"Working an integral or performing a linear regression is something a computer can do quite effectively. Understanding whether the result makes sense - or deciding whether the method is the right one to use in the first place - requires a guiding human hand. When we teach mathematics we are supposed to be explaining how to be that guide. A math course that fails to do so is essentially training the student to be a very slow, buggy version of Microsoft Excel." -- Jordan Ellenberg
"I have 25,237 variables in my database. I compare all these variables against each other to find ones that randomly match up. That's 636,906,169 correlation calculations! This is called data dredging. Instead of starting with a hypothesis and testing it, I instead tossed a bunch of data in a blender to see what correlations would shake out. It's a dangerous way to go about analysis, because any sufficiently large dataset will yield strong correlations completely at random." -- Tyler Vigen
| DATE: | OUTLINES: | SLIDES: | DEMOS: | NOTES: | DESCRIPTION: | |
| 5.1 | 5.1 | Bivariate rv's: Joint/Marginal/Conditional pmf's/pdf's, Probability, Independence | ||||
| 5.2 | 5.2 | Bivariate rv's: Expectation, Variance, Covariance, Correlation | ||||
| 5.3 | 5.3 | Random Samples: iid, Statistics, Sampling Distributions | ||||
| 5.4 | 5.4 | Asymptotics: Central Limit Theorem, Normal Approximation to Binomial & Poisson | ||||
| 5.5 | 5.5 | Sums/Diff's of rv's: Expectation, Variance | ||||
6.1 |
6.1 |
Point
Estimation: Point Estimators, Unbiased Estimators, Standard Error Point Estimation: Uniformly Minimum-Variance Unbiased Estimators (UMVUE's) |
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| 6.2 | 6.2 | Point
Estimation: Method of Moments Estimators (MOME's) Point Estimation: Maximum Likelihood Estimators (MLE's) |
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| 9.1 | 9.1 | [EX 9.1.1 SOLUTIONS] | 2-Sample Inference: Standard Normal Distribution
2-Sample Inference: Large-Sample z-Tests & z-CI's for Any Two Pop. Means (H0: μ1 = μ2) |
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| 9.2 | 9.2 | [EX 9.2.{1,2} SOLUTIONS] | 2-Sample Inference: Gosset's t
Distribution 2-Sample Inference: Independent t-Tests & t-CI's for Two Normal Pop. Means (Unknown σ1≠σ2) 2-Sample Inference: Pooled t-Tests & t-CI's for Two Normal Population Means (Unknown σ1=σ2) |
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| 2-Sample Inference: Experimental Design 2-Sample Inference: Paired t-Tests & t-CI's for Normal Population Mean Differences (H0: μD = 0) |
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| [EX 9.5.{1,2} SOLUTIONS] | 2-Sample Inference: Snedecor's F
Distribution 2-Sample Inference: F-Tests & F-CI's for Two Normal Population Variances |
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| Cat-Num Inference: Many Equi-Variance Normal Pop.
Means (H0: μ1 =
μ2 = ⋯ =
μI) Cat-Num Inference: 1-Factor Fixed Effects Linear Models: Xij = μ + αi + Eij Point Estimation: 1-Factor Least-Squares Estimators (LSE's) Point Estimation: 1-Factor Best Linear Unbiased Estimators (BLUE's) |
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10.1 |
10.1 |
[EX 10.1.{1,2,3} SOLUTIONS] | Cat-Num Inference: 1-Factor ANOVA Motivation,
1-Factor ANOVA Assumptions Cat-Num Inference: 1-Factor Balanced Completely Randomized ANOVA (1F bcrANOVA) Cat-Num Inference: Effect Size Measures of Practical Significance: η2, ε2, ω2 |
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| [EX 10.2.1 SOLUTIONS] | Cat-Num Inference: Gosset's (Studentized)
Q Distribution Cat-Num Inference: Tukey Pairwise Post-Hoc Comparisons when 1F bcrANOVA rejects H0 Cat-Num Inference: t-CI's for Comparisons of Collections of Treatment Means |
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| [EX 10.3.{1,2} SOLUTIONS] | Cat-Num Inference: 1-Factor Unbalanced Completely
Randomized ANOVA (1F ucrANOVA) Cat-Num Inference: Tukey-Kramer Pairwise Post-Hoc Comparisons when 1F ucrANOVA rejects H0 Cat-Num Inferenece: 1-Factor ANOVA Model Assumption Checking |
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| [EX 11.2.{1,2} SOLUTIONS] | Cat-Num Inference: 2-Factor Balanced Experiments Cat-Num Inference: 2-Factor Main Effects, Interactions & Interaction Plots Cat-Num Inference: 2-Factor Fixed Effects Linear Models Point Estimation: 2-Factor LSE's & BLUE's |
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11.2 |
11.2 |
Cat-Num Inference: 2-Factor Balanced Completely
Randomized ANOVA (2F bcrANOVA) Cat-Num Inference: Full & Partial Effect Size Measures of Practical Significance: η2, ω2 Cat-Num Inference: Tukey Pairwise Post-Hoc Comparisons Cat-Num Inference: 2F bcrANOVA Model Assumption Checking |
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| [EX 11.1.{1,2} SOLUTIONS] | Cat-Num Inference: 2-Factor Randomized Complete
Block ANOVA (2F rcbANOVA) Cat-Num Inference: Full & Partial Effect Size Measures of Practical Significance: η2, ω2 Cat-Num Inference: Tukey Pairwise Post-Hoc Comparisons Cat-Num Inference: 2F rcbANOVA Model Assumption Checking |
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| [EX 12.2.{1} SOLUTIONS] | Num-Num Inference: Simple Linear Regression Num-Num Inference: 1-Regressor Fixed Effects Linear Models: Yi = β0 + β1 xi + Ei Num-Num Inference: Ordinary Least-Squares (OLS) Estimators for β0 & β1 Num-Num Inference: Point Estimation of σ2 |
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| [EX 12.3.{1} SOLUTIONS] | Num-Num Inference: Simple Linear Regression Num-Num Inference: Estimated Std. Deviation of OLS Estimator for β1 Num-Num Inference: t-CI's for β1 Num-Num Inference: Model Utility t-Tests Num-Num Inference: Model Utility F-Tests |
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Motivation: Gamma Function Motivation: Chi-square Distributions |
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