solution

Analyse the Benetton data (taken from Exercise 4, Chapter 20). Consider only the following variables: awareness, attitude, preference, intention and loyalty towards Benetton.

a Analyse these data using principal components analysis, using the varimax rotation procedure.

b Interpret the factors extracted.

c Calculate factor scores for each participant.

d If surrogate variables were to be selected, which ones would you select?

e Examine the model fit.

f Analyse the data using common factor analysis, and answer parts b to e.

Exercise 4

In a survey pre-test, data were obtained from 45 participants on Benetton clothes. These data are given in the table overleaf, which gives the usage, gender, awareness, attitude, preference, intention and loyalty towards Benetton of a sample of Benetton users. Usage was coded as 1, 2 or 3, representing light, medium or heavy users. Gender was coded as 1 for females and 2 for males. Awareness, attitude, preference, intention and loyalty were measured on a seven-point Likert-type scale (1 = very unfavourable, 7 = very favourable). Note that five participants have missing values, which are denoted by 9.
Analyse the Benetton data to answer the following questions. In each case, formulate the null and alternative hypotheses and conduct the appropriate statistical test(s):

a Obtain a frequency distribution for each of the following variables and calculate the relevant statistics: awareness, attitude, preference, intention and loyalty towards Benetton.

b Conduct a cross-tabulation of the usage with gender. Interpret the results.

c Does the awareness for Benetton exceed 3.0?

d Do males and females differ in their awareness of Benetton? Their attitude towards Benetton? Their loyalty to Benetton?

e Do the participants in the pre-test have a higher level of awareness than loyalty?

f Does awareness of Benetton follow a normal distribution?

g Is the distribution of preference for Benetton normal?

h Assume that awareness towards Benetton was measured on an ordinal scale rather than an interval scale. Do males and females differ in their awareness of Benetton?

i Assume that loyalty towards Benetton was measured on an ordinal scale rather than an interval scale. Do males and females differ in their loyalty towards Benetton?

j Assume that attitude and loyalty towards Benetton were measured on an ordinal scale rather than an interval scale. Do the participants have a greater awareness of Benetton than loyalty to Benetton?