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ST 314 Data Analysis 06 Part 1

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ST 314 Data Analysis 06

Part 1. (23 points)

Single Factor ANOVA is a method we use when we want to compare a quantitative variable among more than two categories. It evaluates whether the means of different treatment groups, or populations, are equivalent. When we only have two populations then we can perform a two-sample t procedure, but when we have more populations we need to examine the data with Single Factor ANOVA. 

 

In the R script DA6_Single_Factor_ANOVA.R, follow along with the analysis that compares average number of roommates between majors for the ST314 online students. You will need to upload the student information dataset from Canvas.

 

Once you have reviewed the example analysis, conduct your own by choosing one of the following three options:

 

Option 1: Is there evidence average number of terms a student has been studying at OSU differs between majors for ST314 students?

 

Option 2: Is there evidence average weekly gaming hours per week differs between majors for ST314 students?

 

Option 3: Is there evidence average anticipated salary differs between majors for ST314 students?

 

For the option you selected, answer the questions below. Use a significance level of 0.10.

 

1. (3 point) Create side-by-side boxplot of the data and add color and a title to your plot. Paste your plot.

 

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2. (2 point) From the side-by-side box plot, does there look to be a difference between the averages? Explain your reasoning.

 

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3. (2 point) State the appropriate null and alternative hypothesis for the Single Factor ANOVA F test.

 

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4. (3 points) State the conditions for the Single Factor ANOVA F Test. Is it reasonable to seem that these conditions are satisfied? Explain your reasoning. If not, still proceed.

 

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5. Perform the Single Factor ANOVA F test in R.
   1. (2 point) Paste the ANOVA table.

 

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1. 2. (2 points) From the ANOVA table, what is the average between group variability and the average within group variability, respectively the MSTr and MSE?

 

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6. Use the F statistic and p-value from the ANOVA table to state whether there is a significant difference between at least two of the group means.
   1. (2 points) State whether to reject the null.  State the test statistic and p-value.

 

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1. 2. (2 points) Include a statement in terms of the strength of evidence in terms of the alternative. Include context.

 

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7. Using the Tukey’s Multiple Comparison procedure output. Are there any individual comparisons that are significant at the 0.10 significance level?
   1. (2 point) Paste R output for the multiple comparisons procedure. 

 

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1. 2. (2 point) List all comparisons that are significant (or state those that are not).

 

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1. 3. (1 point) Interpret the 90% F-W confidence interval for the difference with the smallest p-value (even if it is not significant).

 

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Gradescope Page Matching (2 points)

When you upload your PDF file to Gradescope, you will need to match each question on this assignment to the correct pages. Video instructions for doing this are available in the Start Here module on Canvas on the page “Submitting Assignments in Gradescope”. Failure to follow these instructions will result in a 2-point deduction on your assignment grade. Match this page to outline item “Gradescope Page Matching”.