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        Psychology 407

        Assignment \#5


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1)  Suppose we are investigating the effect of \emph{school} on the
performance of students on a specific arithmetic test.  We select
grades 5, 6, 7, and 8 in each of four schools.  The schools were
randomly selected from the population of all schools of interest,
and 5 subjects from each grade and school were randomly assigned to
take the test.  A high score implies a good performance on the test.

\normalsize

\begin{tabular}{ccccc}


  &  &  School &  & \\


  & 1 & 2 & 3 & 4 \\


Grade  &  &  &  &  \\


5  & 110,87,79,102,73  & 51,76,43,91,74 & 56,50,64,61,43 & 67,60,50,80,40 \\



6  & 118,96,104,94,126  & 93,64,57,116,84 & 83,72,60,47,105 & 126,101,100,103,126 \\



7  & 82,84,74,60,70 & 111,117,91,105,76 & 102,100,97,131,89 & 68,87,69,65,69 \\



8  & 115,76,85,89,77  & 79,105,106,102,92 & 91,77,98,100,61 & 90,111,91,86,74 \\


\end{tabular}

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\bigskip

Between School SS: 1,264.94

Between Grades SS: 8,090.14

Interaction SS: 12,265.51

Total SS: 37,198.19

\bigskip

i)  Construct the appropriate ANOVA table based upon Model III.

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ii)  Estimate whatever variance components you can.

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iii) Is Paull's criterion (as discussed in class) applicable?  If
so, use it.  Do the results differ?

\bigskip

2)  Suppose we give three exams in a statistics course consisting of
26 students.  Again, a high score indicates a good performance on
the test.  Using the data given below, construct the appropriate
ANOVA table based on a mixed model design without replication.  Can
you test all main effects?  Why or why not?  Is your result still
the same if you use the conservative Geisser-Greenhouse test as
discussed in class?

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\begin{tabular}{cccc}

 &  &  Test & \\

  &  1  & 2 & 3 \\ \hline


Student &  &  &  \\

1  & 63 & 71 &  64 \\




 2 & 75  & 62 & 63 \\




 3 & 64 & 55 & 54 \\




4  & 75 & 71 & 32 \\




 5 & 73 & 67 & 58 \\




 6 & 73 & 62 & 62 \\




 7 & 75 & 70 & 62 \\




8  & 75 & 70 & 72 \\




 9 & 68 & 60 & 44 \\




 10 & 77 & 68 & 52 \\




 11 & 60 & 60 & 50 \\




12  & 76 & 78 & 56 \\




13  & 75 & 79 & 62 \\




 14 & 77 & 70 & 64 \\




15  & 49 & 50 & 39 \\




16  & 74 & 62 & 58 \\




17  & 67  & 55 & 42 \\




18  & 59 & 66 & 48 \\




19  & 76 & 62 & 48 \\




20  & 79 & 73 & 67 \\




21  & 54 & 53 & 49 \\




22  & 77 & 69 & 53 \\




23  & 83 & 84 & 72 \\




24  & 65 & 51 & 37 \\




25  & 63 & 52 & 24 \\




26  & 78 & 67 & 58 \\ \hline

\end{tabular}

\bigskip

Between Tests SS: 3,867.31

Between Students SS: 5,421.91

Residual: 1,932.74







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