In multivariate statistics, Exploratory Factor Analysis (EFA) is a statistical method used to uncover the underlying structure of a relatively large set of variables. EFA is a technique within factor analysis whose overarching goal is to identify the underlying relationships between measured variables. It is commonly used by researchers when developing a scale (a scale is a collection of questions used to measure a particular research topic) and serves to identify a set of latent constructs underlying a battery of measured variables.

It should be used when the researcher has no a priori hypothesis about factors or patterns of measured variables. Measured variables are any one of several attributes of people that may be observed and measured. An example of a measured variable would be the physical height of a human being. Researchers must carefully consider the number of measured variables to include in the analysis. EFA procedures are more accurate when each factor is represented by multiple measured variables in the analysis.

Example: You have set up a questionnaire about customer satisfaction in the civil aviation industry (United Airlines, Delta, Lufthansa). You have identified 30 items to describe and evaluate customer satisfaction (e.g. “convenience of buying tickets”, “convenience of checking-in”, “environment of the lounges”, “friendliness of the flight attendants”, “fulfilling special desires”, “quality of food on board”, “comfort of the seats”, “special offers such as in-flight movies”, “accuracy of arrival”). By using EFA you can reduce the set of 30 items within your analyzing process to a couple of central factors which underlay your set of items. You can consider for example that the items “convenience of buying tickets”, “convenience of checking-in”, “environment of the lounges”, “quality of food on board”, “comfort of the seats” and “special offers such as in-flight movies” are part of a potential dimension. The hard things which airlines can perform to drive their business. However, “friendliness of the flight attendants”, “fulfilling special desires” and “accuracy of arrival” are more part of a process dimension.

That means EFA is finding out exactly these structures – in our example the factor “potential” and “process”. Managers now can get a deeper insight for developing marketing activities to improve the satisfaction of their customers by focusing more on the “potential”-part or on the “process”-part.

### Origin of Exploratory Factor Analysis

Factor analytic methodologies may be conceived on a continuum. This continuum ranges from confirmatory techniques towards pure exploratory procedures. Charles Spearman (1904 onward) was interested in confirming the idea of a general intelligence. With extended experimental evidence, developed through years of studies involving larger test batteries given to larger samples of individuals, Spearman’s theory of a single intellectual factor proved to be inadequate. A possibility had to be created to deal with group factors. In the early 1930s, Thurstone broke with a common presumption based on prior assumptions as to the nature of factors and developed a general theory of multiple factor analysis. Thurstone’s book “Vectors of Mind” (1935) presented the mathematical and logical basis for this theory.

### Calculation of Exploratory Factor Analysis. Formula

To analyze data by using EFA you can use statistical packages such as SPSS or SAS.

### Usage of Exploratory Factor Analysis

- Customer satisfaction surveys.
- Measuring service quality.
- Personality tests.
- Image surveys.
- Identifying market segments.
- Typing customers or products or behavior.

### Steps in Exploratory Factor Analysis

A typical EFA process is as follows:

- Identify the indicators/items which go in the EFA.
- Calculate a correlation matrix (coefficient of correlation from Bravais-Pearson).
- Examine the correlation matrix to be used for a EFA (level of significance, inverse of the correlation matrix, Bartlett-Test, anti-image-covariance-matrix, Kaiser-Meyer-Olkin-Criteria KMO)
- Choose a factor extraction method (principal components analysis, principal factor analysis).
- Discover the factors and of the factor loadings. Factor loadings are the correlation coefficients between the variables (rows in the table) and factors (columns in the table).
- Fix the number of factors to be extracted (for this step it is useful to take the Kaiser-Criteria and the Scree-Test with the elbow-criteria).
- Interpret the factors extracted (e.g. “potential” and “process” in the given example above)

### Strengths of Exploratory Factor Analysis

- Easy to use
- Useful for lots of survey questions,
- Basis of other instruments (e.g. regression analysis with factor scores), easy to combine with other instruments (e.g. confirmatory analysis)

### Limitations of Exploratory Factor Analysis

- Variables have to be interval-scaled.
- Falling number should be larger than three times of the amount of variables.

### Assumptions of Exploratory Factor Analysis

- No outliers, interval data, linearity, multivariate normality, orthogonality for principal factor analysis

Source: Klaus Backhaus, Bernd Erichson, Wulff Plinke – Multivariate Analysemethoden

Source: Joseph F Hair, Ronald L Tatham, Rolph E. Anderson, William Black – Multivariate Data Analysis

Source: John C. Loehlin – Latent Variable Models

Business frameworks like Exploratory Factor Analysis are invaluable to evaluating and analyzing various business problems. You can download business frameworks developed by management consultants and other business professionals at Flevy here.