In this assignment, you will use R Studio to:
Explore and test the assumptions of an analysis of variance (ANOVA)
Carry out an ANOVA or non-parametric Kruskal-Wallis test on a dataset that includes four groups
Carry out a post-hoc test (Tukey or Dunn) Make a box plot of the data, with labels to indicate which means are different from each other based on the results of your post-hoc test.
Lecture 21 includes a demonstration of the R commands you will need for this assignment. You should review that material before you begin. On eClass you will find a text (.txt) file in tab- delimited format. Different versions of this file are available to different students; use the file that is visible to you when you log in to your own eClass account. In the file there are two columns of data, one for the treatment (explanatory) variable and one for the response variable. Your goal is to determine which treatments, if any, have a significant effect on the response variable, and in which direction, while answering/doing the following based on the material presented in Lecture 21:
1) What are the assumptions of ANOVA and are those assumptions met for your dataset?
Include one graph in your answer with a brief explanation of what the graph demonstrates as well as the results of two sets of statistical analyses with single-sentence conclusions with respect to the null hypotheses.
2) Perform either an ANOVA or Kruskal-Wallis test based on the results of 1). Note: you should ignore data transformations for the purposes of this assignment. Include your results in an appropriate table, as well as a single-sentence conclusion with respect to the null hypothesis and a single-sentence conclusion with respect to the scientific hypothesis i.e. what can be concluded about the effect of the explanatory variable on the response variable?).
3) Based on the results of 1) and 2) perform a post-hoc test, as appropriate. Include your results in an appropriate table, along with a single-sentence conclusion with respect to the null hypothesis and a single-sentence conclusion with respect to the scientific hypothesis.
4) Display your data and results in an appropriately labelled bloxplot. This includes letters above the box whiskers to indicate which means are different from one another (see Lecture 21).
Q1: 1 mark for ANOVA assumptions, 1 mark for whether they are met or not, 2 marks for a properly labelled graph, 1 mark for an explanation of what the graph shows, 2 marks for the results of first set of statistical analyses and 1 mark for conclusion, 1 mark for results of second statistical analysis and 1 mark for conclusion.
Total marks for Q1 = 10
Q2: 1 mark for correct test (ANOVA or Kruskal-Wallis), 2 marks for results table, 1 mark each for statistical and scientific conclusions.
Total marks for Q2 = 5
Q3: 1 mark for correct post-hoc test, 2 marks for results table, 1 mark each for statistical and scientific conclusions.
Total marks for Q3 = 5
Q4: 2 marks for an appropriately labelled boxplot and 3 marks for the correct letters differentiating statistical differences among groups.
Total marks for Q4 = 5
Total = 25 marks
Please make sure your name and student number are on the assignment (can be on a separate cover page, but not essential as long as they are easily visible). Make sure you upload both your Word document (or PDF) with the written answers, tables, and graphs, as well as the script you used to produce the answers.
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