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A Brief Tour of Statistics
This work by Thomas Lotze is licensed under a Creative Commons
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• What are Distributions?• Models
– Binomial– Poisson– Uniform– Gaussian (normal)
• Using Distributions to Answer Questions
• Distribution Parameters• Estimating Parameters
• Confidence Intervals and P-values• Why Gaussian?
• Regression
• Logistic Regression• Why Not Gaussian?
• Bootstrapping• Multiple Testing
• Useful Tools
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• What are Distributions?• Models
– Binomial– Poisson– Uniform– Gaussian (normal)
• Using Distributions to Answer Questions
• Distribution Parameters• Estimating Parameters
• Confidence Intervals and P-values• Why Gaussian?
• Regression
• Logistic Regression• Why Not Gaussian?
• Bootstrapping• Multiple Testing
• Useful Tools
9/61Creative Commons licensed, from Jason Tromm on flickr
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14/61Creative Commons licensed, from Antoine Taveneaux on Wikimedia Commons
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• What are Distributions?• Models
– Binomial– Poisson– Uniform– Gaussian (normal)
• Using Distributions to Answer Questions• Distribution Parameters• Estimating Parameters
• Confidence Intervals and P-values• Why Gaussian?
• Regression
• Logistic Regression• Why Not Gaussian?
• Bootstrapping• Multiple Testing
• Useful Tools
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• What are Distributions?• Models
– Binomial– Poisson– Uniform– Gaussian (normal)
• Using Distributions to Answer Questions
• Distribution Parameters• Estimating Parameters
• Confidence Intervals and P-values• Why Gaussian?
• Regression
• Logistic Regression• Why Not Gaussian?
• Bootstrapping• Multiple Testing
• Useful Tools
21/61Creative Commons licensed, from gr0don on flickr
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• What are Distributions?• Models
– Binomial– Poisson– Uniform– Gaussian (normal)
• Using Distributions to Answer Questions
• Distribution Parameters• Estimating Parameters• Confidence Intervals and P-values• Why Gaussian?
• Regression
• Logistic Regression• Why Not Gaussian?
• Bootstrapping• Multiple Testing
• Useful Tools
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• What are Distributions?• Models
– Binomial– Poisson– Uniform– Gaussian (normal)
• Using Distributions to Answer Questions
• Distribution Parameters• Estimating Parameters
• Confidence Intervals and P-values• Why Gaussian?
• Regression
• Logistic Regression• Why Not Gaussian?
• Bootstrapping• Multiple Testing
• Useful Tools
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31/610.10.44
0.050.41
0.010.34
0.0010.30
Probability of 21 or
more successes
Actual
Field
Goal Rate
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• What are Distributions?• Models
– Binomial– Poisson– Uniform– Gaussian (normal)
• Using Distributions to Answer Questions
• Distribution Parameters• Estimating Parameters
• Confidence Intervals and P-values• Why Gaussian?• Regression
• Logistic Regression• Why Not Gaussian?
• Bootstrapping• Multiple Testing
• Useful Tools
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• What are Distributions?• Models
– Binomial– Poisson– Uniform– Gaussian (normal)
• Using Distributions to Answer Questions
• Distribution Parameters• Estimating Parameters
• Confidence Intervals and P-values• Why Gaussian?
• Regression• Logistic Regression• Why Not Gaussian?
• Bootstrapping• Multiple Testing
• Useful Tools
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• What are Distributions?• Models
– Binomial– Poisson– Uniform– Gaussian (normal)
• Using Distributions to Answer Questions
• Distribution Parameters• Estimating Parameters
• Confidence Intervals and P-values• Why Gaussian?
• Regression
• Logistic Regression• Why Not Gaussian?
• Bootstrapping• Multiple Testing
• Useful Tools
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• What are Distributions?• Models
– Binomial– Poisson– Uniform– Gaussian (normal)
• Using Distributions to Answer Questions
• Distribution Parameters• Estimating Parameters
• Confidence Intervals and P-values• Why Gaussian?
• Regression
• Logistic Regression• Why Not Gaussian?• Bootstrapping• Multiple Testing
• Useful Tools
47/61Creative Commons licensed, from Alan Vernon on flickr
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• What are Distributions?• Models
– Binomial– Poisson– Uniform– Gaussian (normal)
• Using Distributions to Answer Questions
• Distribution Parameters• Estimating Parameters
• Confidence Intervals and P-values• Why Gaussian?
• Regression
• Logistic Regression• Why Not Gaussian?
• Bootstrapping• Multiple Testing
• Useful Tools
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• What are Distributions?• Models
– Binomial– Poisson– Uniform– Gaussian (normal)
• Using Distributions to Answer Questions
• Distribution Parameters• Estimating Parameters
• Confidence Intervals and P-values• Why Gaussian?
• Regression
• Logistic Regression• Why Not Gaussian?
• Bootstrapping• Multiple Testing• Useful Tools
55/61Creative Commons licensed, from CharlotteKinzie on flickr
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0.991000.05
0.40100.05
0.0510.05
0.631000.01
0.10100.01
0.0110.01
Probability of
False Detection (in at least 1 test)Number of Tests
Probability of
False Detection (per test)
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• What are Distributions?• Models
– Binomial– Poisson– Uniform– Gaussian (normal)
• Using Distributions to Answer Questions
• Distribution Parameters• Estimating Parameters
• Confidence Intervals and P-values• Why Gaussian?
• Regression
• Logistic Regression• Why Not Gaussian?
• Bootstrapping• Multiple Testing
• Useful Tools
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• R: http://cran.r-project.org/
• Casella & Berger, Statistical Inference
• Wikipedia: http://en.wikipedia.org/wiki/List_of_probability_distributions
• Salsburg, The Lady Tasting Tea
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1. Everything is a Distribution
2. Many Kinds of “Random” (many Distributions)
3. Estimated Parameters are RandomThey have Distributions!
4. Statistical Decisions come from Distribution Estimates
5. Be Skeptical of NormalityMean and Variance are not sufficient!
6. Be Skeptical of Multiple Testing
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• Practical Take-home– Normality test– T-test– Wilcoxon rank-sum test
• Other Distributions– Student’s T– F– Lognormal– Geometric– Levy– Weibull– Benford
• Goodness of fit– Chi-squared test– Q-Q plots
• Distribution Connections• Multivariate Distributions
• Bias/Variance Tradeoff
•Nonparametric Distributions•Model Comparison:
Parameters and Fit (AIC, BIC)
•Bayesian Statistics•Bayes’ Law
•Cognitive Biases•Time series
•Counterintuitive Probability•Monty Haul
•Two Aces
•Poisson Waiting Times•Markov Chain Monte Carlo
•Extreme Value Statistics
