PSYC5180 Quantitative Methods I
Fall 2024
Statistics is a set of tools for making reasoned arguments about data.
Textbook: Moore, D.S., McCabe, G.P. , & Craig, B.A. (2012). Introduction to the practice of statistics. (7th Ed.)(NOT the most recent edition). New York: Freeman. “MM&C” Other readings are on Canvas.
Class meets Tuesday 10:00-12:00 and Friday 2:30-3:30 in 180-NI. Most Fridays will be problem sessions.
Syllabus (dates are approximate)
Week of: Topic Reading
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9/6
Fri. only
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Introduction. Introduction to R.
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Web tutorial sections 1-3, 5
https://www.cyclismo.org/tutorial/R/index.html
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9/10
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Descriptive Statistics, Correlation, Regression
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MM&C Ch.1&2;
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9/17
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Probability, Probability Distributions
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MM&C Ch. 4 ; Strogatz (2010)
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9/24
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Sampling Distributions, Statistics
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MM&C Ch. 5 pp. 297-308
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10/1
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Sampling Distribution of the Mean, Central Limit Theorem, Estimation
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Ch. 6 pp. 342-354
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10/8
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Hypothesis Testing for Means (Fisher & Neyman-Pearson
approaches; z-Tests)
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MM&C Ch. 6 pp. 360-396;
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10/15
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Student’s t-Tests for Means
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MM&C Ch. 7.
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10/22
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Confidence Intervals & Recap
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10/29
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Midterm
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11/5
ELECTION DAY
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Counts & Proportions: Estimation, Sampling Distributions,
Hypothesis Testing
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MM&C Ch. 5 pp. 312-332; MM&C Ch. 8
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11/12
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Effect size and power - practical Issues
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MM&C pp. 389-397, pp 419-420, pp. 463- 464; Cohen (1983).
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11/19
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Chi-square distribution and
Pearson’s approximate Chi-square test
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MMC Ch. 9
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11/26
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Introduction to resampling methods
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MM&C Ch. 16; Wilcox (2003; Chap. 7)
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12/3
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Hypothesis Testing: fundamental issues
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Cohen(1994); Loftus (1996); Simmons et al
(2011); Gigerenzer(2018); Button et al.
(2013)
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12/10
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Backup Day & Takehome Final Exam
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Required software: R and G* Power
We will be using R for calculations and plotting.
Other potential topics depending on time and interest:
Graphical Analysis and Error Bars
Classical Nonparametric Methods (statistics on ranks)
Introduction to Bayesian Methods
Specific Course Goals/Study Questions (bold items are relevant to the midterm)
Demonstrate your ability to use simple mathematical notation (subscripted variables, summation
signs, exponents).
You should be able to correctly interpret stem-and-leaf and box and whiskers graphs, scatter plots, error bars.
What is a random variable? If you take a questionnaire response from 20 subjects and calculate the
mean with an eye towards estimating some population effect, what is/are the random variable(s) you are most interested in?
What is probability? What is a probability distribution? Cumulative probability distribution? Quantile?
What is a correlation coefficient? A regression line? Interpret r2 in terms of variances.
What is a conditional probability? a joint probability? Make a 2x2 and a 3x3 table with entries representing simple, joint, and conditional probabilities of events. What is Bayes Rule?
Define “statistic” and “test statistic”.
Compare and contrast three types of distributions: sample, sampling, and population distributions.
What is “statistical estimation”? What is meant by a “good estimator”? Name two widely-used methods for finding ‘good’ estimators.
What is the central limit theorem? Why is the normal distribution so important?
What is a “standard error”? Why are most test statistics of the form “statistic”/“standard error of the statistic”?
Give, in the form. of a syllogism, the pseudo-logic behind statistical hypothesis tests.
Describe the Neyman-Pearson analysis of statistical decisions, including the two formal types of possible errors. Describe effect size and power, conceptually.
What is “statistical robustness”?
You should be able to calculate and interpret: Pearson correlation coefficients, z tests, t tests (3 types), sign tests, Chi-square tests, measures of effect size and power, permutation tests, randomization tests, bootstrap confidence intervals
What is the relationship between a statistical “p” value, effect size, and sample size? What is the bootstrap? What’s the logic behind resampling statistics?
What is the relationship, if any, between inferential statistics and experimental replication? Compare and contrast the Neyman-Pearson and Fisherian approaches to hypothesis testing.
Discuss the controversy over statistical hypothesis testing, experimenter degrees of freedom, and the ‘crisis of replicability.’ Discuss the probability of replicating a measured effect .