## Multivariate Statistics

Multivariate statistics are data analysis procedures that simultaneously consider more than two variables. Such procedures can be descriptive (e.g. examining the joint distribution of a group of variables) or inferential. Inferential procedures may examine differences in two or more variables across groups (e.g. multivariate analysis of variance), predict one variable using two or more independent variables (e.g. multiple regression, structural equation modeling), estimating relationships between a set of variables where two or more variables are dependent (e.g. path analysis, structural equation modeling). Multivariate analyses can be conducted at the observed level (e.g. multiple regression analysis, cluster analysis), or at the latent level (latent variable modeling). Procedures conducted at the observed level use the entire measured value of a variable (the manifest value), whereas latent procedures estimate the error of measurement of observed variables and takes this parameter into account in further analyses. Latent variable modeling relies on the assumption that a latent (unobservable) variable, or construct (e.g. intelligence), is underlying the data and explains the relationships between the observed variables (e.g. test scores).

Multiple linear regression allows researchers to predict or to explain the variance of a response variable using multiple predictors. For instance, college GPA can be predicted based on SAT scores, the amount of time spent studying, variables measuring students’ motivation, etc. This procedure allows researchers to compare the predictive power of each explanatory variable, to identify the strongest predictors and eliminate the ones that are not statistically significant. The following narrated presentation shows how to conduct multiple linear regression using the stepwise approach. It explains how to estimate regression parameters, the inferences that can be made based on multiple regression, and how to determine whether regression parameters are statistically significant. The software tutorial demonstrates how to conduct a stepwise multiple regression in SPSS.

• Diana Mindrila, Ph.D.
• Phoebe Balentyne, M.Ed.

Exploratory Factor Analysis (EFA) is a statistical procedure that investigates patterns of variation across multiple variables to identify groups of variables that provide similar responses. EFA can be used for data reduction purposes (Principal Component Analysis) or to identify the latent constructs or the dimensions that underlie the data (Common Factor Analysis). The following presentation provides a brief introduction to the topic of EFA and provides an example of common factor analysis.

Diana Mindrila, Ph.D.

Diana Mindrila, Ph.D.