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        Psychology 407

        Assignment \#2


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Suppose we are testing four ways of teaching the oxidation-reduction
method of balancing chemical equations. We randomly assign 80
students to one of four groups (group sample sizes are all 20). The
dependent variable is the number correct in a test of 15 items.

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\begin{tabular}{cc}

Method  &  Group Mean \\ \hline

1  &  10.0 \\

2  &  10.0 \\

3  &  12.0 \\

4  &  6.0 \\

\end{tabular}

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\noindent In the usual analysis of variance table, the mean square
for error was 2.0.

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a) Assume methods 1 and 2 are variations on one particular
``modern'' technique, method 4 is the ``traditional'' technique, and
method 3 is a combination of the ``traditional'' and ``modern''
techniques. Using this substantive information, what would be a
reasonable way to formulate the analysis in terms of planned
comparisons? Carry out your formulation using confidence intervals
and control the overall error rate with the Bonferroni method.

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b) Assuming the overall F-test was significant, carry out a post-hoc
analysis using Scheff\'{e}'s method to answer the same questions you
investigated in (a) using planned comparisons. Compare the
confidence intervals under both approaches.

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(c) Develop confidence intervals for all pairwise differences
between the means using the Tukey, Scheff\'{e}, and Bonferroni
methods. Compare the size of the resulting confidence intervals.



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