This paper provides a comprehensive overview of multivariate analysis as a quantitative research tool, contrasting it with univariate and bivariate approaches. It explains the distinction between dependence and interdependence techniques, covering multiple regression, discriminant analysis, canonical correlation, MANOVA, factor analysis, cluster analysis, and multidimensional scaling. Practical examples drawn from marketing and social research illustrate how each technique is applied. The paper also discusses the role of computer software such as SPSS and SAS in enabling researchers to handle large, complex datasets, arguing that multivariate analysis offers a holistic perspective that provides both breadth and depth in data interpretation.
Research data collected using a quantitative approach can be analyzed and interpreted in different ways, using univariate, bivariate, or multivariate analysis.
Bivariate analysis examines the relationship between two variables. It is commonly analyzed with the aid of cross-tabulation, or cross-tab, allowing the researcher to examine the interaction between the two variables under study. These variables are referred to as the independent (or predictor) variable and the dependent (or outcome) variable. Their interaction is reflected in the cross-tab, and each interaction can be expressed in frequencies (raw counts), percentages, or both. It is critical in bivariate analysis to establish whether the observed relationship is statistically significant, since significance determines whether percentage differences in the results are worth analyzing. (However, the researcher may opt to examine percentage differences even when the relationship is not significant, for directional or diagnostic purposes only.)
Multivariate analysis, by contrast, examines the relationship among more than two variables. What makes this form of statistical analysis especially useful is that it provides both breadth and depth when looking at relationships among the variables under study — insights that could not have been obtained through bivariate analysis alone. Analyzing more than two variables is a rigorous and complex process, which is why a variety of techniques exist under multivariate analysis, including multiple regression, discriminant analysis, canonical correlation, factor analysis, and cluster analysis, among others.
In multivariate analysis, two broad categories of techniques are used: dependence techniques and interdependence techniques, each with its own objective.
Under the dependence technique, multivariate analysis examines the relationship between a variable or set of variables designated as dependent variable(s) and another set designated as independent variable(s). The relationship being analyzed involves the set of variables Xs, which are used to explain or predict the dependent variables Ys. Regression is a prime example of this technique: the relationship between two sets of variables is analyzed not only in terms of its nature and strength, but also in terms of the predictive power of the Xs on the Ys. Through regression, the researcher can also identify the contribution of one or more variables within the independent variable set Xs to the overall model.
The interdependence technique, meanwhile, examines relationships among variables without categorizing them as dependent or independent. All variables are treated and analyzed as a single set. The most commonly used analysis under this technique is factor analysis, which is primarily used to reduce and summarize research data into a more manageable form. Factor analysis helps the researcher identify and explain the relationships — specifically, correlations — among the variables being tested. This type of analysis is particularly useful in market research, where psychographic factors and attitude statements are often treated as one set of variables and factor analyzed to generate a smaller set that reflects, highlights, or explains differences among the variables and across respondent groups or profiles (Weiers, 1984: 473).
As noted above, linear regression examines the predictive power of two sets of variables, Xs and Ys, and provides information about the contribution of one or more independent variables to the relationship generated. Multiple linear regression extends this further: it not only determines the contribution of the independent variables to the relationship, but also accounts for the strength of each independent variable's contribution while controlling for the other independent variables in the model.
Discriminant analysis is a dependence technique that examines the relationship between a non-metric or categorical dependent variable and metric (interval) independent variables. It is used when the researcher wishes to discriminate between categories in the dependent variable — or among multiple categories in Y in the case of multiple discriminant analysis. A popular application of discriminant analysis is in credit card processing, where companies assess applicants based on their likelihood to repay based on each individual's demographic and psychographic profile (Malhotra, 1996: 617).
Canonical correlation analysis measures the strength of the association between sets of independent and dependent variables. This type of analysis is most helpful in validating test results, where the researcher determines which variables are significantly related and then runs further canonical analysis using those identified significant variables (Hair, 1995: 187). For example, canonical correlation analysis can be useful when a researcher wants to determine the usage of multiple credit card ownership and related expenditures based on independent variables such as personal or household income, marital status, occupation, family size, and educational attainment.
"Covers group comparison and data reduction techniques"
"Illustrates MDS and real-world research applications"
"Links computing advances to multivariate analysis growth"
In effect, multivariate analysis gives greater meaning to data, affording the researcher a holistic perspective that aids in the interpretation of results and supports more informed conclusions and recommendations.
Hair, J. (1995). Multivariate Data Analysis with Readings (4th ed.). Prentice Hall International.
Malhotra, N. (1996). Marketing Research: An Applied Orientation. Prentice Hall.
Weiers, R. (1984). Marketing Research. Prentice Hall.
You’re 44% through this paper. Sign up to read the remaining 3 sections.
Sign Up Now — Instant Access Already a member? Log inAlways verify citation format against your institution’s current style guide requirements.