Specify the data for your analysis, enter the number of factors to calculate, and specify the extraction method and type of rotation.

In Variables, specify the columns of data that you want to analyze. You must have two or more columns of numeric data, with each column representing a different measurement. If a missing value exists in any column, Minitab ignores the entire row.
###### Note

If you want to enter a stored correlation or covariance matrix, or the loadings from a previous analysis, instead of using raw data, click Options.

In this worksheet, each column contains measurements of characteristics of each job applicant.

C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 |
---|---|---|---|---|---|---|---|

Company fit | Communication | Self-confidence | Academic record | Resume | Experience | Attitude | Organization |

5 | 9 | 8 | 2 | 2 | 5 | 4 | 8 |

10 | 9 | 5 | 10 | 8 | 5 | 5 | 4 |

4 | 7 | 6 | 6 | 5 | 8 | 7 | 2 |

2 | 2 | 3 | 4 | 4 | 7 | 8 | 4 |

8 | 4 | 3 | 8 | 9 | 2 | 4 | 9 |

7 | 5 | 9 | 5 | 7 | 9 | 8 | 7 |

Enter the number of factors to extract from the data. The number of factors must be at least 1 and cannot exceed the total number of variables. For best results, you should not have more than one factor for every 3 variables in your data. For example, if you have 12 variables, you should extract, at most, 4 factors.

If you do not know the number of factors to extract, leave the field blank and specify principal components as the method of extraction. Click Graphs and display the Scree plot. Minitab calculates the maximum number of factors, which equals the number of variables that you entered. Use the results to determine the number of factors to extract, and then enter that number when you repeat the analysis. For more information, go to Step 1: Determine the number of factors.

If you use maximum likelihood as the method of extraction, you must enter the number of factors. The maximum number of factors with maximum likelihood is one less than the number of variables in your data.

Select a method to extract the factors.

- Principal components: Select this option if you do not know the number of factors to extract, if you cannot assume that the factors and errors obtained after fitting the factor model follow a normal distribution, or you do not have a large number of observations.
- Maximum likelihood: Select this option if you know the number of factors, you can assume that the factors and the errors obtained after fitting the factor model follow a normal distribution, and you have a reasonably large data set.

When you know the number of factors, Maximum likelihood often gives factors that fit the data better (have smaller residuals). However, for some data, the factor loadings from the maximum likelihood method are sensitive to the choice of initial communalities and convergence criterion. The principal components method works in many cases when the maximum likelihood method does not.

Select an option to orthogonally rotate the initial factor loadings. Minitab rotates the axes to give you a different perspective, which can help you to interpret the factors.

The original factor loadings are often difficult to interpret. Rotation usually creates a simpler factor structure and makes the factors more clearly distinguishable. Rotation also tends to remove general factors that load highly on all variables.

Minitab rotates the loadings to minimize a simplicity criterion. A parameter, gamma (γ), within this criterion, is determined by the rotation method. If you use a method with a low value of gamma, the rotation tends to simplify the rows of the loadings. If you use a method with a high value of gamma, the rotation tends to simplify the columns of the loadings.

- None: Do not rotate the loadings.
- Equimax: Rotate the loadings so that a variable loads high on one factor but low on others. This method is a compromise between the Varimax and Quartimax rotations.
- Varimax: Maximize the squared factor loadings in each factor (gamma = 1). Varimax is the most widely used rotation method. This rotation simplifies the columns of the factor loading matrix. In each factor, the large loadings are increased and the small ones are decreased so that each factor has only a few variables with large loadings.
- Quartimax: Maximize the variance of the squared factor loadings in each variable (gamma = 0). This rotation simplifies the rows of the factor loading matrix. In each variable the large loadings are increased and the small ones are decreased so that each variable will only load on a few factors.
- Orthomax with γ: Use loadings based on the value of gamma that you enter. Enter a gamma value between 0 and 1.

Because you cannot predict whether one type of rotation will make your factors more meaningful, try different rotations. If Equimax, Varimax, and Quartimax do not produce meaningful factors, you can use Orthomax with γ to explore rotations between the varimax rotation (gamma = 1) and the quartimax rotation (gamma = 0).