Exam 10: Experimental Design and Analysis of Variance

Source d.f. Sum of Squares Model 3 213.88125 Error 20 11.208333 Total 23 225.0895 -Consider the above one-way ANOVA table.What is the treatment mean square?

Consider the following data from a two-factor factorial experiment.You wish to perform a two-way analysis of variance to analyze the data. Factor I Factor II 1 2 3 1 4 8 5 6 7 5 5 5 6 2 4 5 0 2 3 1 3 2 1 -What is the factor II mean square?

Suppose that a teacher wants to study how four different study methods affect a student's final grade.The study method is the _____ variable.

Source d.f. Sum of Squares Model 3 213.88125 Error 20 11.208333 Total 23 225.0895 -Suppose that you analyze data from a completely randomized experimental design using a one-way ANOVA.You find out later that the data was actually from a randomized block experimental design and use the ANOVA procedure to reanalyze the data.The SSE from your first analysis will be ______ the SSE from your second analysis.

One difference between a one-way ANOVA and a two-way ANOVA is that in a two-way ANOVA we first test for a(n)_________ effect.

Block 1 2 3 4 5 Tr1 2 1 2 3 2 Tr2 4 4 1 1 2.5 TR3 3 4 3 2 3 Mean 2 3 3 2 overall mean =2.5 Consider the randomized block design with 4 blocks and 3 treatments (groups) given above -What is the degrees of freedom for treatments (groups)?

Test H₀: there is no difference between effects of levels of factor II at a =.05.

Find an individual 95 percent confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ where $\bar { x } _ { 1 }$ =51.5, $\bar { x } _ { 2 }$ = 55.8,and MSE = 6.125.There were 4 treatments and 24 observations in total and the number of observations were equal in each group.

In a one-way ANOVA for a completely randomized design,all other things being held constant,as two sample treatment group means get closer further apart the probability of rejecting the null hypothesis increases.

A company that fills containers of water has four machines.The quality control manager needs to determine whether the average fill for these machines is the same.Looking at 19 containers,we have the following data of fill measures in litres: Machine 1 Machine 2 Machine 3 Machine 4 4 6 5 4 4.03 4.0017 3.974 4.005 0.0183 0.0117 0.0182 0.0129 and the following partial ANOVA table (with "group" labeled as "treatment"): Source SS d.f. MS F Treatments 0.002359 Errors Total 0.010579 -Determine the degrees of freedom for the treatment,error,and total and state the critical value of the F statistic at a= 05.

In a one-way ANOVA for a completely randomized design,all other things being held constant,as the sample treatment group means get closer to each other the probability of rejecting the null hypothesis

Consider a two-factor factorial experiment with 4 levels of factor 1,5 levels of factor 2,and 3 observations per cell.If we use a two-way ANOVA to analyze the data from this experiment,the total degrees of freedom is:

A sum of squares that measures the variability among the group sample means is referred to as the _______ sum of squares.

Consider the following partial analysis of variance table from a randomized block design with 10 blocks and 6 groups (treatments). Source SS Treatments 2,477.53 Blocks 3,180.48 Error 11,661.38 Total -What is the between-groups (treatment)mean square?

Consider the following partial analysis of variance table from a randomized block design with 10 blocks and 6 groups (treatments). Source SS Treatments 2,477.53 Blocks 3,180.48 Error 11,661.38 Total -What is the block mean square?

In an experiment,the response variable is also known as the _______ variable.

Test H₀: there is no difference between group means at $\alpha$ = .05.

In a one-way ANOVA for a completely randomized design with 4 groups and 15 observations per each group,the error degrees of freedom is:

Consider the following partial analysis of variance table from a randomized block design with 6 blocks and 4 groups (treatments). Source Sum of Squares Treatments 15.93 Blocks 42.09 Error 23.84 Total 81.86 -What is the mean square error?

Source d.f. Sum of Squares Model 3 213.88125 Error 20 11.208333 Total 23 225.0895 -Consider the above one-way ANOVA table.What is the mean square error?