Exam 14: Analysis of Variance

In ANOVA the populations are classified according to one or more criterion, called ____________________.

In a two-factor ANOVA, the sum of squares due to both factors, the interaction sum of squares, and the error sum of squares must all add up to the total sum of squares.

In a completely randomized design for ANOVA, the numerator and denominator degrees of freedom are 4 and 25, respectively. The total number of observations must equal:

A balanced experiment requires that the sample size for each treatment be equal.

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 -{LSAT Scores Narrative} Use Tukey's method with $\alpha$ = 0.05 to determine which population means differ.

In a two-factor ANOVA, the total sum of squares is broken down into the sum of SS(A) + SS(B) + SSE + SS(____________________).

The distribution of the test statistic for analysis of variance is the F-distribution.

The purpose of designing a randomized block experiment is to reduce the between-treatments variation (SST) to more easily detect differences between the treatment means.

Which of the following statements about multiple comparison methods is false?

In ANOVA, the F-test is the ratio of two sample variances. In the one-way ANOVA (completely randomized design), the variance used as a numerator of the ratio is:

The F-test used in one-way ANOVA is an Extension of the t-test of $\mu$ ₁ - $\mu$ ₂.

In a two-factor ANOVA, always test for ____________________ first.

The ANOVA procedure tests to determine whether differences exist between two or more population ____________________.

Consider the following ANOVA table: Source of Variation df Treatments 4 2 2.0 0.80 Error 30 12 2.5 Total 34 14 The number of treatments is

In one-way analysis of variance, between-treatments variation is measured by the:

Which of the following is false regarding SSB?

SST measures the variation ____________________ treatments.

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} Did Tukey's method and Fisher's LSD method in the previous two questions yield the same results? Will this always be the case?

In the randomized block design ANOVA, the sum of squares for error equals:

We can use the F-test to determine whether $\mu$ ₁ is greater than $\mu$ ₂.