Exam 13: Two-Way Analysis of Variance

An experiment is done as a 3 × 5 ANOVA and the experiment is replicated twice. How large should the F statistic be to reject the null hypothesis for the first main effect at the .05 level?

Which of the following statements about a two-way analysis of variance model is/are TRUE?

A research project studied the physical properties of wood materials constructed by bonding together small flakes of wood.The two factors considered were the size of the flakes and species of tree.The sizes of the flakes were S1: 0.15 inches by 2 inches and S2: 0.25 inches by 2 inches,and the species of tree used were aspen,birch,and maple.For each combination of flake size and tree species,three samples of wood material were constructed.For each sample,the physical property measured was the tension modulus of elasticity in the direction perpendicular to the alignment of the flakes,in pounds per square inch (psi). The table below gives the means for the different size-species groups: For these data,a two-way ANOVA was run and the partial ANOVA table is given below. What is the value of the F statistic for testing interaction?

The assumptions underlying a two-way ANOVA and a one-way ANOVA are different.

A researcher wished to compare the effect of the different rates of stepping on volunteers' heart rates in a step-aerobics workout.A collection of thirty adult volunteers,fifteen women and fifteen men,were selected from a local gym.The men were randomly divided into three groups of five subjects each.Each group did a standard step-aerobics workout,with Group 1 at a low rate of stepping,Group 2 at a medium rate of stepping,and Group 3 at a rapid rate.The women were also randomly divided into three groups of five subjects each.As with the men,each group did a standard step-aerobics workout,with Group 1 at a low rate of stepping,Group 2 at a medium rate of stepping,and Group 3 at a rapid rate.The mean heart rate at the end of the workout for all the subjects was determined in beats per minute. A partial ANOVA table for these data is given below. What are the advantages of studying the two factors simultaneously in the same experiment?

A study compares two levels of Factor A and four levels of Factor B,with four observations in each cell.How large does the F statistic need to be for rejecting the null hypothesis that no interaction is present between the two factors at the 5% significance level?

A study compares the average number of accidents by gender for three different age groups.The profile plot of the group means is shown below. Based on this plot,does there seem to be an interaction effect between gender and age group?

A study was done to determine whether gender and type of student (graduate students or undergraduate)performed differently on a final exam in a statistics course.The mean scores of each group are shown below. Create a profile plot.Does there appear to be any interactions?

A research project studied the physical properties of wood materials constructed by bonding together small flakes of wood.The two factors considered were the size of the flakes and species of tree.The sizes of the flakes were S1: 0.15 inches by 2 inches and S2: 0.25 inches by 2 inches,and the species of tree used were aspen,birch,and maple.For each combination of flake size and tree species,three samples of wood material were constructed.For each sample,the physical property measured was the tension modulus of elasticity in the direction perpendicular to the alignment of the flakes,in pounds per square inch (psi). The table below gives the means for the different size-species groups: For these data,a two-way ANOVA was run and the partial ANOVA table is given below. What is the value of the degrees of freedom for the model,DFM?

An experiment is done as a 3 × 5 ANOVA and the experiment is replicated twice. What is the total number of observations in this experiment?

Plots that show graphs of the marginal means of each factor at every level are called _______.

It is not possible to have an interaction effect in a two-way ANOVA unless one of the factors has a main effect.

A study was done to determine how gender and stress level affect one's self-rated level of happiness on a scale of 1 to 10.The data are shown below. What is the P-value for the main effect for stress? (Note: Include the interaction in your ANOVA model and assume all assumptions have been reasonably met. )