Intro-to-Statistics-in-R-2017

This repository contains Rmd and html files for hands-on practicums given at CRG in 2016-2017.

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MODULE I. Descriptive Statistics & Intro to Probability.

1. Descriptive statistics

• Explore data
  • Exercise with table(), cut(), and quantile()
  • Looking at subset of data
  • Missing (NA) values
  • Exercise on missing values
• Summary statistics
  • Outliers
• Plots
  • Box-plot
  • Histogram
  • Exercise with hist()
  • Scatterplot
  • Combining plots
  • Empirical cumulative distribution functions (eCDFs)
  • Exercise with eCDF

2. Distributions

• Normal distribution
  • Probability Density function (PDF)
  • Z-transformation of a random sample from a normal distribution
  • Cumulative Distribution Function (CDF)
  • The 68-95-99.7 rule
  • Quantile function, or How to obtain the critical values of -z and z for a specified area under the standard normal curve.

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MODULE II. Statistical Inference. Parametric tests.

• Parametric tests
  • One-sample test on the sample mean for the random sample drawn from the normally distributed population with known variance: z-test
  • One-sample test on the sample mean for the sample with unknown variance: t-test
  • Two-sample paired and unpaired tests with unknown variance: t-test
  • Test for proportions: prop.test()
  • Fisher's exact test on proportions
• Confidence intervals and t-distribution

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Module III. Statistical Inference. False Discovery Rate. Power analysis. Part 1.

• FWER, FDR
• Power analysis
• Sample size estimation
  • Sample size case study 1: Central Tendency (means) difference
  • Sample size case study 2: Central Tendency (means) difference, less noisy
  • Sample size case study 3: Proportions

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Module III. Statistical Inference. Power analysis. Part 2. (re-iteration of Part 1 with more exercises)

• Sample size estimation
• Power of tests
  • Types of errors
  • Power of the one-sample t test
  • Power of the two-sample t test
  • Calculating power using the package “pwr”

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MODULE IV. Statistical inference. Non-parametric tests. Data transformation.

• QQ-plot
• Tests on normality
• Data transformation
• Non-parametric tests

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MODULE V. Statistical modeling. Regression. ANOVA.

• Problems on linear regression
• ANOVA
  • Examine the data
  • One-way ANOVA
  • Post-hoc tests
  • Test assumptions
  • Two-way ANOVA
• Data transformation
  • Normality
  • Variance stabilization
  • Box-Cox
• Regression
  • Plots of residuals vs. fitted values
  • Regression: interpretation
  • Comparison of methods
  • Coordinates transformation

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