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        Psychology 407

        Assignment \#7


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1) The effect of five levels of associative strength of
adjective-noun pairs on recognition threshold was investigated.  Ten
word pairs having associative strengths of .30--.39 (treatment level
$a_{1}$), ten having associative strengths of .40--.49 (treatment
level $a_{2}$), and so on were from Palermo and Jenkins'  (1964)
list.  The adjective of a word pair was presented tachistoscopically
for 100 milliseconds.  Immediately afterwards, the noun was
presented for 20 milliseconds.  If the noun was not recognized, the
exposure time for the noun on a subsequent trial was increased by 5
milliseconds.  This was continued until the noun was recognized. The
dependent variable was mean time in milliseconds required to
recognize the ten nouns in a list.  Twenty-five subjects were
assigned to five rows of a Latin square so that those within a row
were similar with respect to noun recognition thresholds.  The
columns of the Latin square corresponded to five graduate students
who were conducting the testing sessions.  The following data were
obtained.

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\begin{tabular}{cccccc}

  & $c_{1}$ & $c_{2}$ & $c_{3}$ &  $c_{4}$ & $c_{5}$ \\

 $b_{1}$  & $a_{1}$(72)  &  $a_{2}$(62)   &  $a_{3}$(66)   &  $a_{4}$(51)   &  $a_{5}$(40)   \\



 $b_{2}$ &  $a_{2}$(65)   &  $a_{3}$(61)   &  $a_{4}$(40)   &  $a_{5}$(44)   &  $a_{1}$(59)   \\



 $b_{3}$ &  $a_{3}$(55)   &  $a_{4}$(46)   &  $a_{5}$(35)   &  $a_{1}$(63)   &  $a_{2}$(54)   \\



 $b_{4}$ &  $a_{4}$(34)   &  $a_{5}$(29)   &  $a_{1}$(54)   &   $a_{2}$(44)  &  $a_{3}$(50)   \\



 $b_{5}$ &  $a_{5}$(51)   &  $a_{1}$(49)   &  $a_{2}$(43)   &  $a_{3}$(30)   &  $a_{4}$(25)   \\







\end{tabular}

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a)  Write down the model that would be appropriate.  What factors
should be considered fixed/random?  Will this make a difference in
how the various tests are carried out for this particular design?

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b) Provide the usual ANOVA source table.  Interpret.

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c) Using Tukey's HSD method, carry out all pairwise comparisons
between the 5 levels of the treatment (i.e., $a_{1}$ to $a_{5}$).
Use a family confidence coefficient of .95.

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2)  An industrial psychologist was interested in decreasing the time
required to assemble an electronic component.  Three assembly
fixtures, Treatment $A$, including the one currently in use,
$a_{1}$, were evaluated.  Five operators at each of the six
workplaces within the plant, treatment $B(A)$, were selected
randomly.  The assembly fixtures were randomly assigned to the six
workplaces and the operators at those workplaces.  After a
three-week familiarization period, the following data on the number
of units assembled per hour were collected.

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\begin{tabular}{cccccc}

 $a_{1}$  &   $a_{1}$   &   $a_{2}$   &   $a_{2}$   &  $a_{3}$   &  $a_{3}$   \\



 $b_{1}$  &   $b_{2}$  &   $b_{3}$  &   $b_{4}$  &  $b_{5}$  &  $b_{6}$
 \\  \hline




 17 & 13  & 21  & 25  & 26 & 32 \\




  7 &  23 & 24  & 29  & 34 & 32 \\




   9 &  14 & 14  & 26  & 32 & 37 \\




  12 & 18  & 19  & 24  & 30 & 34 \\




  15 &  22 & 17  & 21  & 28 & 35 \\



\end{tabular}

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(Treat factor $A$ as fixed; $B$ as random)

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a) Obtain the usual ANOVA source tables, treating $B$ as nested
within $A$.  Interpret.

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b) Is this design balanced?  Show numerically the relation between
SS(A) and SSB + SSAB if we would ``equate'' $b_{3}$, $b_{4}$ and
$b_{5}$, $b_{6}$ to $b_{1}$, $b_{2}$, and then consider this design
to be completely crossed.

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c) Evaluate all pairwise differences between the levels of factor
$A$ using Tukey's procedure (with a confidence coefficient of .95).


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