Exam 11: Analysis of Variance

In a one-way ANOVA,if the computed F statistic exceeds the critical F value you may

Instruction 11-2 An airline wants to select a computer software package for its reservation system.Four software packages (1,2,3,and 4)are commercially available.The airline will choose the package that bumps as few passengers as possible during a month.An experiment is set up in which each package is used to make reservations for five randomly selected weeks.(A total of 20 weeks was included in the experiment. )The number of passengers bumped each week is obtained,which gives rise to the following Microsoft ANOVA Source of Variation SS df MS F P -value F crit Between Groups 212.4 3 8.304985 0.001474 3.238867 Within Groups 136.4 8.525 Total 348.8 -Referring to Instruction 11-2,at a significance level of 1%,

Instruction 11-8 An agronomist wants to compare the crop yield of three varieties of chickpea seeds.She plants all three varieties of the seeds on each of five different patches of fields.She then measures the crop yield in bushels per acre.Treating this as a randomised block design,the results are presented in the table that follows. Fields Smith Walsh Trevor 1 11.1 19.0 14.6 2 13.5 18.0 15.7 3 15.3 19.8 16.8 4 14.6 19.6 16.7 5 9.8 16.6 15.2 -Referring to Instruction 11-8,using an overall level of significance of 0.01,what is the critical value of the Studentised range Q used in calculating the critical range for the Tukey multiple comparison procedure?

Instruction 11-9 An agronomist wants to compare the crop yield of three varieties of chickpea seeds.She plants 15 fields,five with each variety.She then measures the crop yield in bushels per acre.Treating this as a completely randomised design,the results are presented in the table that follows. Trial Smith Walsh Trevor 1 11.1 19.0 14.6 2 13.5 18.0 15.7 3 15.3 19.8 16.8 4 14.6 19.6 16.7 5 9.8 16.6 15.2 -Referring to Instruction 11-9,the among-group variation or SSA is ________.

Instruction 11-2 An airline wants to select a computer software package for its reservation system.Four software packages (1,2,3,and 4)are commercially available.The airline will choose the package that bumps as few passengers as possible during a month.An experiment is set up in which each package is used to make reservations for five randomly selected weeks.(A total of 20 weeks was included in the experiment. )The number of passengers bumped each week is obtained,which gives rise to the following Microsoft ANOVA Source of Variation SS df MS F P -value F crit Between Groups 212.4 3 8.304985 0.001474 3.238867 Within Groups 136.4 8.525 Total 348.8 -Referring to Instruction 11-2,the within groups degrees of freedom is

Instruction 11-8 An agronomist wants to compare the crop yield of three varieties of chickpea seeds.She plants all three varieties of the seeds on each of five different patches of fields.She then measures the crop yield in bushels per acre.Treating this as a randomised block design,the results are presented in the table that follows. Fields Smith Walsh Trevor 1 11.1 19.0 14.6 2 13.5 18.0 15.7 3 15.3 19.8 16.8 4 14.6 19.6 16.7 5 9.8 16.6 15.2 -Referring to Instruction 11-8,the decision made at a 0.01 level of significance on the F test for the block effects implies that the blocking has been advantageous in reducing the experiment error.

Instruction 11-10 The marketing manager of a company producing a new cereal aimed for children wants to examine the effect of the colour and shape of the box's logo on the approval rating of the cereal.He combined four colours and three shapes to produce a total of 12 designs.Each logo was presented to two different groups (a total of 24 groups)and the approval rating for each was recorded and is shown below.The manager analysed these data using the α = 0.05 level of significance for all inferences. COLOURS SHAPES Red Green Blue Yellow Circle 54 67 36 45 44 61 44 41 Square 34 56 36 21 36 58 30 25 Diamond 46 60 34 31 48 60 38 33 Analysis of Variance Source df SS MS F p Colours 3 2711.17 903.72 72.30 0.000 Shapes 2 579.00 289.50 23.16 0.000 Interaction 6 150.33 25.06 2.00 0.144 Error 12 150.00 12.50 Total 23 3590.50 -Referring to Instruction 11-10,the mean square for error is ________.

Instruction 11-6 As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She recorded three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below. Trial 1 43 37 41 43 2 46 38 45 45 3 43 39 42 46 -Referring to Instruction 11-6,what is the critical value of Levene's test for homogeneity of variances at a 5% level of significance?

When the F test is used for ANOVA,the rejection region is always in the right tail.

Instruction 11-6 As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She recorded three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below. Trial 1 43 37 41 43 2 46 38 45 45 3 43 39 42 46 -Referring to Instruction 11-6,the test is valid only if the population of speeds is normally distributed.

Instruction 11-10 The marketing manager of a company producing a new cereal aimed for children wants to examine the effect of the colour and shape of the box's logo on the approval rating of the cereal.He combined four colours and three shapes to produce a total of 12 designs.Each logo was presented to two different groups (a total of 24 groups)and the approval rating for each was recorded and is shown below.The manager analysed these data using the α = 0.05 level of significance for all inferences. COLOURS SHAPES Red Green Blue Yellow Circle 54 67 36 45 44 61 44 41 Square 34 56 36 21 36 58 30 25 Diamond 46 60 34 31 48 60 38 33 Analysis of Variance Source df SS MS F p Colours 3 2711.17 903.72 72.30 0.000 Shapes 2 579.00 289.50 23.16 0.000 Interaction 6 150.33 25.06 2.00 0.144 Error 12 150.00 12.50 Total 23 3590.50 -Referring to Instruction 11-10,the mean square for the interaction of colour and shape is ________.

Instruction 11-6 As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She recorded three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below. Trial 1 43 37 41 43 2 46 38 45 45 3 43 39 42 46 -Referring to Instruction 11-6,based on the Tukey-Kramer procedure with an overall level of significance of 0.05,the retailer would decide that there is no significant difference between any pair of mean speeds.

Instruction 11-8 An agronomist wants to compare the crop yield of three varieties of chickpea seeds.She plants all three varieties of the seeds on each of five different patches of fields.She then measures the crop yield in bushels per acre.Treating this as a randomised block design,the results are presented in the table that follows. Fields Smith Walsh Trevor 1 11.1 19.0 14.6 2 13.5 18.0 15.7 3 15.3 19.8 16.8 4 14.6 19.6 16.7 5 9.8 16.6 15.2 -Referring to Instruction 11-8,what is the critical value for testing the block effects at a 0.01 level of significance?

Instruction 11-8 An agronomist wants to compare the crop yield of three varieties of chickpea seeds.She plants all three varieties of the seeds on each of five different patches of fields.She then measures the crop yield in bushels per acre.Treating this as a randomised block design,the results are presented in the table that follows. Fields Smith Walsh Trevor 1 11.1 19.0 14.6 2 13.5 18.0 15.7 3 15.3 19.8 16.8 4 14.6 19.6 16.7 5 9.8 16.6 15.2 -Referring to Instruction 11-8,using an overall level of significance of 0.01,what is the critical range for the Tukey multiple comparison procedure?

In a two-way ANOVA,it is easier to interpret main effects when the interaction component is not significant.

There is an interaction between factors Y and X if the effect of factor Y is dependent on the level of factor X.

Instruction 11-6 As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She recorded three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below. Trial 1 43 37 41 43 2 46 38 45 45 3 43 39 42 46 -Referring to Instruction 11-6,what should be the conclusion for the Levene's test for homogeneity of variances at a 5% level of significance?

Instruction 11-6 As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She recorded three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below. Trial 1 43 37 41 43 2 46 38 45 45 3 43 39 42 46 -Referring to Instruction 11-6,based on the Tukey-Kramer procedure with an overall level of significance of 0.05,the retailer would decide that there is a significant difference between all pairs of mean speeds.

When would you use the Tukey-Kramer procedure?

Instruction 11-9 An agronomist wants to compare the crop yield of three varieties of chickpea seeds.She plants 15 fields,five with each variety.She then measures the crop yield in bushels per acre.Treating this as a completely randomised design,the results are presented in the table that follows. Trial Smith Walsh Trevor 1 11.1 19.0 14.6 2 13.5 18.0 15.7 3 15.3 19.8 16.8 4 14.6 19.6 16.7 5 9.8 16.6 15.2 -Referring to Instruction 11-9,the within-group variation or SSW is ________.