Module 6: Tests of Means & ANOVA

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

Learning Objectives

Chapter 12

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

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

Chapter 15

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

What null hypothesis is tested by ANOVA
Describe the uses of ANOVA
Determine whether a factor is a between-subjects or a within-subjects factor
Define factorial design
State what the Mean Square Error (MSE) estimates when the null hypothesis is true and when the null hypothesis is false
State what the Mean Square Between (MSB) estimates when the null hypothesis is true and when the null hypothesis is false
State the assumptions of a one-way ANOVA
Compute MSE & MSB
Compute \(F\) and its two degrees of freedom parameters
Describe the shape of the F distribution
State the relationship between the \(t\) and \(F\) distributions
Partition the sums of squares into condition and error
Format data to be used with a computer statistics program
Define main effect, simple effect, interaction, and marginal mean
State the relationship between simple effects and interaction
Compute the source of variation and df for each effect in a factorial design
Plot the means for an interaction
Define three-way interaction
State why unequal \(n\) can be a problem
Define confounding
Compute weighted and unweighted means
Distinguish between Type I and Type III sums of squares
Describe why the cause of the unequal sample sizes makes a difference in the interpretation
Compute Tukey HSD test
Describe an interaction in words
Describe why one might want to compute simple effect tests following a significant interaction
Define a within-subjects factor
Explain why a within-subjects design can be expected to have more power than a between-subjects design
Be able to create the Source and df columns of an ANOVA summary table for a one-way within-subjects design
Explain error in terms of interaction
Discuss the problem of carryover effects
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	Due date	Assignment type	Short name	Long name	Points	Effort (low)	Effort (high)	Expected word total
6	2024-02-23	Questions	CH12M	Chapter 12 questions	3	4	8	125
6	2024-02-23	Questions	CH15M	Chapter 15 questions	3	6	12	125
6	2024-02-23	Quiz	CH12Q	Chapter 12 quiz	15	25	25	0
6	2024-02-23	Quiz	CH15Q	Chapter 15 quiz	15	25	50	0
6	2024-02-23	Activity	AE	Activity E: Presenting Data	20	75	210	1,250
6	2024-03-01	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

(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.)
From the end-of-chapter exercises for each chapter, choose three questions from the provided list.
Do not choose from the “Questions from Case Studies” section.
Create a Quarto HTML 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 HTML file you submit will likely break anywhere other than your project.
Submit your rendered HTML 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.

You are only required to do 3 questions in total.
Make sure to indicate the chapter and question that you are answering in your answer document.

Chapter 12, choose from: any except 1, 4, 7, 8, 11, 13, 16-20

Chapter 15, choose from: any