Exam 14: Analysis of Variance

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. ​ ​ -{Food Irradiation Narrative} Set up the ANOVA Table.Use α = 0.01 to determine the critical values.

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

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:

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

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:

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:

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.

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. ​ ​ -{Migraine Treatments Narrative} Test at the 5% significance level to determine if differences exist among the levels of factor B.

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:

The F-test of the randomized block design of the analysis of variance has the same requirements as the independent samples design; that is,the random variable must be normally distributed and the population variances must be equal.

The F-test in ANOVA is an expansion of the t-test for two independent population means.

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. ​ ​ -{Acid Reflux Narrative} Can we infer at the 5% significance level that the treatment means differ?

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?

{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 statements is true?

Which of the following is a required condition for ANOVA?

Fisher's least significant difference method (LSD)substitutes the pooled variance estimator from the equal variances t-test with the MSE from ANOVA.