Question

1. Factorial analysis of variance (factorial ANOVA) extends ANOVA to research scenarios with two or more IVs that are categorical. True or False
2. Factorial analysis of variance (factorial ANCOVA) examines group differences in a single quantitative dependent variable based upon two or more categorical independent variables, while controlling for a covariate that may influence the DV. True or False
3. One-way multivariate analysis of variance (MANOVA) is utilized to simultaneously study two or more related IVs, while controlling for the correlations among the IVs.            True or False
4. One-way multivariate analysis of covariance (MANCOVA) investigates group differences among several IVs, while also controlling for covariates that may influence the DVs.    True or False
5. Factorial multivariate analysis of variance (factorial MANOVA) extends MANOVA to research scenarios with two or more DVs that are categorical. True or False
6. Factorial multivariate analysis of covariance (MANCOVA) extends factorial MANCOVA to research scenarios that require the adjustment of one or more covariates on the IV. True or False
7. The primary purpose of predicting group membership is to identify specific IVs that best predict group membership as defined by the IVs. True or False
8. Discriminant analysis and logistic regression are appropriate statistical techniques when the DV is categorical. True or False

Answer 1

Factorial analysis of variance (factorial ANOVA) extends ANOVA to research scenarios with two or more IVs that are categorical.

TRUE

A factorial ANOVA compares means across two or more independent variables where the two or more independent variables split the sample in four or more groups. The factorial ANOVA tests to prove an assumed cause-effect relationship between the two or more categorical independent variables and single dependent variables. Thus the factorial ANOVA should be used when the research question asks for the influence of two or more independent variables on one dependent variable.

Factorial analysis of variance (factorial ANCOVA) examines group differences in a single quantitative dependent variable based upon two or more categorical independent variables, while controlling for a covariate that may influence the DV.

TRUE

The ANCOVA tests whether the independent variables still influence the dependent variable after the influence of the covariate(s) has been removed. The factorial ANCOVA includes more than one independent variable and covariate and single quantitative dependent variable. The factorial ANCOVA is most useful in two ways: 1) it explains a factorial ANOVA’s within-group variance, and 2) it controls confounding factors.

The factorial ANCOVA eliminates the covariates effect on the relationship between independent variables and the dependent variable which is tested with a factorial ANOVA. The concept is very similar to the partial correlation analysis. Technically it is a semi-partial regression and correlation.

One-way multivariate analysis of variance (MANOVA) is utilized to simultaneously study two or more related IVs, while controlling for the correlations among the IVs.

FALSE

One-way multivariate analysis of variance (MANOVA) is utilized to simultaneously study two or more related dependent variables, while controlling for the correlations among the dependent variables. MANOVA assumes that the independent variables are categorical and the dependent variables are continuous or scale variables. The MANOVA creates a linear combination of the dependent variables to create a grand mean and assesses whether there are group differences on the set of dependent variables.

One-way multivariate analysis of covariance (MANCOVA) investigates group differences among several IVs, while also controlling for covariates that may influence the DVs.  

TRUE

The MANCOVA looks at the influence of one or more independent variables on one dependent variable while removing the effect of one or more covariate factors. To do that the One-Way MANCOVA first conducts a regression of the covariate variables on the dependent variable. Thus it eliminates the influence of the covariates from the analysis. Then the residuals (the unexplained variance in the regression model) are subject to an MANOVA, which tests whether the independent variable still influences the dependent variables after the influence of the covariate(s) has been removed. The One-Way MANCOVA includes one independent variable, one or more dependent variables and the MANCOVA can include more than one covariate.

Factorial multivariate analysis of variance (factorial MANOVA) extends MANOVA to research scenarios with two or more DVs that are categorical.

FALSE

Factorial multivariate analysis of variance (factorial MANOVA) extends MANOVA to research scenarios with two or more independent variables that are categorical.

Factorial multivariate analysis of covariance (MANCOVA) extends factorial MANCOVA to research scenarios that require the adjustment of one or more covariates on the IV.

FALSE

Factorial multivariate analysis of covariance (MANCOVA) extends factorial MANCOVA to research scenarios that require the adjustment of one or more covariates on the dependent variables.

The primary purpose of predicting group membership is to identify specific IVs that best predict group membership as defined by the IVs.

TRUE

Discriminant analysis and logistic regression are appropriate statistical techniques when the DV is categorical.

TRUE