Exam 14: Analysis of Variance

A randomized block design with 4 treatments and 5 blocks produced the following sum of squares values: SS(Total) = 2000, SST = 400, SSE = 200. The value of MSB must be 350.

The analysis of variance is a procedure that allows statisticians to compare two or more population:

When the effect of a level for one factor depends on which level of another factor is present, the most appropriate ANOVA design to use in this situation is the:

A complete factorial experiment is an experiment in which the number of replicates is the same for each treatment on which data is collected.

NARRBEGIN: Motorcycle Repair Cost Motorcycle Repair Cost Motorcycle insurance appraisers examine motorcycles that have been involved in accidental collisions and estimate the cost of repairs. An insurance executive claims that there are significant differences in the estimates from different appraisers. To support his claim he takes a random sample of six motorcycles that have recently been damaged in accidents. Three appraisers then estimate the repair costs of all six motorcycles. The data are shown below. Bstimatad Repair Cost Motorcycles Appraiser 1 Appraiser 2 Appraiser 3 1 650 600 750 2 930 910 1010 3 440 450 500 4 750 710 810 5 1190 1050 1250 6 1560 1270 1450 NARREND -{Motorcycle Repair Cost Narrative} Can we infer at the 5% significance level that the executive's claim is true?

A(n) ____________________ experiment requires that the sample size for each treatment be equal.

The F-test of a randomized block design of the analysis of variance has the same requirements as the independent samples design; that is, the random variable must be ____________________ distributed and the population ____________________ must be equal.

SSE in the independent samples design is equal to the sum of SSB and SSE in the randomized block design.

Which of the following is not true of Tukey's Multiple Comparison Method?

NARRBEGIN: GMAT Scores GMAT Scores A recent college graduate is in the process of deciding which one of three graduate schools he should apply to. He decides to judge the quality of the schools on the basis of the Graduate Management Admission Test (GMAT) scores of those who are accepted into the school. A random sample of six students in each school produced the following GMAT scores. Assume that the data are normally distributed with equal variances for each school. GMAT Scores School 1 School 2 School 3 650 105 590 620 550 510 630 700 520 580 630 500 710 600 490 690 650 530 NARREND -{GMAT Scores Narrative} Set up the ANOVA Table. Use $\alpha$ = 0.05 to determine the critical value.

The F-test of the randomized block design of the analysis of variance has the same requirements as the independent samples design; that is, the random variable must be normally distributed and the population variances must be equal.

NARRBEGIN: Gold Funds Gold Funds An investor studied the percentage rates of return of three different gold funds. Random samples of percentage rates of return for four periods were taken from each fund. The results appear in the table below: Gold Funds Percentage Rates Fund 1 Fund 2 Fund 3 12 4 9 15 8 3 13 6 5 14 5 7 17 4 4 NARREND -{Gold Funds Narrative} Test at the 5% significance level to determine whether the mean percentage rates for the three funds differ.

The sum of squares for error is also known as the between-treatments variation.

Fisher's least significant difference (LSD) multiple comparison method is flawed because

NARRBEGIN: Keyboard Configuration an Keyboard Configuration and Size The data shown below were taken from a 2 * 3 factorial experiment to examine the effects of factor A (keyboard configuration, 3 levels) and factor B (keyboard size, 2 levels) on typing speed. Each cell consists of the times needed for each of 4 randomly assigned keyboardists to type a standard document under each set of conditions (in minutes). nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; Factor B Factor A 1 2 1 26 24 19 21 20 20 21 23 2 30 33 24 27 25 31 29 29 3 26 31 22 23 27 24 17 26 NARREND -{Keyboard Configuration and Size Narrative} Test at the 5% significance level to determine if time differences exist among the keyboard sizes.

NARRBEGIN: Sub Sandwich Customers Sub Sandwich Customers The marketing manager of a Sub Shop chain is in the process of examining some of the demographic characteristics of her customers. In particular, she would like to investigate the belief that the ages of the customers of Sub Shops, hamburger emporiums, and fast-food chicken restaurants are different. The ages of eight randomly selected customers of each of the restaurants are recorded and listed below. From previous analyses we know that the ages are normally distributed with equal variances for each group. Customers' Agas Subs Hamburaer Chicken 23 26 25 19 20 28 25 18 36 17 35 23 36 33 39 25 25 27 28 19 38 31 17 31 NARREND -{Sub Sandwich Customers Narrative} Do these data provide enough evidence at the 5% significance level to infer that there are differences in ages among the customers of the three restaurants?

The test of whether the block means differ uses an F-test whose test statistic is ____________________ divided by ____________________.

We use the analysis of variance (ANOVA) technique to compare two or more population means.

When the problem objective is to compare more than two populations, the experimental design that is the counterpart of the matched pairs experiment is called the randomized block design.

NARRBEGIN: GMAT Scores GMAT Scores A recent college graduate is in the process of deciding which one of three graduate schools he should apply to. He decides to judge the quality of the schools on the basis of the Graduate Management Admission Test (GMAT) scores of those who are accepted into the school. A random sample of six students in each school produced the following GMAT scores. Assume that the data are normally distributed with equal variances for each school. GMAT Scores School 1 School 2 School 3 650 105 590 620 550 510 630 700 520 580 630 500 710 600 490 690 650 530 NARREND -In a completely randomized design, 12 experimental units were assigned to the first treatment, 15 units to the second treatment, and 18 units to the third treatment. A partial ANOVA table is shown below: Source of Variation Treatments * * * 9 Error * * 35 Total * * a.Fill in the blanks (identified by asterisks) in the above ANOVA table. b.Test at the 5% significance level to determine if differences exist among the three treatment means.