# GLM Univariate Analysis

This feature requires the Statistics Base option.

The GLM Univariate procedure provides regression analysis and analysis of variance for one dependent variable by one or more factors and/or variables. The factor variables divide the population into groups. Using this General Linear Model procedure, you can test null hypotheses about the effects of other variables on the means of various groupings of a single dependent variable. You can investigate interactions between factors as well as the effects of individual factors, some of which may be random. In addition, the effects of covariates and covariate interactions with factors can be included. For regression analysis, the independent (predictor) variables are specified as covariates.

Both balanced and unbalanced models can be tested. A design is balanced if each cell in the model contains the same number of cases. In addition to testing hypotheses, GLM Univariate produces estimates of parameters.

Commonly used a priori contrasts are available to perform hypothesis testing. Additionally, after an overall F test has shown significance, you can use post hoc tests to evaluate differences among specific means. Estimated marginal means give estimates of predicted mean values for the cells in the model, and profile plots (interaction plots) of these means allow you to easily visualize some of the relationships.

Residuals, predicted values, Cook's distance, and leverage values can be saved as new variables in your data file for checking assumptions.

WLS Weight allows you to specify a variable used to give observations different weights for a weighted least-squares (WLS) analysis, perhaps to compensate for a different precision of measurement.

Example. Data are gathered for individual runners in the Chicago marathon for several years. The time in which each runner finishes is the dependent variable. Other factors include weather (cold, pleasant, or hot), number of months of training, number of previous marathons, and gender. Age is considered a covariate. You might find that gender is a significant effect and that the interaction of gender with weather is significant.

Methods. Type I, Type II, Type III, and Type IV sums of squares can be used to evaluate different hypotheses. Type III is the default.

Statistics. Post hoc range tests and multiple comparisons: least significant difference, Bonferroni, Sidak, Scheffé, Ryan-Einot-Gabriel-Welsch multiple F, Ryan-Einot-Gabriel-Welsch multiple range, Student-Newman-Keuls, Tukey's honestly significant difference, Tukey's b, Duncan, Hochberg's GT2, Gabriel, Waller-Duncan t test, Dunnett (one-sided and two-sided), Tamhane's T2, Dunnett's T3, Games-Howell, and Dunnett's C. Descriptive statistics: observed means, standard deviations, and counts for all of the dependent variables in all cells. Levene tests for homogeneity of variance.

Plots. Spread-versus-level, residual, and profile (interaction).

GLM Univariate Data Considerations

Data. The dependent variable is quantitative. Factors are categorical. They can have numeric values or string values of up to eight characters. Covariates are quantitative variables that are related to the dependent variable.

Assumptions. The data are a random sample from a normal population; in the population, all cell variances are the same. Analysis of variance is robust to departures from normality, although the data should be symmetric. To check assumptions, you can use homogeneity of variances tests and spread-versus-level plots. You can also examine residuals and residual plots.

To Obtain GLM Univariate Tables

This feature requires the Statistics Base option.