Foundations of Statistics

Author

✍ Faik Erkam Minsin  

Reference

• Book: Using R for Introductory Statistics by John Verzani

Code

• Scripted on: Notepad++
• Executed on: R 4.1.1 and R Studio
• Dependent on : Standard R libraries, UsingR and MASS libraries

Contents

Chapter 1: Data

• Instructions on installing R and R Studio
• Some R essentials
  • Using R as a calculator
  • Assignment
  • Using c() to enter data
  • Using functions on a data vector
  • Creating structured data
• Accessing data by using indices
  • Assigning values to data vector
  • Logical values
  • Missing values
  • Managing the work environment
• Reading in other sources of data
  • Using R's built-in libraries and data sets
  • Using the data sets that accompany this book
  • Other methods of data entry

Chapter 2: Univariate Data

• Categorical Data
  • Tables
  • Barplots
  • Pie Charts
  • Factors
• Numeric Data
  • Stem-and-leaf plots
  • Strip Charts
  • The center:mean,median,and mode
  • Variation:the variance,standard deviation,and IQR
• Shape of a distribution
  • Histogram
  • Modes,symmetry, and skew
  • Box plots

Chapter 3: Bivariate Data

• Pairs of categorical variables
  • Making two-way tables from summarized data
  • Making two-way tables from unsummarized data
  • Marginal distributions of two-way tables
  • Conditional distributions of two-way tables
  • Graphical summaries of two-way contingency tables
• Comparing independent samples
  • Side-by-side boxplots
  • Density plots
  • Strip charts
  • Quantile-quantile plots
• Relationships in numeric data
  • Using scatterplots to investigate relationships
  • The correlation between two variables
• Simple Linear Regression
  • Using the regression model for prediction
  • Finding the regression coefficients using lm()
  • Transformations of the data
  • Interacting with a scatterplot
  • Outliers in the regression model
  • Resistant regression lines: lqs() and rlm()
  • Trend lines

Chapter 4: Multivariate Data

• Viewing multivariate data
  • Summarizing categorical data
  • Comparing independent samples
  • Comparing relationships
• R basics: data frames and lists
  • Creating a data frame or list
  • Accessing values in a data frame
  • Setting values in a data frame or list
  • Applying functions to a data frame or list
• Using model formula with multivariate data
  • Boxplots from a model formula
  • The plot() function with model formula
  • Creating contingency tables with xtabs()
  • Manipulating data frames: split() and stack()
• Lattice graphics
• Types of data in R
  • Factors
  • Coercion of objects

Chapter 5: Describing Populations

• Populations
  • Discrete random variables
  • Continuous random variables
  • Sampling from a population
  • Sampling distributions
• Families of distributions
  • Binomial, normal, and some other named distributions
  • Popular distributions to describe populations
  • Sampling distributions
• The central limit theorem
  • Normal parent population
  • Nonnormal parent population

Chapter 6: Simulation

• The normal approximation for the binomial
• for loops
• Simulations related to the central limit theorem
• Defining a function
  • Editing a function
  • Function arguments
  • The function body
• Investigating distributions
  • Script files and source()
  • The geometric distribution
• Bootstrap samples
• Alternates to for loop

Chapter 7: Confidence Intervals

• Confidence interval ideas
  • Finding confidence intervals using simulation
• Confidence intervals for a population proportion, p
  • Using prop.test() to find confidence intervals
• Confidence intervals for the population mean, mu
  • One-sided confidence intervals
• Other confidence intervals
• Confidence intervals for differences
  • Difference of proportions
  • Difference of means
  • Matched samples
• Confidence intervals for the median
  • Confidence intervals based on the binomial
  • Confidence intervals based on signed-rank statistic
  • Confidence intervals based on the rank-sum statistic

Chapter 8: Significance Tests

• Significance test for a population proportion
  • Using prop.test() to compute p-values
• Significance test for the mean (t-tests)
• Significance tests and confidence intervals
• Significance tests for the median
  • The sign test
  • The signed-rank test
• Two-sample tests of proportion
• Two-sample tests of center
  • Two sample tests of center with normal populations
  • Matched samples
  • The Wilcoxon rank-sum test for equality of center

Chapter 9: Goodness of Fit

• The chi-squared goodness-of-fit test
  • The multinomial distribution
  • Pearson's chi-squared statistic
• The chi-squared test of independence
  • The chi-squared test of homogeneity
• Goodness-of-fit tests for continuous distributions
  • Kolmogorov-Smirnov test
  • The Shapiro-Wilk test for normality
  • Finding parameter values using fitdistr()

Chapter 10: Linear Regression

• The simple linear regression model
  • Model formulas for linear models
  • Examples of the linear model
  • Estimating the parameters in simple linear regression
  • Using lm() to find the estimates
• Statistical inference for simple linear regression
  • Testing the model assumptions
  • Statistical inferences
  • Using lm() to find values for a regression model
• Multiple linear regression
  • Fitting the multiple regression model using lm()
  • Interpreting the regression parameters
  • Statistical inferences
  • Model selection

Chapter 11: Analysis of Variance

• One-way ANOVA
  • Using R's model formulas to specify ANOVA models
  • Using oneway.test() to perform ANOVA
  • Using aov() for ANOVA
  • The nonparametric Kruskal-Wallis test
• Using lm() for ANOVA
  • Treatment coding for analysis of variance
  • Comparing multiple differences
• ANCOVA
• Two-way ANOVA
  • Treatment coding for additive two-way ANOVA
  • Testing for row or column effects
  • Testing for interactions

Chapter 12: Two Extensions of the Linear Model

• Logistic regression
  • Generalized linear models
  • Fitting the model using glm()
• Nonlinear models
  • Fitting nonlinear models with nls()