Exam 13: Two-Way Analysis of Variance

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.Based on the profile plot,which main effect appears to be the largest?

Consider a two-way ANOVA in which Factor A is at four levels,Factor B has three levels,and there are four observations in each cell.Which of the following are TRUE statements about the ANOVA in this situation?

In a two-way ANOVA,the total sum of squares (SST)can be broken down into which terms?

A study compares the strength of a product between two different materials used to make the product and five different labs that created these products.The profile plot of the group means is shown below. Based on this plot,does there seem to be an interaction effect between material and lab?

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 is the value of the degrees of freedom for interaction?

A study compares three levels of Factor A and two levels of Factor B,with five observations in each cell.What are the degrees of freedom for the F statistic that is used to test for interaction?

If the interaction effect is significant in a two-way ANOVA,then it is best to examine main effects by looking at _____.

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. The profile plot and the P-value for the test for interaction show little evidence of interaction.What can we conclude?

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).Which statement best describes the type of experiment being run?

Which of the plots below show a possible interaction?

What are the null hypotheses being tested in a two-way ANOVA?

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 interaction at the .05 level?

What is the benefit of doing a two-way ANOVA rather than a one-way ANOVA on two factors separately?

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 is the value of the degrees of freedom for error?

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. What is the name of the two-way ANOVA needed for the analysis?

In a two-way ANOVA,the model sum of squares (SSM)can be broken down into which terms?

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. If the data were analyzed as a one-way ANOVA with six "treatments" corresponding to the six combinations of stepping rate and gender,what would have been the sum of squares for error?

In a two-way ANOVA,both factors must have the same number of levels.

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 can we say about the P-value for the main effect of the stepping rate group?

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 gender? (Note: Include the interaction in your ANOVA model and assume all assumptions have been reasonably met. )