Note: Your answers to the questions below should follow the expectations for homework found here. Questions outside of class can be asked on the Module Assignments-Questions Teams channel (see link on homepage).

Calculations

Suppose that the following observations were made for individuals in two groups.

Group A -- 13, 14, 17, 20
Group B -- 21, 23, 26, 27, 28

Use these data to answer the following questions.

  1. Calculate the two group means.
  2. Calculate the grand mean (i.e., both groups combined).

One potential model for these data is that each observation can be represented by a single mean, the grand mean. Use this model (and what you calculated above) to answer the following questions.

  1. Calculate the residual for each individual.
  2. Describe as fully as possible what the residual for the first individual in Group A means.
  3. Describe as fully as possible what the residual for the last individual in Group B means.
  4. Calculate the RSS for this model.
  5. Calculate the residual df for this model.
  6. Calculate the residual MS for this model. How does the square root of this value compare to the absolute values of your residuals?
  7. Describe as fully as possible what the square root of this residual MS means.

Another potential model is that each observation can be represented by its corresponding group mean. Use this model (and what you calculated above) to answer the following questions.

  1. Calculate the residual for each individual.
  2. Describe as fully as possible what the residual for the first individual in Group A means.
  3. Describe as fully as possible what the residual for the last individual in Group B means.
  4. Calculate the RSS for this model.
  5. Calculate the residual df for this model.
  6. Calculate the residual MS for this model. How does the square root of this value compare to the absolute values of your residuals?
  7. Describe as fully as possible what the square root of this residual MS means.

Results from using the grand mean are usually labeled with “total”, whereas those results using group means are usually labeled with “within.” With this in mind, answer the following questions.

  1. Calculate RSSTotal-RSSWithin. What do you think this value measures or represents?
  2. Calculate dfTotal-dfWithin. What do you think this value measures or represents?