# Project #17607 - One-way and Two-way ANOVA

Must use MINITAB for analysis and post graphs/charts/tables in Microsoft WORD with interpretations and conclusions in proper presentation format.

Please communicate and justify the statistical modeling and analysis principles you use and how well you explain and interpret the results in a way that researchers not familiar with longitudinal data models and methods can understand. In particular, a good report will explain clearly:

(a) The statistical model you have chosen to answer the research questions;

(b) Your rationale for choosing the model, any assumptions you have made, and why these assumptions are reasonable for the study;

(c) The method used to fit the model;

(d)The results of the analysis with appropriate interpretations and conclusion, described in terms of the subject-matter.

(e) In writing your report, provide background on the situation, give a general statement of the problem, summarize the data (e.g. table or graph), and interpret the results. Thus, your report should be organized into a sequence of sections that presents all of this in a logical way.

Question No – 1 Analysis of variance methods are often used in clinical trials where the goal is to assess the effectiveness of one or more treatments for a particular medical condition. One such study compared three treatments for dandruff and a placebo. The treatments were 1% pyrithione zinc shampoo two times (PyrII), 2% ketoconazole shampoo (Keto),and a placebo shampoo (placebo). After six weeks of treatment, eight sections of the scalp were examined and given a score that measured the amount of scalp flaking on a 0 to 10 scale. The response variable was the sum of these eight scores. An analysis of the baseline flaking measure indicated that randomization of patients to treatments was successful in that no differences were found between the groups .At baseline there were 112 subjects in each of the three treatment groups and 28 subjects in the placebo group. During the clinical trial, 3 dropped out from the PyrII group and 6 from the keto group. No patients dropped out of the other two groups.

(a) Find the mean, standard deviation, and standard error for the subjects in each group. Summarize these, along with the sample sizes, in a table and make a graph of the means.

(b) Run the analysis of variance of these data. Write a short summery of the results and your conclusion. Be sure to include the hypotheses tested, the test statistic with degrees of freedom, and the p-value.

(c) Plot the residuals versus case number (the first variable in the data set).Describe the plot. Is there any pattern that would cause you to questions the assumption that the data are independent?

(d) Examine the standard deviations for the four of equal standard deviations for ANOVA in this data set? Explain your answer.

(e) Prepare Normal quintile plots for each treatment group. What do you conclude form these plots?

(f) Obtain the residuals form the analysis of variance and prepare a Normal quintile plot of these. What do you conclude?

(g) Use the Bonferroni or another multiple-comparisons procedure that your software provides to compare the individual group means in the dandruff study. Write a short summery of your conclusions (Available under General linear model in ANOVA)

(h) There are several natural contrasts in this experiment that describe comparisons of interest to the experimenters. They are (1) Placebo versus the average of the three treatments; (2) Keto versus the average to the two Pyr treatments; and (3) PyrI versus PyrII.

(i) Express each of these three contrasts in terms of the means (μ’s) of the treatments.

(ii) Give estimates with standard errors for each of the contrasts.

(iii) Perform the significance tests for the contrasts. Summarize the results of your tests and your conclusions.

Question No -2 The PLANTS1 data set gives the percent of nitrogen in four different species of plants grown in a laboratory. The species are Leucaena leuconephala, Acacia saligna, prosopis juliflora, and Eucalyptus citriodora. The researchers who collected these plants in parts of the country of Jordan where there is very little rainfall. To examine the effect of water, they varied the amount per day from 50 millimeters (mm) to 650 mm in 100 mm increments. There were nine plants are to be used primarily for animal food, with some parts that can be consumed by people, high nitrogen content is very desirable.

(a) Find the means for each species by –water combination. Plot these means versus water for the four species, connecting the means for each species by lines. Describe the overall pattern.

(b) Find the standard deviations for each species-by-water combination. Is it reasonable to pool the standard deviations for this problem? Note that with sample sexes of size 9, we expect these standard deviations to be quite variable.

(c) Run the two-way analysis of variance. Give the results of the hypothesis tests for the main effects and the interaction.

(d) Examine the residuals. Are there any unusual patterns or outliers? If you think that there is one or more points that are somewhat extreme, rerun the two- way analysis without these observations. Does this change the results in any substantial way?

(e) Run a separate one-way analysis of variance for each water level. If there is evidence that the species are not all the same, use a multiple-comparisons procedure to determine which pairs of species are significantly different. In what way, if any, do the differences appear to vary by water level? Write a short summary of your conclusions.

(f) Run a separate one-way analysis of variance for each species and summarize the results. Since the amount of water is a quantitative factor, we can also analyze these dada using regression. Run simple linear regressions separately for each species to predict nitrogen percent from water. Use plots to determine whether or not a line is a good way to approximate this relationship. Summarize the regression results and compare them wit

 Subject Mathematics Due By (Pacific Time) 11/26/2013 07:00 am
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