Exam 14: Analysis of Variance

Tukey's multiple comparison method is ____________________ (more/less) powerful than Fisher's LSD method.

One-way ANOVA is applied to independent samples taken from four normally distributed populations with equal variances. If the null hypothesis is rejected, then we can infer that

The F-test in ANOVA tests whether or not the population variances are equal.

In one-way ANOVA, the term $\bar{\bar{X}}$ refers to the:

A randomized block design experiment produced the following data. Treatment Block 1 2 3 1 25 27 25 2 19 18 17 3 15 20 16 4 23 27 20 5 30 31 28 a.Set up the ANOVA Table. Use $\alpha$ = 0.05 to determine the critical values. b.Test to determine whether the treatment means differ. (Use $\alpha$ = 0.05.) c.Test to determine whether the block means differ. (Use $\alpha$ = 0.05.)

The randomized block design with exactly two treatments is equivalent to a two-tail:

NARRBEGIN: TV News Viewing Habits TV News Viewing Habits A statistician employed by a television rating service wanted to determine if there were differences in television viewing habits among three different cities in New York. She took a random sample of five adults in each of the cities and asked each to report the number of hours spent watching television in the previous week. The results are shown below. (Assume normal distributions with equal variances.) Hour Spent Watehing News on Television Albany Syracuse Utica 25 28 23 31 33 18 18 35 21 23 29 17 27 36 15 NARREND -{TV News Viewing Habits Narrative} Can she infer at the 5% significance level that differences in hours of television watching exist among the three cities?

The primary interest of designing a randomized block experiment is to:

In a two-factor ANOVA, there are 4 levels for factor A, 5 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:

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 different keyboard configurations.

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 four treatment 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 ____________________ design.

The F-test in ANOVA requires that the random variable be ____________________ distributed with equal ____________________.

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} Can we infer at the 5% significance level that the treatment means differ?

When we perform a blocked experiment by using the same subject for each treatment, this is called a(n) ____________________ design.

The null hypothesis of ANOVA is that all the population means are ____________________.

The F-test statistic in a one-way ANOVA is equal to:

In the one-way ANOVA where there are k treatments and n observations, the degrees of freedom for the F-statistic are equal to, respectively:

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

If you plan to compare all possible combinations of pairs of population means, the multiple comparison method to use is ____________________ method.