Exam 14: Analysis of Variance

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

A randomized block experiment having five treatments and six blocks produced the following values: SST = 252,SS(Total)= 1,545,SSE = 198.The value of SSB must be 1095.

The sum of squares for error is also known as the between-treatments variation.

Multiple comparison methods are used to determine whether or not any differences occur amongst a group of population means.

Tukey's multiple comparison method is more powerful than Fisher's LSD Method at finding differences in pairwise 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. Source of Variation Treatments * 4 * * Blocks 3,120 6 * * Error * * 115 Total 12,600 34 -{Acid Reflux Narrative} Can we infer at the 5% significance level that the treatment means differ?

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.

A complete factorial experiment is an experiment in which the number of replicates is the same for each treatment on which data is collected.

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

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 -{Food Irradiation Narrative} Can the company infer at the 1% significance level that differences in the bacteria count exist among the four irradiation methods?

We use the analysis of variance (ANOVA)technique to compare two or more population means.

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 -{Food Irradiation Narrative} Set up the ANOVA Table.Use $\alpha$ = 0.01 to determine the critical values.

Gold Funds An investor studied the percentage rates of return of three different gold funds.Random samples of percentage rates of return for four periods were taken from each fund.The results appear in the table below: Gold Funds Percentage Rates Fund 1 Fund 2 Fund 3 12 4 9 15 8 3 13 6 5 14 5 7 17 4 4 -{Gold Funds Narrative} Test at the 5% significance level to determine whether the mean percentage rates for the three funds differ.

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

If SST explains a significant portion of the total variation,we conclude that the population means ____________________ (do/do not)differ.

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

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

Which of the following is a required condition for ANOVA?

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:

The analysis of variance is a procedure that allows statisticians to compare two or more population: