Exam 14: Analysis of Variance

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 Fisher's LSD method with $\alpha$ = 0.05 to determine which school's means differ.

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} Set up the ANOVA Table. Use $\alpha$ = 0.01 to determine the critical values.

One-way ANOVA is applied to independent samples taken from three normally distributed populations with equal variances. Which of the following is the null hypothesis for this procedure?

In employing the randomized block design, the primary interest lies in reducing sum of squares for blocks (SSB).

How does conducting multiple t-tests compare to conducting a single F-test?

The analysis of variance (ANOVA) technique analyzes the variance of the data to determine whether differences exist between the population means.

The Bonferroni adjustment to Fisher's Least Significant Difference (LSD) multiple comparison method is made by dividing the specified experimentwise Type I error rate by the number of pairs of population means.

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} Can he infer at the 10% significance level that the GMAT scores differ among the three schools?

The distribution of the test statistic for analysis of variance is the:

Each observation for a particular combination of treatments is called a replicate.

In the one-way ANOVA where k is the number of treatments and n is the number of observations in all samples, the number of degrees of freedom for error is:

If the numerator (MST) degrees of freedom is 3 and the denominator (MSE) degrees of freedom is 18, the total number of observations must equal 21.

If there is enough evidence to conclude that there is interaction in a two-factor ANOVA, do not proceed to conduct the F-tests for each factor individually.

In ANOVA, a criterion by which the populations are classified is called a factor.

The test statistic of the single-factor ANOVA equals:

The within-treatments variation provides a measure of the amount of variation in the response variables that is caused by the treatments.

In Fisher's least significant difference (LSD) multiple comparison method, the LSD value will be the same for all pairs of means if: