Exam 14: Analysis of Variance

Consider the following ANOVA table: Soupes of Variation Treatments 128 4 32 2.963 Error 270 25 10.8 Total 398 29 The total number of observations is:

____________________ multiple comparison method is based on the Studentized range statistic.

The sum of squares for error (SSE) measures the amount of variation that is explained by the ANOVA model, while the sum of squares for treatments (SST) measures the amount of variation that remains unexplained.

A randomized block experiment having five treatments and six blocks produced the following values: SST = 252, SS(Total) = 1,545, SSE = 198. The value of SSB must be 1095.

Each observation for particular combination of treatments is called a(n) ________________.

NARRBEGIN: LSAT Scores LSAT Scores A recent college graduate is in the process of deciding which one of three Law schools he should apply to. He decides to judge the quality of the schools on the basis of the Law School Admission Test (LSAT) scores of those who are accepted into the school. A random sample of six students in each school produced the following LSAT scores. An F-test using ANOVA concluded that average LSAT scores differ for at least two of the schools. LSAT Scores School 1 School 2 School 3 650 510 590 620 550 510 630 700 520 580 630 500 710 600 490 690 650 530 NARREND -The average cost of remodeling one room in a house was compared for four different remodeling companies. A random sample of 10 rooms remodeled by each company were selected all with the same square footage, and cost of remodeling each room was recorded. (Rooms were randomly chosen from different houses.) The data are shown below. An F-test using ANOVA concluded that average costs differ for at least two of the remodeling companies. Remodeling Company 1 2 3 4 610 404 599 272 354 663 426 405 234 521 429 197 399 518 621 363 278 499 426 297 358 374 414 538 379 562 322 181 548 505 460 318 196 375 494 412 444 438 637 499 Use Tukey's and LSD multiple comparison methods to determine which remodeling companies differ in their average cost. Compare the results and discuss. (Keep the experimentwise Type I error at or close to 5%.)

NARRBEGIN: Food Irradiation Food Irradiation In recent years the irradiation of food to reduce bacteria and preserve the food longer has become more common. A company that performs this service has developed four different methods of irradiating food. To determine which is best, it conducts an experiment where different foods are irradiated and the bacteria count is measured. As part of the experiment the following foods are irradiated: meat, poultry, veal, tuna, and yogurt. The results are shown below. Bactaria Count Food Method 1 Method 2 Method 3 Method 4 Meat 47 53 36 68 Poulty 53 61 48 75 Veal 68 85 55 45 Tuna 25 24 20 27 Yogurt 44 48 38 46 NARREND -{Food Irradiation Narrative} Can the company infer at the 1% significance level that differences in the bacteria count exist among the four irradiation methods?

Which of the following components in an ANOVA table is not additive?

NARRBEGIN: MigraineTreatments Migraine Treatments The following data were generated from a 2 * 2 factorial experiment with 3 replicates, where factor A levels represent two different injection procedures of an anesthetic to the occipital nerve (located in the back of the neck), and factor B levels represent two different drugs, which physicians recommend to increase the effectiveness of the injections. Three migraine patients were randomly selected for each combination of injection and drug. Factor B Factor A 1 2 1 7 13 10 11 8 12 2 10 10 11 15 0 11 NARREND -{Migraine Treatments Narrative} a.Create the ANOVA table. b.Test at the 5% significance level to determine if factors A and B interact.

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, 15 experimental units were assigned to each of four treatments. Fill in the blanks (identified by asterisks) in the partial ANOVA table shown below. Source of Variation Treatments * * 240 * Error * * * Total 2512 *

The alternative hypothesis of ANOVA is that ____________________ population means are different.

Conducting t-tests for each pair or population means is statistically equivalent to conducting one F-test comparing all the population means.

NARRBEGIN: MigraineTreatments Migraine Treatments The following data were generated from a 2 * 2 factorial experiment with 3 replicates, where factor A levels represent two different injection procedures of an anesthetic to the occipital nerve (located in the back of the neck), and factor B levels represent two different drugs, which physicians recommend to increase the effectiveness of the injections. Three migraine patients were randomly selected for each combination of injection and drug. Factor B Factor A 1 2 1 7 13 10 11 8 12 2 10 10 11 15 0 11 NARREND -{Migraine Treatments Narrative} Test at the 5% significance level to determine if differences exist among the levels of factor B.

SSE measures the variation ____________________ treatments.

Consider the following partial ANOVA table: Source of Variation df Treatments 75 * 25 6.67 Error 60 * 3.75 Total 135 19 The numerator and denominator degrees of freedom for the F-test (identified by asterisks) are

If SST explains a significant portion of the total variation, we conclude that the population means ____________________ (do/do not) differ.

A randomized block design with 4 treatments and 5 blocks produced the following sum of squares values: SS(Total) = 1,951, SST = 349, SSE = 188 . The value of SSB must be:

NARRBEGIN: Health Inspectors' Ages Health Inspectors' Ages In order to examine the differences in ages of health inspectors among five counties, a Health Department statistician took random samples of six inspectors' ages in each county. The data are listed below. An F-test using ANOVA showed that average age differs for at least two counties. Ages of hipectors among Five sehoal Districts 1 2 3 4 5 41 39 36 45 53 53 48 28 37 55 28 41 29 46 49 45 51 33 48 56 40 49 27 51 48 59 50 26 49 61 NARREND -{Health Inspectors' Ages Narrative} Use Fisher's LSD procedure with $\alpha$ = .05 to determine which population means differ.

In the two-factor ANOVA where a is the number of factor A levels, b is the number of factor B levels, r is the number of replicates, and n is the total number of observations, the number of degrees of freedom for error is:

In the two-factor ANOVA where a is the number of factor A levels, b is the number of factor B levels, and r is the number of replicates, the number of degrees of freedom for interaction is: