Homework No. 4: H and C

Outline of Psychological Measurement

Response = J[C(H(A), H(B))]

Aj and Bi are the stimuli for Column j and Row i.

sAj and sBi are the subjective, scale values for the stimuli.

Yij is the subjective impression of the combination of Aj and Bi.

Rij is the overt response to this combination.

H are the functions that assign subjective values to the stimuli.

C is the combination function combining the subjective values.

J is the judgment function that assigns responses to impressions.

In this assignment, we let J be the identity function; i.e., Rij = Yij

Homework:

Make predictions for a 4 x 4, A x B, symmetric, factorial design using integers from 1 to 4 for levels of A and B. (sAj = Aj = j; sBi = Bi = i). Plot predictions as a function of A with a separate curve for each level of B.

Part A: H and J are identity functions.

1. Additive: Tij = sAj + sBi

2. Multiplicative: Pij = sAj sBi

3. Subtractive: Dij = sAj - sBi

4. Ratio: Rij = sAj/sBi

Part B: Repeat Part A, but now let H be a power function (square):

sAj = H(Aj) = A2 Similarly, let sBi = H(Bi) = B2

Part C: Repeat Part A, but substitute A.5 and B.5 for H(A) and H(B)

(H(B) = square root of B).

Part D: Repeat Part A, substituting log(A+1) and log(B+1) for H(A) and H(B).

Part E: What remains the same, irrespective of H, for the additive model? What changes? How can you use these graphical properties to separate H and C? Given a new set of data, how would you decide what model is appropriate? How would you determine H? Before you answer this question, organize your sixteen graphs for Parts A through D and additive, multiplicative, subtractive, and ratio models.