# 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.

- From the menus choose:
- Select a dependent variable.
- Select variables for Fixed Factor(s), Random Factor(s), and Covariate(s), as appropriate for your data.
- Optionally, you can use WLS Weight to specify a weight variable for weighted least-squares analysis. If the value of the weighting variable is zero, negative, or missing, the case is excluded from the analysis. A variable already used in the model cannot be used as a weighting variable.

This procedure pastes UNIANOVA command syntax.