Statistics Notebook
Summary
Introduction
1
Statistical Vocabulary
1.1
Descriptive Statistics
1.1.1
Measures of Central Tendency
1.1.2
Measures of Dispersion
1.1.3
Measures of shape
1.1.4
Moments
1.2
Inferential Statistics
1.2.1
Deduction vs. Induction
1.2.2
Parametric vs. Nonparametric
1.2.3
Linear vs. Nonlinear
1.3
Level of Measurement
1.4
Eta Squared
1.5
P-value
1.6
Type I, Type II Errors, Statistical Power
1.7
Effect Size
1.8
Unbiased Estimator
1.9
T-value
1.10
F-value
1.11
Degree of Freedom
1.12
R-squared
1.13
Z-score
1.14
Odds Ratio
1.15
Covariate
2
Probability
2.1
Binomial Distribution
2.1.1
Outcome Tables
2.1.2
Contingency Tables
2.2
Probabilities in the Long Run
2.2.1
Sampling
3
Inference
3.1
Confidence Intervals
3.1.1
Confidence Interval of T-test
4
Bayesian and Frequentist Statistics
4.1
Bayes’ Theorem
4.2
Markov chain Monte Carlo (MCMC)
4.3
The difference between HDI and confidence intervals
4.4
The Null Hypothesis Significance Test (NHST)
4.4.1
Flaws of NHST
5
Comparing Groups
5.1
ANOVA
5.2
R illustration of Frequentist ANOVA
5.3
The Bayesian Approach to ANOVA and R Illustration
5.4
Post-hoc Tests of ANOVA
5.5
One-way & Two-way ANOVA
6
Associations between Variables
6.1
Covariance
6.1.1
R illustration
6.1.2
Inferential Reasoning About Correlation
6.2
Null Hypothisis Testing On the Correlation
6.2.1
Bayesian Reasoning About Correlation
6.3
Categorical Association
6.3.1
Bayesian Reasoning about Chi-Square Test
6.4
Other Correlation Approaches
7
Linear Multiple Regression
7.1
Frequentist Approach of Multiple Regression
7.2
Making Sense of Adjusted R-squared
7.3
Multicollinearity
7.4
The Bayesian Approach to Linear Regression
7.5
Comparing the Bayesian and Frequentist Approaches
8
Interactions in ANOVA and Regression
8.1
Interation in ANOVA
8.2
Bayesian Approach of Interaction in ANOVA
8.3
Interation in Regression
8.4
Bayesian Analysis of Regression Interactions
9
Logistic Regression
9.1
Bayesian Estimation of Logistic Regression
9.2
Conclusion
10
Analyzing Change over Time
10.1
Repeated Measures
10.2
Time Series
10.3
Finding Change Points in Time Series
10.4
Probabilities in Change-point Analysis
10.5
Conclusion
11
Dealing with Too Many Variables
11.1
Principal Component Analysis
11.2
Mean Composites vs. Factor Scores
11.3
Internal Consistency Reliability
11.4
Rotation
12
All Together
References
R Packages Used
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Jinfen Li
Statistics
References