grad_stats

Graduate statistics course covering basic estimation, the general linear model, and applications into more complex crossed and nested models.

All analyses are taught using the general linear model and a model comparison approach.

Please note that all of the materials in this repository are based on supporting materials for a graduate statistics classes taught by Keith Lohse while at the University of Utah and Auburn University. The supplemental text for the course was: Judd, C. M., McClelland, G. H., & Ryan, C. S. (2011). Data analysis: A model comparison approach. Routledge.

Video lectures are all available on YouTube (linked below). Note that Sections 1-11 focus on conceptual understanding of the different methods and study designs (corresponding slides are in the "lectures" folder). Section 12 is an applied "how to" section about how to implement these analyses in R using example datasets (all scripts are in the "scripts" folder), which assumes a deeper unstanding of the concepts. I strongly recommend you do not jump into the application section without a solid understanding of the fundamentals covered in the previous sections. Example lab assignments to test your understanding (with answer keys) are in the "lab_assignments" folder.

Section 1: Introduction to Statistics

• 1a. Introduction to Statistics (https://www.youtube.com/watch?v=6FtyjrciHAg)
• 1b. Measurement and Types of Data (https://www.youtube.com/watch?v=OsflKLrfmhk)
• 1c. Introduction to Statistical Inference (https://www.youtube.com/watch?v=iirL88UVhhE)

Section 2: Descriptive Statistics

• 2a. Organizing and Displaying Data (https://www.youtube.com/watch?v=76dqE2JKC5w)
• 2b. Measures of Central Tendency (https://www.youtube.com/watch?v=gL2iuMvhhRY)
• 2c. Measures of Variability (https://www.youtube.com/watch?v=H9gWvdNBZoY)
• 2d. Degrees of Freedom and the Sample Variance (https://www.youtube.com/watch?v=eSJAjlavPwU)

Section 3: Sampling and the Central Limit Theorem

• 3a. The Distribution of Sample Means (https://www.youtube.com/watch?v=xcWyS1PD3gg)
• 3b. The Central Limit Theorem (https://www.youtube.com/watch?v=B9DPv2hyhDA)
• 3z. Z-Scores and Probability Under the Normal Curve (https://www.youtube.com/watch?v=z4OQBPqrN7s)

Section 4: Fundamentals of Hypothesis Tests - aka One Sample T-Tests

• 4a. Null Hypothesis Signficance Tests (https://www.youtube.com/watch?v=z4OQBPqrN7s)
• 4b. T-Statistics and the T-Distribution (https://www.youtube.com/watch?v=BIKrONQia3A)
• 4C. P-Values and Common Misinterpretations (https://www.youtube.com/watch?v=kHz3AUkgILA)
• 4D. Introduction to Statistical Power (https://www.youtube.com/watch?v=93RjkuCQ6FM)

Section 5: Finding the Line of Best Fit - aka Pearson's Correlation and Simple Regression

• 5a. Bivariate Correlations (https://www.youtube.com/watch?v=x1niVnWhGhs)
• 5b. Simple Regression (https://www.youtube.com/watch?v=rLLBhW-cp2s)
• 5c. R^2 and the Sum of Squared Errors (https://www.youtube.com/watch?v=0xWDulRHd9M)
• 5d. Statistical Inference in Correlation and Regression (https://www.youtube.com/watch?v=U9kr1gD-0-E)
• 5e. Correlation and Causation (https://www.youtube.com/watch?v=MCROtI-L-AI)

Section 6: Regression with Categorical Predictor - aka Independent Samples T-Test

• 6a. Regression with Categorical Predictor (https://www.youtube.com/watch?v=4ApfcAGcSKk)
• 6b. Model Fit and R^2 (https://www.youtube.com/watch?v=iAE4UeoVE9A)
• 6c. Regression Assumptions (https://www.youtube.com/watch?v=6IXXAniv9kQ)

Section 7: Models with Multiple Categorical Predictors - aka One-Way ANOVA

• 7a. Introducing Models with Multiple Predictors (https://www.youtube.com/watch?v=Z2MRcI74AgU)
• 7b. "Controlling For" Other Variables (https://www.youtube.com/watch?v=qGPsc8mc2iE)
• 7c. Multiple Categorical Predictors (https://www.youtube.com/watch?v=OqW7LBjU4uw)
• 7d. The F-Statistic and F-Distribution (https://www.youtube.com/watch?v=OK4Xns4zabs)

Section 8: Multiple Categorical Factors with Multiple Levels - aka Multi-Way ANOVA

• 8a. Models with Multiple Categorical Predictors (https://www.youtube.com/watch?v=tAPOZhFm-tU)
• 8b. Building an ANOVA Table (https://www.youtube.com/watch?v=fPcTVWgZeXs)
• 8c. Main-Effects and Interactions (https://www.youtube.com/watch?v=GqL9lPFzePY)
• 8d. Standardized Effect Sizes in ANOVA (https://www.youtube.com/watch?v=wNBc93wfayw)
• 8e. Strategies for Post-Hoc Testing (https://www.youtube.com/watch?v=Qr1hxsMIGck)

Section 9: Mixing Continuous and Categorical Factors - aka AN(C)OVA

• 9a. Analysis of Covariance (https://www.youtube.com/watch?v=tZ0s49CIPK4)

Section 10: Dealing with Statistically Dependent Measures - aka Paired Sample T-Test and RM ANOVA

• 10a. The Dependent Samples T-Test (https://www.youtube.com/watch?v=9VZE0iREvGM)
• 10b. Repeated Measures (RM) ANOVA (https://www.youtube.com/watch?v=ckoew3ObBms)
• 10c. Partitioning Variance and Builing the RM ANOVA Table (https://www.youtube.com/watch?v=CD4mchw3X8o)

Section 11: Other Topics: Statiscal Power, Regression Diagnostics, Etc.

• 11a. Refresher on Statistical Power (https://www.youtube.com/watch?v=c2PM6MgFkbk)
• 11b. A Priori Power and Sensitivity for a Two Sample T-Test (https://www.youtube.com/watch?v=adUMgpV-F9U)
• 11c. Ill-Mannered Error Terms (https://www.youtube.com/watch?v=FwC5OJgXde0)
• 11d. Leverage in General Linear Models (https://www.youtube.com/watch?v=1QqwvHbEUVc)
• 11e. Outlying Residuals (https://www.youtube.com/watch?v=BKqP7Sm8Cxc)
• 11f. Cook's Distance and Measures of Influence (https://www.youtube.com/watch?v=bKYxBtRUSZs)
• 11g. Should We ever Remove Outliers? (https://www.youtube.com/watch?v=1qyrEkyXxaA)
• 11h. Violations of Normality and Homoscedasticity (https://www.youtube.com/watch?v=SICenfxKJy4)

Section 12: How-To Videos Using R

• 12a. How to do a one-sample t-test in R (https://www.youtube.com/watch?v=ZdgNOWY3cs4)
• 12b. How to do a two-sample t-test in R (https://www.youtube.com/watch?v=5oVKpyO84OI)
• 12c. How to do a one-way ANOVA in R (https://www.youtube.com/watch?v=KpRJzxvEdGs)
• 12d. How to do a multi-way ANOVA in R (https://www.youtube.com/watch?v=KpRJzxvEdGs)