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Midterm Exam

Psychology 407

Spring 2008
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Name: \rule{5in}{.02in}

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Whenever possible, use fractions throughout.




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Questions I through III are all based on the following story-line and data:

A certain university was engaged in teaching Peace Corps volunteers the foreign languages they would need during their tours of duty.  An experiment (very small scale) was carried out to determine the effectiveness of the different teaching methods that were used.  All students were first given a language-aptitude test, which provided the measures that we will label by the letter X.

The experiment that was carried out was to evaluate two methods of teaching the foreign languages and to determine the value of language laboratory sessions.  The two teaching methods were: (1) formal classroom meetings with lectures, and (2) no formal classroom meetings --- only conversation periods held in a congenial atmosphere.  In addition, half of the students being taught by each teaching method spent three hours a day in the language laboratory wing the tape-recording equipment.  The other half of the students in each method group never entered the language lab.  subjects were randomly assigned to the four conditions, and the total instructional time was the same for all individuals.  Each volunteer was independently rated (by an expert) on a ten-point scale (1 to 10) for their language ability after the completion of the course.  These scores are represented by the letter Y.

The data that resulted from this experiment are as follows:

\begin{tabular}{c|cc|cc}

 & classroom &  &conversation & \\ \hline
 lab & X & Y & X & Y \\ \hline
  & 62 & 5 & 46 & 5 \\
    & 75 & 7 & 53 & 4 \\ 
     & 41 & 3 & 57 & 3 \\
       & 88 & 8 & 49 & 7 \\
         & 72 & 7 & 62 & 6 \\ \hline
     no lab      & 84 & 2 & 58 & 9 \\
             & 91 & 3 & 72 & 10 \\
               & 68 & 1 & 61 & 8 \\
                 & 77 & 1 & 65 & 8 \\
                   & 85 & 3 & 59 & 10 \\ \hline
                   
                   \end{tabular}
                   
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                     To aid in the computations that you might find yourself in need of completing, the following table given the various sums and (raw) sums of squares for the Y variable --- within the each of the four cells, within each of the rows and columns, as well as overall.  Sums are given first; sums of squares second.
                     
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                     \begin{tabular}{|c|c|c|}
                     
                     30; 196 & 25; 135 & 55; 331 \\ \hline
                     
                     10; 24 & 45; 409 & 55; 433 \\ \hline
                     
                     40; 220 & 70; 544 & 110; 764 \\ \hline
                     
                     \end{tabular}
                     
                     
                   
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  Suppose the data are treated in the form of a one-way analysis-of-variance layout with 4 groups: group 1 -- lab/classroom; group 2 -- lab/conversation; group 3 -- no lab/classroom; group 4 -- no lab/conversation.
  
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  a) Complete the analysis-of-variance source table -- label all terms appropriately.  (Form the test statistic, and indicate what degrees-of-freedom you would use in assessing significance.)
  
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