Module 6: Tests of Means & ANOVA

Module 6 takes a deep dive into t tests and ANOVAs, among other tests.

Learning Objectives

These are the learning objectives for this portion of the class:

  1. Compute the probability of a sample mean being at least as high as a specified value when \(\sigma\) is known or estimated
  2. Compute a two-tailed probability
  3. State the assumptions for testing the difference between two means
  4. Estimate the population variance assuming homogeneity of variance
  5. Compute the standard error of the difference between means
  6. Compute \(t\) and \(p\) for the difference between means
  7. Format data for computer analysis
  8. Define pairwise comparison
  9. Describe the problem with doing \(t\) tests among all pairs of means
  10. Calculate the Tukey HSD test
  11. Define linear combination
  12. Specify a linear combination in terms of coefficients
  13. Do a significance test for a specific comparison
  14. Determine whether you have correlated pairs or independent groups
  15. Compute a \(t\) test for correlated pairs
  16. Determine whether to use the formula for correlated comparisons or independent-groups comparisons
  17. Compute \(t\) for a comparison for repeated-measures data
  18. Compute the Bonferroni correction
  19. Calculate pairwise comparisons using the Bonferroni correction

These are the learning objectives for this portion of the class:

  1. What null hypothesis is tested by ANOVA
  2. Describe the uses of ANOVA
  3. Determine whether a factor is a between-subjects or a within-subjects factor
  4. Define factorial design
  5. State what the Mean Square Error (MSE) estimates when the null hypothesis is true and when the null hypothesis is false
  6. State what the Mean Square Between (MSB) estimates when the null hypothesis is true and when the null hypothesis is false
  7. State the assumptions of a one-way ANOVA
  8. Compute MSE & MSB
  9. Compute \(F\) and its two degrees of freedom parameters
  10. Describe the shape of the F distribution
  11. State the relationship between the \(t\) and \(F\) distributions
  12. Partition the sums of squares into condition and error
  13. Format data to be used with a computer statistics program
  14. Define main effect, simple effect, interaction, and marginal mean
  15. State the relationship between simple effects and interaction
  16. Compute the source of variation and df for each effect in a factorial design
  17. Plot the means for an interaction
  18. Define three-way interaction
  19. State why unequal \(n\) can be a problem
  20. Define confounding
  21. Compute weighted and unweighted means
  22. Distinguish between Type I and Type III sums of squares
  23. Describe why the cause of the unequal sample sizes makes a difference in the interpretation
  24. Compute Tukey HSD test
  25. Describe an interaction in words
  26. Describe why one might want to compute simple effect tests following a significant interaction
  27. Define a within-subjects factor
  28. Explain why a within-subjects design can be expected to have more power than a between-subjects design
  29. Be able to create the Source and df columns of an ANOVA summary table for a one-way within-subjects design
  30. Explain error in terms of interaction
  31. Discuss the problem of carryover effects
  32. Be able to create the Source and df columns of an ANOVA summary table for a design with one between-subjects and one within-subjects variable

Consumables

Each week there will be a number of items for you to consume, be it reading, watching, listening, or a combination thereof.

Consumable materials for module grouped by required or supplemental content.
Module Required? Text/Resource Chapter/Title Estimated time in minutes Type
6 Required Online Statistics Textbook Chapter 12: Tests of Means 120 Mathematics
6 Required Online Statistics Textbook Chapter 15: Analysis of Variance 120 Mathematics
6 Supplemental Manga Guide to Statistics Chapter 7: Let's Explore Hypothesis Tests 60 Mathematics
6 Supplemental StatsCast What is a t-test? 10 Mathematics
6 Supplemental thatRnerd Analysis of Variance (ANOVA) in R 8 Mathematics
6 Supplemental Crash Course Statistics Test Statistics 13 Mathematics
6 Supplemental Crash Course Statistics T-Tests: A Matched Pair Made in Heaven 12 Mathematics
6 Supplemental Crash Course Statistics Degrees of Freedom and Effect Sizes 14 Programming
6 Supplemental Berkeley Statistics Using t-tests in R 20 Programming
6 Supplemental Cyclismo Calculating Confidence Intervals 20 Programming
6 Supplemental Introduction to Statistics and Data Science Chapter 10: Confidence Intervals 45 Programming
6 Supplemental Research By Design Using t Tests with Two Samples 6 Mathematics
6 Supplemental Research By Design Independent Samples t Test Introduction 16 Mathematics
6 Supplemental Research By Design Paired Samples t Test Introduction 15 Mathematics
6 Supplemental Research By Design Probability Pyramiding - Why ANOVA? 8 Mathematics
6 Supplemental Research By Design ANOVA - Variance Between and Within 13 Mathematics
6 Supplemental Research By Design Assumptions and Hypotheses for One-Way ANOVA 13 Mathematics
6 Supplemental Research By Design One-Way Anova (by hand) 16 Mathematics
6 Supplemental Research By Design Tukey's HSD Post Hoc Test 8 Mathematics

The total amount of time estimated on required texts and resources is 240 minutes, while you should expect to spend at most an additional 297 minutes on supplemental material.

The total amount of time estimated you should spend on these assignments depends on the amount of effort required, itself based on your previous experience with statistics, generally, and R, in particular. You can expect to spend somewhere between 615 and 1025 minutes on this module beyond the readings. The estimated total number of words you’re likely to write in this module is 3,250.

Assignments for this module.
Module Assignment type Short name Long name Points Effort (low) Effort (high) Expected word total
6 Questions CH12M Chapter 12 questions 3 4 8 125
6 Questions CH15M Chapter 15 questions 3 6 12 125
6 Quiz CH12Q Chapter 12 quiz 15 25 25 0
6 Quiz CH15Q Chapter 15 quiz 15 25 50 0
6 Activity AE Activity E: Presenting Data 20 75 210 1,250
6 Final FP Advanced research topic paper and presentation 100 480 720 1,750

Module 6 Activity

This module’s activity covers the presentation of data.

Final project

This module also includes the final project!

Quiz

Don’t forget about your chapter quizzes! Find them in the Quizzes menu in D2L.

Chapter Questions

Each week’s chapters follow the same basic process but may be slightly different in terms of which questions you can and cannot choose from. Be sure to read the instructions carefully!

Steps to completion

  1. (Setup: create your copy of the Chapter Questions Posit Cloud project once it’s available. Inside you will find a document template for creating your submitted responses.)
  2. From the end-of-chapter exercises for each chapter, choose three questions from the provided list.
  3. Do not choose from the “Questions from Case Studies” section.
  4. Create a Quarto PDF document using the provided template and answer the questions. This is an opportunity to practice your formatting and information presentation skills as many questions require varied approaches to response.
    1. Be absolutely certain that you leave the embed-resources: true YAML key present! Otherwise, the PDF file you submit will likely break anywhere other than your project.
  5. Submit your rendered PDF file (one per module) to the relevant module’s “Participation” dropbox.
    1. For example, in the Module 1 Exercises dropbox you should upload a single document for Chapter 1 questions and responses, and your Chapter 6 questions and responses.
    2. You will need to make sure your files are named appropriately by changing the output-file YAML key. Your template has instructions to remind you of this.


Make sure to indicate the chapter and question that you are answering in your answer document.

Chapter 12 do 3, 5, 9

Chapter 15 do 1, 2, 3