Exam 14: Analysis of Variance

One example of a blocking variable is the dosage level that each subject is assigned to in a randomized experiment.

Which of the following statements is true?

In one-way ANOVA, the amount of total variation that is unexplained is measured by the:

The numerator and denominator degrees of freedom for the F-test in a one-way ANOVA are, respectively,

In a two-factor ANOVA, there are 5 levels for factor A, 4 levels for factor B, and 3 observations for each combination of factor A and factor B levels. The number of treatments in this experiment equals 20.

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

In a two-factor ANOVA, always test for interaction last.

When the objective is to compare more than two populations, the experimental design that is the counterpart of the matched pairs experiment is called a:

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} Set up the ANOVA Table. Use $\alpha$ = 0.05 to determine the critical value.

NARRBEGIN: Acid Reflux Acid Reflux A partial ANOVA table in a randomized block design is shown below, where the treatments refer to different acid reflux medicines, and the blocks refer to groups of men with similar levels of stomach acid. Source of Variation Treatments * 4 * * Blocks 3,120 6 * * Error * * 115 Total 12,600 34 NARREND -{Acid Reflux Narrative} Fill in the missing values (identified by asterisks) in the above ANOVA Table.

The techniques used to detect which population means differ are called multiple ____________________ methods.

In a one-way ANOVA, error variability is computed as the sum of the squared errors, SSE, for all values of the response variable. This variability is the:

The equation: SS(Total) = SS(A) + SS(B) + SS(AB) + SSE applies to which ANOVA model?

Which of the following statements is false?

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

A complete 3*2 factorial experiment is called balanced if:

The analysis of variance (ANOVA) tests hypotheses about population variances and requires all the population means to be equal.

NARRBEGIN: Arthritis Pain Formulas Arthritis Pain Formulas A pharmaceutical manufacturer has been researching new medications formulas to provide quicker relief of arthritis pain. Their laboratories have produced three different medications and they want to determine if the different medications produce different responses. Fifteen people who complained of arthritis pains were recruited for an experiment; five were randomly assigned to each medication. Each person was asked to take the medicine and report the length of time until some relief was felt (minutes). The results are shown below. (Assume normal distributions with equal variances.) Time in Minutes Whtil pelef is Felt (min) Medication 1 Medication 2 Medication 3 4 2 6 8 5 7 6 3 7 9 7 8 8 1 6 NARREND -{Arthritis Pain Formulas Narrative} Do these data provide sufficient evidence to indicate that differences in the average time of relief exist among the three medications? Use $\alpha$ = 0.05.

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} Set up the ANOVA Table. Use $\alpha$ = 0.05 to determine the critical values.

If our analysis includes all possible levels of a factor, the technique for analyzing the data is called a(n) ____________________-effects ANOVA.