实验设计和数据分析代写 Experimental design and data analysis

Experimental design and data analysis

实验设计和数据分析代写 Hemoglobin is measured (g/100 ml.) in the blood of brown trout after 35 days of treatment with four rates of sulfamerazine:

Exercise 3. Concentrations of epinephrine  实验设计和数据分析代写

The concentrations (in nanograms per millimeter) of plasma epinephrine were measured for 10 dogs under isofluorane, halothane, and cyclopropane anesthesia, represented as three columns in data frame dogs.txt  Download dogs.txt. We are interested in differences in the concentration for the different drugs.

1. a)  Is it reasonable to assume that the three columns of txtwere taken from normal populations?


2. b)  Investigate whether the columns isofluoraneand halothaneare correlated. Apply relevant tests to verify whether the distributions of these columns are different. Is a permutation test applicable?


3. c)  Conduct a one-way ANOVA to determine whether the type of drug has an effect on the concentration of plasma epinephrine. Give the estimated concentrations for each of the three anesthesia drugs.


4. d)  Does the Kruskal-Wallis test arrive at the same conclusion about the effect of drug as the test in c)? Explain possible differences between conclusions of the Kruskal-Wallis and ANOVA tests.

Exercise 4. Hemoglobin in trout

Hemoglobin is measured (g/100 ml.) in the blood of brown trout after 35 days of treatment with four rates of sulfamerazine: the daily rates of 0, 5, 10 and 15 g of sulfamerazine per 100 pounds of fish, denoted as rates 1, 2, 3 and 4, respectively. (Beware that the levels of the factor rate are coded by numbers.) Two methods (denoted as A and B) of administering the sulfamerazine were used. The data is collected in data set hemoglobin.txt  Download hemoglobin.txt.

1. a)  Present an R-code for the randomization process to distribute 80 fishes over all combinations of levels of factors rateand method.


2. b)  Perform the two-way ANOVA to test for effects of factors rate, methodand their interaction on the response variable hemoglobin. Comment on your findings.


3. c)  Which of the two factors has the greatest influence? Is this a good question? Consider the additive model. Which combination of rate and method yield the highest hemoglobin? Estimate the mean hemoglobin value for rate 3by using method A. What rate leads to the highest mean hemoglobin?


4. d)  Test the null hypothesis that the hemoglobin is the same for all rates by a one-way ANOVA test, ignoring the variable method. Is it right/wrong or useful/not useful to perform this test on this dataset?

Exercise 5. Sour cream  实验设计和数据分析代写

The file cream.txt  Download cream.txtcontains data on an experiment to produce sour cream. Yogurt was placed in sweet cream, and yogurt bacteria were allowed to develop. Bacteria produce lactic acid, and as a surrogate for the number of yogurt bacteria.  The acidity of the cream was measured. Interest was in the effect of the type of yogurt (denoted as starter) on acidity. The mixtures of yogurt and sweet cream were kept at constant temperature in a yogurt maker, in which five different positions could be used.

The experiment was carried out with five batches of sweet cream, which were meant to have the same composition. With each batch each of five types of starter was used, with the yogurt placed in one of the five positions. The combinations of levels of three factors form a three-dimensional latin square. (You may need to install the R-package lme4, which is not included in the standard distribution of R.)

1. a)  Analyze the data in a three-way experiment without interactions with acidityas response and starter, batchand position as factors. By using summary command, can you tell whether there is a significant difference between the effects of starter 1 and starter 2 on acidity?


2. b)  Recall that the main interest is in the effect of starter on the acidity; factors positionsand batchesrepresent the block variables. Remove insignificant block variable(s) if there are such, and perform an ANOVA for the resulting “fixed effects” model. Which starter(s) lead to significantly different acidity?


3. c)  For the model from b), can we also apply the Friedman test to test whether there is an effect of starter on acidity? Motivate your answer.


4. d)  Repeat b) by performing a mixed effects analysis, modeling the block variable(s) (if there are any) as a random effect by using the function lmer. Compare your results to the results found by using the fixed effects model in b).

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