new users to learn than command-based systems (Temple, Barker, & Sloane, 1990). However, their widespread adoption places new demands on the traditional process of using text-based instructions to train people to use software applications. Command-based software can be taught well with simple text instructions because the user interacts with the software simply by entering a defined sequence of commands for each operation performed. However, GUIs require multiple operations at different locations on the screen as well as choices from specific menus. Because users interact with graphical objects, it is help ful to demonstrate what the different objects look like, where they are located, and so forth. Thus, presenting training information visually seems more appropriate for teaching the use of these systems. Users can see how to perform procedures and can immediately observe the 28 1

Welch (1947) proposed an adjusted t test that can be used to correct the serious bias in Type I error protection that is otherwise present when both sample sizes and variances are unequal. The implications of the Welch adjustment for power of tests for the difference between two treatments across k levels of a concomitant factor are evaluated in this article for k x 2 designs with unequal sample sizes and unequal variances. Analyses confirm that, although Type I error is uniformly controlled, power of the Welch test of significance for the main effect of treatments remains rather seriously dependent on direction of the correlation between unequal variances and unequal sample sizes. Nevertheless, considering the fact that analysis of variance is not an acceptable option in such cases, the Welch t test appears to have an important role to play in the analysis of experimental data.