Statistics in R - The R Language for Statistical Analysis

Explore R statistical packages, from the base stats to nor test and demat comp, install toss and tk, and use them for normality tests, multiplicity corrections, and parametric inference.

Explore inference on proportions for large samples with the R prop.test, interpreting one- or two-sided tests, p-values, and 95% confidence intervals; note small-sample options with t-test or a correction factor.

Assess normality with Shapiro-Wilk and Anderson-Darling tests, using histograms and a quantile plot; interpret p-values against 5% to decide between normal and nonparametric tests.

Analyze the diamonds dataset depth with qq plots and histograms, then apply normality tests from the Northwest package, including Shapiro-Wilk (sampled to 5000), Cramer-von Mises, and Kolmogorov-Smirnov, to assess non-normality.

Discover the exercise database at Armani's tutorials dot com, with ten question blocks on functions, data frames, and graphs, and learn how to access and use it for R practice.

Learn to perform a one-sample t test in R to assess a population mean, specify X argument and mu, choose the alternative, and interpret a 95% confidence level and p-values.

An in-depth look at the two-sample independent t test (Welch test) in R, comparing means across auto vs manual transmission using box plots, t.test, and equal-variance considerations.

Apply a two-sample t-test on the ships data from the MASS package to compare incidence across two periods, using a box plot and noting a non-significant result with p-value 0.4.

Apply the Mann Whitney U test, a nonparametric alternative to the t-test, to compare medians between two independent groups (manual vs automatic) with a 95 percent confidence interval.

Perform an analysis of variance (ANOVA) on iris data to compare the means across three species, using box plots and F-test results, then pursue post-hoc comparisons.

Learn Tukey hsd post hoc testing after anova to adjust p-values for pairwise group differences, using iris species with equal group sizes; view confidence intervals and mean differences.

Explore chi-squared tests for independence using contingency tables and p-values, compare with the Kruskal-Wallis non-parametric test for non-normally distributed data in R.

Practice anova in R with a data frame of groups A, B, and C, run post hoc tests for multiple comparisons, and choose nonparametric alternatives when data are non-normal.

Create a three-level grouping (A, B, C) dataset, visualize with box, violin, and q plots, then run anova and tukey post hoc tests to compare groups.

MASS bacteria dataset is used to test independence between treatment group and presence or absence of bacteria with a chi squared test on a contingency table, yielding p < 0.05.

Explore how to compute and compare Pearson, Spearman, and Kendall correlations for numeric data in R, interpret correlation tests, confidence intervals, and covariance using iris examples.

Summarizes descriptive statistics (mean, median, min, max) and correlations, with scatterplot matrices and Pearson approaches; explains data types and normality for selecting parametric or nonparametric tests.

Explore how outliers influence results and compare three-sigma and box-plot rules using Q1, Q3, and quartile distance, plus model-based and proximity-based multivariate methods for detecting and visualizing anomalies.

Explore univariate outlier detection in R using mean minus t times the standard deviation, the esd method, and box plots, plus outliers package tests like Dixon and chi square.

Learn multivariate outlier detection in R using the outlier package, exploring sign1, sign2, and PC out methods based on PCA to identify outliers in high-dimensional datasets.

Study theory of statistical modeling and predict the outcome variable from predictors using linear regression, intercepts, slopes, and coefficients. Learn about residuals, scatterplots, and simple versus multiple linear regression.

Compare linear and generalized linear models, noting non-normal error terms and non-constant variance, and interpret glm coefficients as multiplicative effects via e^b; discuss polynomial regression and smoothing for nonlinear data.

Explore modeling theory with polynomial regressions and splines: linear, quadratic, and penalized that auto-select smoothness; learn how generalized additive models assign smoothing functions to predictors in local data settings.

Explores linear regression on the speed–distance data, showing how speed predicts stopping distance with a strong positive correlation, model coefficients, residual checks, and extrapolation using predict.

Explore multiple linear regression in R by modeling mpg with weight and rear axle ratio, interpret coefficients, assess model fit (R^2 ~ 0.76), and extend with squared terms.

Load the ggplot2 diamonds dataset, fit a linear regression of price on depth, x, y, and cut, and interpret the model summary, noting about 78% explained and the correlation matrix.

Apply logistic regression on a binary outcome to predict transmission type using a generalized linear model with the binomial family, refining predictors by significance and predicting probabilities.

Examine logistic regression with the plant growth data, using weight to predict group membership. Fit the model, test weight significance, and predict if weight 7.5 belongs to group 2.

Learn to fit simple, multiple, and logistic regressions in R, interpret coefficients, p-values, and r-squared, and use plots to check assumptions and make predictions.

Demonstrate k nearest neighbors classification in R using the Motor Trend Car road tests data to predict cylinder count from weight and mpg with knn.

Explore bootstrapping and averaging in random forests to boost accuracy, compare them with bagging, and assess performance using a test set.

Explore the R Commander graphical user interface for R, install the Rcmdr package, and learn when to use the interactive interface versus command line coding for data import and plotting.

Explore getting data into Rcmdr: import from files or create datasets with the editor, subset and clean data, and visualize with histograms and scatterplots using preinstalled datasets.

Build a linear model in R Commander to predict DAX from SMI, CAC, and FTSE, and evaluate with AIC, R-squared, and diagnostic plots.