Psychology 202a

Advanced Psychological Statistics I

Fall Semester, 2020

Syllabus for Fall, 2020

Instructor:

Jack L. Vevea (psyc202a@gmail.com)
(Please note that this is a special email address for this class; I will not monitor it after the conclusion of the class. My regular email is jvevea@ucmerced.edu.)
Social Science and Management Building 306a
Office hours: Wednesday, 2:00-4:00, or by appointment. (Office hours will be held at the same Zoom link that is used for class.)

Telephone: (209) 658-1706 (but email is usually a much quicker way to reach me)

Assistant:

Sonja Winter (psyc202a@gmail.com)
Social Science and Management Building 320
Office hours: Monday 12:00-1:00 and Friday 3:00-4:00. These will be held at Sonja's Zoom link on catcourses.

Text:

Howell, David C.(2013).
Statistical Methods for Psychology (Fifth, Sixth, Seventh, or Eighth Edition).
Belmont, CA: Thomson Wadsworth.

Note: all reading assignments refer to the eighth edition. Here is a grid that gives equivalents for other editions.

Meeting times:

We will meet Tuesdays and Thursdays from 10:30 to 11:45 PM. All meetings will be virtual via Zoom until further notice.

Course description:

Psychology 202a will focus on description and inference in the context of the general linear model.

Course learning goals:

In the class, you will:
  • review simple descriptive and inferential statistical techniques;
  • review the concepts of random variables and probability;
  • review the concept of the sampling distribution;
  • review confidence intervals and simple inference about means;
  • gain a deeper understanding of correlation and linear regression with one predictor;
  • learn enough about regression with multiple predictors to facilitate discussion of linear inferential models;
  • review a conventional approach to the analysis of variance (ANOVA);
  • learn about ANOVA as a special case of linear regression;
  • investigate the mathematics that operates behind the scenes in ANOVA;
  • learn about ANOVA with random effects;
  • learn about the importance of assumptions in statistical inference;
  • learn about power analysis;
  • learn about computer-intensive methods.

    • Course learning outcomes:

    By the end of the class, you will be able to:
  • use graphical methods and descriptive statistics to characterize simple and conditional distributions (demonstrated in homework and exams);
  • apply probabilistic reasoning techniques (rules for combining probabilities, Bayes' theorem) to real problems (demonstrated in homework and exams);
  • demonstrate an understanding of the concept of sampling distributions (assessed on the first exam);
  • use computer simulation to assess characteristics of probability distributions (demonstrated in homework);
  • perform and interpret simple tests about means and differences between means, both manually and with the aid of the computer (demonstrated in homework by production and interpretation of computer analyses; demonstrated on exams by interpretation of computer analyses and by hand computations using partially complete computer output);
  • perform confidence intervals about means and differences between means, both by hand and with the aid of the computer (demonstrated in the same manner as skills involving the corresponding tests);
  • identify and evaluate assumptions relevant to simple tests and confidence intervals (demonstrated in the same manner as the previous two learning outcomes);
  • compute and interpret correlations and simple linear regressions (demonstrated in homework and exams);
  • compute and interpret multiple regression models (demonstrated in homework by production and interpretive discussion of computer analyses; demonstrated on exams by interpretation of computer output);
  • produce and interpret added-variable plots (demonstrated in homework);
  • demonstrate an understanding of the logic behind ANOVA (assessed in homework in which you will compute a simple ANOVA using inefficient formulas that highlight the concepts);
  • compute and interpret various forms of ANOVA (demonstrated in homework by production and interpretation of computer analyses; demonstrated on exams by interpretation of computer output and by hand computations based on partially complete computer output);
  • compute and interpret pre- and post-hoc contrasts and comparisons (demonstrated in homework and exams);
  • implement manual coding of ANOVA problems using a multiple regression approach (demonstrated in homework and exams);
  • identify situations in which random-effects models are appropriate, and adjust ANOVA methods accordingly (demonstrated in homework and on exams);
  • conduct power analyses associated with the statistical inference approaches covered in the class, using both R and proprietary software (demonstrated in homework assignments; knowledge of what affects power will be assessed on exams);
  • use computer-intensive methods as an alternative to conventional approaches to statistical inference (demonstrated in homework).

    • General comments on the purpose of the class:

    While you should not think of this class as a class in statistical computing, we will use statistical software (specifically R) frequently throughout the semester. Typically students are able to pick up what they need to know about using R from work in class and posted transcripts. However, for those who prefer more formal support, here is a tutorial that introduces some of the basics. (Don't be offended by the word "undergraduate" in the title; we know you aren't undergraduates, but the document is still useful.)

    The overall goal of this course is not to offer a sequential presentation of all the basic statistical techniques you might need for simple analyses of psychological data. Rather, it is to teach the skill of thinking statistically, and to foster a deeper understanding that will enable the student to learn and understand analytic techniques independently.

    A part of that goal necessarily involves revisting material that is already familiar, and attempting to understand it in new and deeper ways. A quote from T.S. Eliot's Little Gidding may clarify the spirit of that aspect of the class: 

         We shall not cease from exploration
     And the end of all our exploring
     Will be to arrive where we started
     And know the place for the first time.

    Prerequisites:

    Graduate status. The class assumes that students have had some prior exposure to statistics through an undergraduate introductory course. While it is possible to do well without that experience, it will mean considerable extra effort in the first weeks of the class; please see the instructor if this applies to you.

    Although the course does not emphasize mathematics, you should know something about the basics of algebra (the ideas of equations and manipulation of variables) and geometry (plotting points on a plane, the equation of a line). If you feel ill-prepared in of those areas, a quick review might be in order.

    Evaluation:

    The current plan is for grading to be based on a combination of written homework, a midterm exam, and a comprehensive final exam. (We have tentative permission to hold both exams in person on campus, using rooms that are sufficiently large to allow social distancing. Further details will be announced as the exam dates approach.) Homework will count for 40% of your final grade, and each exam will count for 30%.

    In the event that permission for on-campus exams is rescinded, they will be replaced by a final special project. In that event, homework and the final project will each count for 50% of your grade.

    These components make up the final grade in the following manner. First, each component (homework, midterm exam, final exam) gets a grade point value: A+ = 4.3, A = 4.0, A- = 3.7, B+ = 3.3, B = 3.0, B- = 2.7, and so on. The weighted average of the grade points from the three components determines your final grade. The following table shows the mapping of grade point averages to letter grades:

    Grade Point Range Letter Grade
    GPA > 4.25 A+
    3.75 < GPA < 4.25 A
    3.50 < GPA < 3.75 A-
    3.25 < GPA < 3.50 B+
    2.75 < GPA < 3.25 B
    2.50 < GPA < 2.75 B-
    2.25 < GPA < 2.50 C+
    1.75 < GPA < 2.25 C
    1.50 < GPA < 1.75 C-
    0.75 < GPA < 1.50 D
    GPA < 0.75 F

    In the rare case where a student is precisely on the cusp between two letter grades, classroom participation determines whether the student receives the higher or lower grade.

    Academic Integrity

    Students should be familiar with University policies on academic integrity. You will find relevant information here.

    In the overall context of that policy, the following information is specific to this class:

  • Cooperative work on the computational aspects of homework assignments is strongly encouraged, but you are expected to work independently on discussion and interpretation. The words you submit in your written assignments should be entirely your own. You may resubmit modified homework assignments up until one week after the return of the initial submission.
  • You are expected to work independently on exams. You will be allowed to use your books and notes during the exams. However, that policy exists to avoid the need for tedious memorization; you should not view access to your notes as a substitute for basic understanding of the material.

    • Students with Disabilities

    UC Merced has a variety of services available to accommodate students with disabilities. Information is available here.

    How to submit homework assignments

    You should submit homework assignments through CatCourses. After you navigate to the CatCourses page for this course, click on the "Assignments" button in the list on the left. Then, click on the link to the specific homework assignment you are submitting. Make sure to combine everything into one document because CatCourses will allow only one file. That file must have a .doc, .docx, or .pdf file extension (no .odt, .zip, .pages file extensions). All deadlines are at midnight on the due date, and the CatCourses system will not accept submissions after that time.

    Course Outline

    August 27
    Initial class meeting: introduction, using the class web page.

    Obtaining and using R.

    September 1
    Some technical vocabulary. Understanding empirical distributions. Central tendency. Simple graphical methods.
    Reading: All of Chapter One; Chapter Two, Sections One through Seven.
    September 3
    Central tendency, continued. Measures of variability. Some subtleties of graphing.
    Reading: Chapter Two, Sections Eight and Nine.
    September 8
    Measures of variability, continued.
    No new reading.
    September 10
    Other aspects of shape. Putting it all together: the use of graphics and descriptive statistics to describe distributions. Changes in distributions under linear and nonlinear transformation. Special case: the Z score.
    Reading: Chapter Two, Sections 11 and 12; Chapter Three, Section Six.
    Homework One is available (due September 17).
    September 15
    Conditional distributions.
    No new reading.
    September 17
    Introduction to probability. Random variables and probability distributions. The frequentist approach to understanding probability. The distinction between discrete and continuous random variables. Computer simulation as a tool for understanding probability distributions.
    Reading: Chapter Three, Sections One through Three; Chapter Five, Sections One through Six.
    September 22
    Rules for combining probabilities. Conditional probabilities and Bayes' theorem.
    Reading: Chapter Three, Section Four ; Chapter Five, Section Seven through Nine.
    September 24
    Statistics: a special kind of random variable. Sampling distributions. Introducing hypothesis testing through the binomial distribution. The Central Limit Theorem.
    Reading: Chapter Four, Sections One through Six, Sections Eight through 10, Sections 12 and 13.
    Homework Two is available (due October 1).
    September 29
    Tests about means and differences between means. Inference about means when sigma is unknown.
    Reading: Chapter Seven, Sections One through Three.
    October 1
    Effect sizes and confidence intervals.
    Reading: Chapter Three, Section Five; Chapter Four, Section 11; Chapter Seven, pages 203-204.
    October 6
    Tests about differences between means when sigma is unknown: The two-sample independent-groups t test.
    Reading: Chapter Seven, Sections Five through Seven.
    Homework Three is available (due October 13).
    October 8
    Review for the midterm exam.
    October 13
    Midterm examination.
    October 15
    Review of the midterm exam.
    October 20
    Confidence intervals and effect sizes associated with the t test. The t test for related samples.
    Reading: Chapter Seven, Section Four.
    A review of correlation.
    Reading: Chapter Nine, Sections One through Six.
    October 22
    Correlation, continued.
    An introduction to simple linear regression.
    Reading: Chapter Nine, Sections Seven through 12.
    Homework Four is available (due October 29).
    October 27
    Simple linear regression: inference and assumptions. The decomposition of the sum of squares. Regression diagnostics. The problem of restriction of range.
    Reading: Chapter Nine, Sections 13 through 15.
    October 29
    The two-sample, independent-groups t-test, revisited.

    The t test as a linear model: dummy coding, effects coding, nonsense coding.

    No new reading.
    Homework Five is available (due November 5).
    November 3
    An introduction to multiple linear regression. Added-variable plots.
    Reading: Chapter 15, Sections One through Six.
    November 5
    Introduction to the analysis of variance (ANOVA): conceptual approach. ANOVA: computational approach.
    Reading: Chapter 11, Sections One through Nine.
    November 10
    ANOVA and the linear model. Contrasts and comparisons.
    Reading: Chapter 12, Sections One through Three; Chapter 16, Sections One and Two.
    Homework Six is available (due November 17).
    November 12
    Contrasts and comparisons, continued.
    Reading: Chapter 12, Sections Six through Eight.
    November 17
    Power analysis.
    Reading: Chapter Four, Section Seven; all of Chapter Eight. Chapter Nine, Section 16; Chapter 11, Section 12.
    November 19
    Power analysis, continued.
    No new reading.
    November 24
    Catch-up day.
    November 26
    Thanksgiving holiday; no class meeting.
    December 1
    Factorial ANOVA: concepts and computation.
    Reading: Chapter 13, Sections One through Five.
    December 3
    Homework Seven is available (due December 10).
    Factorial ANOVA and the linear model.
    Reading: Chapter 13, Sections Six, Seven, Nine and Ten.
    December 8
    Some special issues in ANOVA: unbalanced designs, random-effects models.
    Reading: Chapter 11, Section 10; Chapter 13, Sections Eight and 11; Chapter 16, Section Four.
    December 10
    Review for exam.
    No new reading.
    December 12, 3:00 - 6:00 PM
    Final examination.