Factor analysis: definition, use and analysis

Factor analysis: definition, use and analysis


Factor analysis, a subfamily of multivariate analysis, brings together different methods designed to analyze complex data tables. The objective: to highlight the existence and the absence of influencing factors between the variables, and to rank them.

> Download these marketing experience templates” align=”middle”/>Example: the company conducts a satisfaction survey for its online store; she interviews individuals from four distinct age groups, and asks them to rate their satisfaction on a scale of 1 to 5; the results entered in a double-entry table are difficult to understand; with factor analysis, the company transforms the table into a graph to better visualize the significant variance factors and identify the relevant groupings; in particular, it finds a strong link of dependence between age and satisfaction among 18-25 year olds, whereas the age factor is relatively indifferent in terms of satisfaction among those over 60 years old.

Whatever the method, factor analysis has the following characteristics:

  • Of the descriptive methods : unlike explanatory methods with a predictive aim, factor analysis methods are mainly used for exploratory purposes. It is a question of graphically describing the results, in a readable way, to better observe them.
  • L’absence of starting hypotheses : these exploration methods are implemented to discover or not variance factors, without any a priori on the results of the search.
  • A massive volume of data : factorial analysis facilitates the observation of the results of surveys or studies which provide a considerable number of answers, and which bring into play numerous variables of various natures.
  • A Graphic Representation : the analysis generates, after advanced mathematical calculations or via automation software, a cloud of data. This format facilitates the readability of the results to possibly highlight the links between the variables.
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When to do a factor analysis?

Performing a factor analysis is relevant when the survey introduces many variables into the questionnaire, submitted to a considerable number of individuals. In this context, the data table is difficult not only to elaborate, but also to analyze. On the one hand because the data are complex to organize between them, on the other hand because of their volume. It is necessary to simplify. Factor analysis allows you to reduce the number of variables, to highlight and prioritize the only factors that cause significant variance.

By way of illustration: factor analysis is useful for the company to segment its large contact base. The company collects customer data relating to age, gender, geographical location, socio-professional category or family situation to understand consumer behavior. The data is represented in a matrix, in the form of a scatter plot: discrepancies and interesting data groupings appear. The company observes, for example, that the factor of age is decisive in purchasing behavior, while the factor of gender is less influential and the factor of family situation is indifferent; for the age factor, a grouping of data appears: 18-25 year olds consume on the social network sales channel; the company creates a profile on this basis, and adapts its marketing strategy.

How to do a factor analysis?

Lead the investigation

Factor analysis is descriptive in nature: the information is condensed to select the only relevant variables from a massive volume of data. This is a preliminary step to the explanatory analysis, which makes it possible to draw useful conclusions for the purpose of valuing the data. The starting point of factor analysis: obtaining data, as part of a study or survey.

  1. Determination of the objective of the survey. Example: the company wonders how its communication channels direct the audience to its sales channels.
  2. Collection of data. In the example, the company develops and distributes a questionnaire to ask its contacts about their purchasing behavior and how they got to know the brand.
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Process survey results

The collected data is organized in a multi-entry table. Insofar as the number of variables is large, and when the sample questioned is extensive, the table obtained is an accumulation of figures which, although ordered, do not highlight exploitable results.

Generate a point cloud

Factorial analysis of correspondences, principal component analysis or even discriminant factorial analysis: whatever method is chosen, factorial analysis makes it possible to transform the rows and columns of the table into a cloud of points on a two-axis plane. This step is carried out using dedicated mathematical formulas. Software can perform the calculations automatically.

The graph thus obtained offers better readability in comparison with the original table: not only because it is a visual representation, but also because the factorial analysis made it possible to generate a summary of the variables, keeping the most relevant in within the framework of a fair approximation, and removing the variables that do not provide information.

How to interpret a factor analysis?

Interpreting a factor analysis amounts to observing the deviations and groupings of points that appear on the graph:

  • When a grouping of points appears, it is possible to deduce a dependency link between the variables.
  • Dependencies can be prioritized based on the level of proximity of points.
  • The distance and the angle of the difference between two groupings of points make it possible to exclude the link of dependence.
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In the previous example, the company wishes to observe and highlight the existence and the absence of influencing factors between the way in which the customer has known the brand and his purchasing behavior. The scatter plot shows the variables as follows:

  • The points which represent the customers who buy in store are close to the points which represent the customers who have known the brand thanks to an advertising campaign on Facebook: the company deduces from this that Facebook advertising attracts customers in physical stores.
  • The points which represent the contacts who have not yet purchased the brand’s products are distant from the points which represent the contacts who have known the brand through word-of-mouth: the company deduces from this that word-of-mouth ear does not convince of the strengths of the brand.
  • The scatter plot does not show any grouping between customers who buy online and customers who have known the brand through a commercial on television: the company deduces from this that television advertising does not direct customers more towards the online sales channel than other communication channels.

At the end of the factorial analysis, the results can be refined by means of an explanatory analysis method.

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