Psychology 407 Assignment #7

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.

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)

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?

b) Provide the usual ANOVA source table. Interpret.

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.

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.

\begin{matrix}a_{1} & a_{1} & a_{2} & a_{2} & a_{3} & a_{3} \\ b_{1} & b_{2} & b_{3} & b_{4} & b_{5} & b_{6} \\ 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{matrix}

(Treat factor A as fixed; B as random)

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

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.

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