The steps involved in conducting factor analysis are illustrated in Figure 19.3. The first step is 10 define the factor analysis problem and identify the variables 10 be factor analyzed. Then a correlation matrix of these variables is constructed and a method of factor analysis selected. The researcher decides on the number of factors to be extracted and the method’ of rotation. Next, the rotated factors should be interpreted. Depending upon the objectives, the factor scores may be calculated, or surrogate variables selected, to represent the factors in subsequent multivariate analysis. Finally, the fit of the factor analysis model is determined. We discuss these steps in more detail in the following sections,”

**Formulate the Problem **

Problem formulation includes several tasks. First, the objectives of factor analysis should be identified. The variables to be included in the factor analysis should be specified based on past research, theory, and judgment of the researcher. It is important that the variables be appropriately measured on an interval or ratio scale. An appropriate sample size should be used. As a rough guideline, there should be at least four or five times as many observations (sample size) as there are variables.

In many marketing research situations, the sample size is small and this ratio is considerably lower. In these cases, the results should be interpreted cautiously. To illustrate factor analysis, suppose the researcher wants to determine the underlying benefits consumers seek from the purchase of a toothpaste. A sample of 30 respondents was interviewed using mall-intercept interviewing. The respondents were asked to indicate their degree of agreement with the following statements using a 7·point scale (l = strongly disagree, 7 = strongly agree):

V1: It is important to buy a toothpaste that prevents cavities.

V2: I like a toothpaste that gives shiny teeth.

V3: A toothpaste should strengthen your gums.

V4: I prefer a toothpaste that freshens breath.

V5: Prevention of tooth decay is not an important benefit offered by a toothpaste.

V6: The most important consideration in buying a toothpaste is attractive teeth.

The data obtained are given in Table 19.1. For illustrative purposes, we consider only a small number of observations. In actual practice, factor analysis is performed on a much larger sample such as that in the Dell running case and other cases with real data that are presented in this book. A correlation matrix was constructed based on these ratings data.