Tasks 3:  Planned Contrasts Using Scheffé Method
This problem continues with the same data set presented above. 

Based on the researchers hypotheses, it is necessary to test this group of orthogonal contrasts:

Contrast	$\displaystyle {c}_{{1}}$	$\displaystyle {c}_{{2}}$	$\displaystyle {c}_{{3}}$	$\displaystyle {c}_{{4}}$
$\displaystyle \psi_{{1}}$	$\displaystyle {1}$	$\displaystyle {1}$	$\displaystyle {1}$	$\displaystyle -{3}$
$\displaystyle \psi_{{2}}$	$\displaystyle -{2}$	$\displaystyle {1}$	$\displaystyle {1}$	$\displaystyle {0}$
$\displaystyle \psi_{{3}}$	$\displaystyle {0}$	$\displaystyle {1}$	$\displaystyle -{1}$	$\displaystyle {0}$

Questions for reflection:  What is actually being tested with these contrasts?  In particular, for each contrast, which combined group averages are being compared to what?  Finally, confirm that each contrast is valid and that each pair is orthogonal.

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The researcher prefers to control for experiment-wise significance ($\displaystyle \alpha_{{\text{fw}}}={0.05}$), and decides to use the Scheffé test.  What is the critical value for these contrasts (report to 3 decimal places):
$\displaystyle {t}_{{\text{c.v.}}}=$

Calculate the t-ratio for each contrast (report all values to 3 decimal places):
    Contrast 1:
          $\displaystyle \psi_{{1}}=$
          $\displaystyle {t}_{{1}}=$
    Conclusion:     Contrast 2:
          $\displaystyle \psi_{{2}}=$
          $\displaystyle {t}_{{2}}=$
    Conclusion:     Contrast 3:
          $\displaystyle \psi_{{3}}=$
          $\displaystyle {t}_{{3}}=$
    Conclusion: