Let us now return to the interpretation of the standard results from a factor analysis (see Reviewing the Results of a Principal Components Analysis). We will henceforth use the term factor analysis generically to encompass both principal components and principal factors analysis. Let us assume that we are at the point in our analysis where we basically know how many factors to extract. We may now want to know the meaning of the factors, that is, whether and how we can interpret them in a meaningful manner. To illustrate how this can be accomplished, let us work "backwards," that is, begin with a meaningful structure and then see how it is reflected in the results of a factor analysis. Let us return to our satisfaction example; shown below is the correlation matrix for items pertaining to satisfaction at work and items pertaining to satisfaction at home.

STATISTICA FACTOR ANALYSIS |
Correlations (factor.sta) Casewise deletion of MD n=100 |
|||||

Variable |
WORK_1 |
WORK_2 |
WORK_3 |
HOME_1 |
HOME_2 |
HOME_3 |

WORK_1 |
1.00 |
.65 |
.65 |
.14 |
.15 |
.14 |

WORK_2 |
.65 |
1.00 |
.73 |
.14 |
.18 |
.24 |

WORK_3 |
.65 |
.73 |
1.00 |
.16 |
.24 |
.25 |

HOME_1 |
.14 |
.14 |
.16 |
1.00 |
.66 |
.59 |

HOME_2 |
.15 |
.18 |
.24 |
.66 |
1.00 |
.73 |

HOME_3 |
.14 |
.24 |
.25 |
.59 |
.73 |
1.00 |

The work satisfaction items are highly correlated amongst themselves, and the home satisfaction items are highly intercorrelated amongst themselves. The correlations across these two types of items (work satisfaction items with home satisfaction items) are comparatively small. It thus seems that there are two relatively independent factors reflected in the correlation matrix, one related to satisfaction at work, the other related to satisfaction at home.

Interpreting the Factor Structure

See also, Exploratory Data Analysis and Data Mining Techniques.