41301 2008 : Homework

Homework Assignment # 1

1. In 1988 a study was conducted to determine the impact of scores assigned to an ordinal scale on the distribution of responses on that scale. The underlying response was regarding the question: "how successful would you say you have been in your life". An eleven category scale created ranging from "not at all successful" to "extremely successful". Two different scoring methods were used. By one method (method A) the 11 integers from 0 to 10 were assigned to the categories (“0" corresponding to "not at all successful”). By method B the integers from -5 to +5 were assigned ("-5" corresponding to "not at all successful"). Two independent samples representing the same population were drawn. One sample of 480 respondents was given scale A, while the second sample (of size 552) was given scale B. Distributions of response are given in Table 1 below.

a) Analyze the difference between the response patterns on the two scales. In your analysis conduct a relevant test comparing the two distributions, and use standardized residuals to determine the structure of the difference between the response patterns.

b) Try to provide a meaningful interpretation to your result.

Comments and suggestions for HW #1- problem1

1) To avoid zero entries you will have to combine the first 3 categories in Scale A.

2) To make the distributions comparable you will have to do the same for data in Scale B.

3) Relate to the distribution in Scale B as the “observed distribution” (or tested distribution). Find the “observed frequencies” [pic] from this distribution

4) Relate to the distribution on scale A as the “reference distribution” , from which you obtain the probabilities [pic].

5) Use these