Two-way analysis of variance (ANOVA)

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Presentation transcript:

Two-way analysis of variance (ANOVA)

Two-way analysis of variance (ANOVA) Research question type: Explaining a continuous variable with 2 categorical variables What kind of variables?: Continuous and 2 independent categorical variables (factors) Common Applications: Comparing means of a single variable at difference levels of two conditions (factors) * http://www.statstutor.ac.uk/resources/uploaded/coventrytwowayanova.pdf

Two-way analysis of variance (ANOVA) Assumption: random samples should follow normal distribution random samples should have same variance

<R example> * http://www.statmethods.net/stats/anovaAssumptions.html

<R example> * http://www.statmethods.net/stats/anovaAssumptions.html

<R example> * http://faculty.smu.edu/kyler/courses/7311/twoway_2up.pdf

Two-way analysis of variance (ANOVA) Example: The effective life (in hours) of batteries is compared by material type (1,2, or 3) and operating temperature (-10,20,45) * http://www.statstutor.ac.uk/resources/uploaded/coventrytwowayanova.pdf

Two-way analysis of variance (ANOVA) Hypotheses: H0: There is no difference in mean battery life H1: not H0 * http://www.statstutor.ac.uk/resources/uploaded/coventrytwowayanova.pdf

Two-way analysis of variance (ANOVA) Since the lines in the plot are not parallel, there is an interaction effect The lines would be approximately parallel if there were no interaction. So, how battery life changes with temperature depends on the material, and vice versa. * http://www.statstutor.ac.uk/resources/uploaded/coventrytwowayanova.pdf

<R example> * http://faculty.smu.edu/kyler/courses/7311/twoway_2up.pdf

Two-way analysis of variance (ANOVA) Let`s see Table The below table also indicates that the interaction effect is significant * http://www.statstutor.ac.uk/resources/uploaded/coventrytwowayanova.pdf

Two-way analysis of variance (ANOVA) Material, temperature, as well as their interaction are significant. So, they are needed to explain battery life * http://www.statstutor.ac.uk/resources/uploaded/coventrytwowayanova.pdf

<R example> * http://faculty.smu.edu/kyler/courses/7311/twoway_2up.pdf