Estimation and Hypothesis Testing
Learn about Two-Way ANOVA, a statistical method to analyze the effects of two independent variables on one dependent variable. Understand main and interaction effects, assumptions, and how it differs from one-way ANOVA in factorial designs.
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Boundless Statistics
Estimation and Hypothesis Testing
Two-Way ANOVA
Two-Way ANOVA
Two-way ANOVA examines the influence of different categorical independent variables on one dependent variable.
Learning Objectives
Distinguish the two-way ANOVA from the one-way ANOVA and point out the assumptions necessary to perform the test.
Key Takeaways
Key Points
The two-way ANOVA is used when there is more than one independent variable and multiple observations for each independent variable.
The two-way ANOVA can not only determine the main effect of contributions of each independent variable but also identifies if there is a
significant interaction effect between the independent variables.
Another term for the two-way ANOVA is a factorial ANOVA, which has fully replicated measures on two or more crossed factors.
In a factorial design multiple independent effects are tested simultaneously.
Key Terms
two-way ANOVA: an extension of the one-way ANOVA test that examines the influence of different categorical independent variables on one
dependent variable
orthogonal: statistically independent, with reference t o variates
homoscedastic if all random variables in a sequence or vector have the same finite variance
The two-way analysis of variance {ANOVA) test is an extension of the one-way ANOVA test that examines the influence of different categorical
independent variables on one dependent variable. While the one-way ANOVA measures the significant effect of one independent variable (IV),
the two-way ANOVA is used when there is more than one IV and multiple observations for each IV. The two-way ANOVA can not only determine
the main effect of contributions of each IV but also identifies if there is a significant interaction effect between the IVs.
Assumptions of the Two-Way ANOVA
As with other parametric tests, we make the following assumptions when using two-way ANOVA:
The populations from which the samples are obtained must be normally distributed.
Sampling is done correctly. Observations for within and between groups must be independent.
The variances among populations must be equal (homoscedastic).
Data are interval or nominal.
Estimation and Hypothesis Testing
Two-Way ANOVA
Two-Way ANOVA
Two-way ANOVA examines the influence of different categorical independent variables on one dependent variable.
Learning Objectives
Distinguish the two-way ANOVA from the one-way ANOVA and point out the assumptions necessary to perform the test.
Key Takeaways
Key Points
The two-way ANOVA is used when there is more than one independent variable and multiple observations for each independent variable.
The two-way ANOVA can not only determine the main effect of contributions of each independent variable but also identifies if there is a
significant interaction effect between the independent variables.
Another term for the two-way ANOVA is a factorial ANOVA, which has fully replicated measures on two or more crossed factors.
In a factorial design multiple independent effects are tested simultaneously.
Key Terms
two-way ANOVA: an extension of the one-way ANOVA test that examines the influence of different categorical independent variables on one
dependent variable
orthogonal: statistically independent, with reference t o variates
homoscedastic if all random variables in a sequence or vector have the same finite variance
The two-way analysis of variance {ANOVA) test is an extension of the one-way ANOVA test that examines the influence of different categorical
independent variables on one dependent variable. While the one-way ANOVA measures the significant effect of one independent variable (IV),
the two-way ANOVA is used when there is more than one IV and multiple observations for each IV. The two-way ANOVA can not only determine
the main effect of contributions of each IV but also identifies if there is a significant interaction effect between the IVs.
Assumptions of the Two-Way ANOVA
As with other parametric tests, we make the following assumptions when using two-way ANOVA:
The populations from which the samples are obtained must be normally distributed.
Sampling is done correctly. Observations for within and between groups must be independent.
The variances among populations must be equal (homoscedastic).
Data are interval or nominal.
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Statistics