Inferences about Means and Mean Differences
Faculty of Arts Part III: Inferences about Means and Mean Differences
Course Overview
Course Title: PSYC 2101 Statistics in the Social Sciences
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Table of Contents
Part III: Inferences about Means and Mean Differences
Weeks Suggested: 5, 6, 7, & 8
Chapters Covered:
Chapter 9: Introduction to the t Statistic
Chapter 10: The t Test for Two Independent Samples
Chapter 11: The t Test for Two Related Samples
Chapter 12: Introduction to Analysis of Variance
Assignment: Assignment 3: Inferences About Means and Mean Differences
Midterm Practice Examination
Introduction to Statistical Inference
Definition: Statistical inference involves extending conclusions from a sample to a broader population.
Purpose: To test hypotheses regarding differences in statistical values, deciding whether to accept or reject said hypotheses.
Overview of Topics: Focuses on the t statistic and Analysis of Variance (ANOVA).
Chapter 9: Introduction to the t Statistic
Learning Objectives
Determine when to use the t statistic versus z-score in hypothesis testing.
Utilize the t statistic for hypothesis testing effectively.
Measure effect size for the t statistic.
Study Plan
Reading Assignment: Chapter 9, pp. 292–317.
Practice Exercises: Complete exercises and check solutions at the end of the Study Guide.
Practice Exercises
Exercise 1: Evaluate the impact of mnemonics on Grade 2 students' vocabulary test scores.
Standardized test mean: $µ = 24$
Class mean: $M = 30$, with sum of squares (SS) = 276.
Tasks: Perform a two-tailed hypothesis test with $α = .05$; show steps of hypothesis testing.
Exercise 2: Investigate the effect of temperature on laboratory rabbits' food consumption.
Normal intake: $µ = 550$ grams; tested at $30.0° C$; mean consumption: $M = 548$ with SS = 185.
Tasks: Determine the significance of temperature change; calculate effect size.
SPSS Activity
Reference pages 317–318 in the text for SPSS steps in performing the t-test.
Review of Learning Objectives
Self-evaluate understanding of the chapter's objectives and consult faculty for uncertainties.
Chapter 10: The t Test for Two Independent Samples
Learning Objectives
Identify studies suitable for independent-measures t-tests.
Use the independent-measure t statistic for testing mean differences.
Compute effect sizes (Cohen’s d or r2).
Study Plan
Reading Assignment: Chapter 10, pp. 324–351.
Practice Exercises: Complete and check solutions.
Practice Exercises
Exercise 1: Compare community spirit in two student groups from different schools, assessing volunteer hours.
Group A: $M = 20$ hours, SS = 125; Group B: $M = 24$ hours, SS = 122.
Tasks: Compute pooled variance; perform a two-tailed hypothesis test and measure effect size.
Exercise 2: Test the significant differences in error estimates between two student groups in a perception experiment.
Group A: $M = 7.2$, SS = 22; Group B: $M = 7.6$, SS = 25.
Tasks: Hypothesis test and show work.
SPSS Activity
Reference pages 351–354 for SPSS on independent-measures t test.
Review of Learning Objectives
Revisit objectives for mastery; consult with faculty for clarity on any issues.
Chapter 11: The t Test for Two Related Samples
Learning Objectives
Identify studies for repeated-measures t hypothesis testing.
Use repeated-measures t statistic effectively.
Evaluate the effect size of mean differences between treatments.
Compare advantages and disadvantages of repeated-measures versus independent-measures studies.
Study Plan
Reading Assignment: Chapter 11, pp. 360–382.
Practice Exercises: Resolve exercises and check solutions.
Practice Exercises
Exercise 1: Assess a physical education program's effectiveness on behavior for Grade 3 students with ADHD, comparing misbehavior before and after the program.
Tasks: Conduct hypothesis testing with a two-tailed test; compute effect size.
Exercise 2: Examine if involvement in co-curricular activities impacts GPA while statistically controlling for various factors (intelligence, program, etc.).
Tasks: Hypothesis test and calculate Cohen’s d for effect size.
SPSS Activity
Reference pages for instructions on using SPSS for repeated-measures t test.
Review of Learning Objectives
Self-check against learning objectives; continue to seek support from faculty as needed.
Chapter 12: Introduction to Analysis of Variance (ANOVA)
Learning Objectives
Articulate the logic and purpose of ANOVA.
Carry out ANOVA for independent measures research studies.
Apply post-test techniques (Tukey’s HSD, Scheffe Test).
Measure effect size using $ ext{η}^2$ (eta squared).
Study Plan
Reading Assignment: Chapter 12, pp. 392–428. Reference supplementary material on notation and formula pages (401–408).
Procedures for ANOVA
Identify relevant values:
Number of groups: $k$
Number of scores in each group: $n_c$
Total scores: $N = ext{sum}(n_c)$
Degrees of freedom: $df{Tot} = N - 1$, $df{BT} = k - 1$, $df_{WT} = N - k$
Perform necessary calculations for sum of squares (Total, Between Treatment, Within Treatment).
Calculate Mean Squares and F-ratio.
If significant, conduct post hoc tests.
Measure effect size: $ ext{η}^2 = rac{SS{BT}}{SS{TOT}}$.
Practice Exercises
Exercise 1: Test differences between three types of advertising based on sales.
Conduct ANOVA; follow up with Tukey's HSD; calculate η2.
SPSS Activity
Reference pages for detailed ANOVA instructions through SPSS.
Summary of Part III: Inferences about Means and Mean Differences
Covered the t statistic versus z statistic; degrees of freedom; hypothesis testing; measuring effect size; implications of sample size and variance.
Discussed independent and related measures t tests including significance testing.
Explored ANOVA for comparing group means, including its logic and effect size implications via η2.
Assignment 3: Inferences About Means and Mean Differences
This assignment contributes 16% towards the final grade; ensure proper format upon submission.
Midterm Practice Examination
Prepare thoroughly for the midterm by reviewing all chapters and practice exam resources. Maintain familiarity with essential formulas and reference tables if applicable.