Two different methods are presented in the chapter for testing trends with unequal n. This exercise explores how these methods differ. Consider a four-group study where the groups represent equally spaced levels of a quantitative factor. Assume that the following data have been obtained: Further assume that mean square within (MSW) = 2. a. One approach described in the text is a hierarchical approach. Find the contrast coefficients for testing the statistical significance of the linear trend for these data using this approach. b. Based on the coefficients of part a, test the linear trend for statistical significance. c. The other approach described in the text is an unweighted approach. What are the contrast coefficients for the linear trend using this approach? d. Based on the coefficients of part c, test the linear trend for statistical significance. e. Plot the sample means obtained here as a function of the level of the quantitative factor. Which plot of those in does your plot most resemble? Does your plot suggest the existence of a linear trend? f. Which approach, hierarchical or unweighted, seems preferable here? Why? g. Explain why the linear trend is significant here with the hierarchical approach.
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