Statistics for Data Analysis Using R

Explore descriptive statistics theory, focusing on population and sample concepts. Learn measures of central tendency and variation, including mean, mode, median, range, standard deviation, and interquartile range, with downloadable slides.

Clarify population and sample, and define parameters and statistics, including mean, standard deviation, proportion, with sample size n and population size N.

Explore descriptive statistics and its difference from inferential statistics, and summarize data using central tendency and variability. Learn mean, median, mode, percentiles, quartiles, range, and standard deviation with practical examples.

Explore central tendency measures—mean, mode, and median—along with their sensitivities to outliers, and learn to compute percentiles and quartiles using simple data examples for population and sample contexts.

Analyze measures of variation—range, interquartile range, and standard deviation—covering outlier effects, box-and-whisker plots, and the sample versus population distinction (S vs Sigma).

Apply descriptive statistics in R by computing mean, mode, median, range, interquartile range, and standard deviation using code; learn how to access help in R and review notes and assignment.

Explore descriptive statistics in R by calculating mean, median, mode, range, interquartile range, and standard deviation. Learn to access help in R with help, ?, and ?? for function details.

Calculate the mean of a height vector in R. Handle missing values with na.rm and remove na as needed, then use trim to discard extremes.

Learn to measure central tendency in R by computing the median from a height vector via sorting, and derive the mode indirectly from a frequency table.

Explore variation measurement in R by computing range, quantiles and quartiles, and interquartile range. Learn to distinguish and calculate sample versus population standard deviation using length and n to adjust.

Explore vectors, factors, lists, matrices, and data frames in R, and see how Excel columns relate to vectors and data frames to worksheets for importing external data.

Introduce data organization in R by exploring vectors and data types, and demonstrate type checking and conversion with is.numeric, is.character, is.logical, as.character, and as.numeric.

Explore creating and manipulating vectors in R, including numeric and character vectors, using c and seq, indexing by position or name, and assigning names to vectors.

Explore how vectors are created with c() and transformed into factors to reveal categories and levels. Understand nominal versus ordinal data and define ordered factors with explicit levels for summaries.

Learn how a list bundles vectors, factors, matrices, and data frames into a single structure, name its elements, and access them using indexing or the dollar sign.

Understand how to create and name a two-dimensional matrix in R, combining hours and marks into columns, and read data from csv with read.csv, then access items with [row, column].

Explore how to create and manipulate data frames in R, mixing numeric, character, and logical data, and access, summarize, and analyze them with mean, summary, and indexing.

Explore data visualization in r by learning basic commands to plot scatter plots, histograms, and box-and-whisker plots. Use these graphs to convey data clearly to management.

Learn to plot data in R with the plot function, producing scatter plots, histograms, and box and whisker plots. Compare descriptive statistics for data summaries, and try the nycflights13 dataset.

Plot an R scatter plot from nycflights13 data to show how arrival delay relates to departure delay, with arrival delay on the x-axis and departure delay on the y-axis.

Export and zoom the scatter plot to study the relationship between arrival delays and departure delays, and add a main title with arrival delay and departure delay labels.

Draw lines on a scatter plot with abline by setting y intercept and slope, exploring 45-degree and horizontal lines, then re-plot to refine visuals.

Change the plot characters (pch) from circles to plus signs by setting pch = 3 on the arrival versus departure delay scatter plot, and explore other shapes to differentiate categories.

Explore how to customize plots in R by changing pch symbols, filtering data by carrier, and layering points, colors, and text to compare UA and AA on a single plot.

Learn to create side-by-side plots in R with par and mfrow, displaying two graphs for UA and AA with identical x and y limits for clear comparison.

Explore adding text to plots in R with text and margin text using mtext, placing labels by x, y and adj, and drawing lines with h and v.

Learn to customize a scatter plot in R by adjusting point size with cex, color and color.main for elements, and fonts with font.main and font.labels, plus adding text and mtext.

Explore how to create multiple scatter plots in one diagram with the pairs function, examining relationships between arrival delay, departure delay, distance, and air time in the nycflights13 flights data.

Plot the temperature against time using a single variable time series in R, demonstrated with the built-in weather dataset and its hourly measurements.

Master histogram creation for the nycflights13 distance data by drawing histograms, adjusting breaks, and filtering by carrier (UA or AA) to compare flight distances, with x-axis distance and y-axis frequency.

Learn to create box and whisker plots in R using the nycflights13 dataset, plotting distance by carrier and making side-by-side comparisons with partitioning.

Revisit descriptive statistics, reviewing center tendency and variation, and demonstrate using R packages like psych to compute and present data summaries.

Learn to use the psych package in R to compute descriptive statistics, describe data frames, and describeBy for group-level summaries with the nycflights13 dataset.

Define basic probability and explore unions, intersections, and conditional probability, along with addition and multiplication laws, factorials, permutations, and combinations. Lay the groundwork for probability distribution.

Define probability as the ratio of favorable outcomes to total outcomes, illustrated using a dice example. Explain sample space, experiment, trial, event, and the probability range between 0 and 1.

Explore probability through union and intersection using Venn diagrams, illustrating A and B on a dice roll to show A∪B and A∩B, and explain mutually exclusive, independent, and complementary events.

Explore addition and multiplication rules in probability, using Venn and tree diagrams to compute P(A∪B) and P(A∩B), with independent and dependent cases like dice and marbles.

Explore factorials, permutations, and combinations, including factorial 0 = 1. Distinguish when order matters and apply nPr and nCr formulas, e.g., 5P2 = 20 and 5C2 = 10, in probability.

Introduces central limit theorem and three key distributions: normal, binomial, and Poisson, using R and the visualize package to plot and illustrate their properties for inferential statistics.

Explain the central limit theorem: the sampling distribution of the mean becomes approximately normal for large samples, regardless of population shape, with standard error sigma over sqrt(n), demonstrated in R.

demonstrates the central limit theorem by generating 10,000 uniform numbers with runif, drawing sample means of 4, 9, and 100 items, and illustrating their normal distribution and shrinking standard error.

Explore the normal probability distribution, a symmetric bell-shaped curve defined by mean and standard deviation. Find areas under the curve using sigma levels and z-scores for the standard normal distribution.

Explore how to use R’s four functions for the standard normal distribution—rnorm, pnorm, qnorm, and dnorm—to generate random numbers, compute probabilities, and plot the curve.

Plot the normal distribution using dnorm with a -4 to 4 z-value vector. Explain creating a smooth line plot and assessing areas beyond ±3 sigma with pnorm.

Learn to visualize distributions in r with the visualize package, using visualize.norm to explore the standard normal and custom mu and sigma, including left, right, and tail areas.

Explore the binomial probability distribution for discrete data, with independent n trials, two outcomes, and constant p, illustrated by coin flips; derive mean, variance, and the binomial formula.

Explore binomial distribution fundamentals with fixed trials and independent trials, and master rbinom, pbinom, qbinom, and dbinom for probabilities, quantiles, and visualize using the visualize package.

Explore how dbinom computes the probability of each number of heads in ten coin flips and visualize these binomial probabilities with a barplot using the visualize package.

Load the visualize package and plot a binomial distribution with n=10 and p=0.5, showing five or less and five or more, and relate mean and variance to np and np(1-p).

Explore the Poisson distribution for discrete data, compare it with binomial, and apply the mean mu and the Poisson formula to model rare events.

Explore Poisson distribution in R, using rpois, ppois, qpois, and dpois to compute probabilities, with lambda 3.6 and seven people (about 4.24%) in a booking-counter scenario.

Plot the Poisson distribution in R by computing 0-10 probabilities with dpois (lambda 3.6) and visualize the results with a bar chart.

Explore Poisson distribution plotting in R with the visualize package, using lambda 3.6 to compute probabilities for seven or fewer, five or more, and tails or bounded options.

Delve into hypothesis testing in inferential statistics by examining samples to judge populations, and compare means and variances using tests like z, t, chi-square, F, and ANOVA with R demonstrations.

Explore hypothesis tests for mean and variance, including one-sample z and t tests, two-sample and paired t tests, and ANOVA.

Compare type 1 and type 2 errors in hypothesis testing using a perfume example, and explain alpha, beta, confidence level, and how sample size affects power.

Learn how p-values indicate the probability the null hypothesis is true; low p-values lead to rejection, high p-values fail to reject at a chosen alpha and confidence level.

Master the one-sample z test to assess mean shifts, formulating null and alternate hypotheses, choosing alpha, computing the z statistic, and interpreting one- and two-tail results.

Explore performing a one-sample z test in R on perfume volumes (n=100, x̄=152, σ=2) to test if the mean exceeds 150 at 95% confidence, via z statistics and p-value approaches.

Install and load the BSDA package, run z.test on perfume_volumes machine 1 with mu 150, sigma.x 2, and alternative greater, and reject the null with p-value 2.2e-16.

Apply the one sample t test to assess if the mean volume differs from 150 cc, using the t statistic with sample s and two-tailed 95% confidence; fail to reject.

Plot t distributions for dof 19, 9, and 4 with dt in R to illustrate the one sample t test and assess whether a perfume’s mean volume changes.

Shows performing a one-sample t test in R with bottle volumes, using the Visualize package to plot the t distribution and reject the null that the mean is 150 cc.

Perform a one-sample chi-square test for variance, comparing sample variance to the population variance, and decide via a 95% one-tailed test of null vs alternative.

Learn to perform a one-sample variance test in R with EnvStats, comparing a sample variance of 5 to historical 4. Interpret the chi-square result to assess variance increase.

Learn to conduct a one-sample chi-square test for variance in R, using built-in functions and the Envstats package, compute the statistic and critical value, and interpret a fail-to-reject outcome.

apply the two-sample z test to compare two means, formulating mu1 = mu2 versus not equal and computing z from X1bar and X2bar using sigma1^2/n1 and sigma2^2/n2.

Learn how to perform a two-sample z test in R using the BSDA package, comparing mean volumes from two machines, interpreting a p-value, and visualizing results.

Visualize two sample z test results with the visualize package by comparing mean volumes of two machines, using box plots and overlapping histograms for clear presentation.

Perform a two-sample z-test to detect a 1cc difference between machines by setting mu = -1. The null hypothesis is that the mean difference equals -1 (p = 0.94).

Explain the theory of two-sample t tests, distinguishing independent and dependent samples, compare with paired t-test, and derive the t statistic with pooled variance when variances are equal.

Compare two-sample t tests with equal variances in R using a perfume volume example, check variance with var.test, perform t.test, and visualize with a boxplot.

Learn to perform a two-sample t test with unequal variances in R using var.test and t.test on mc1 and mc3, interpret the p-value, and compare box plots to assess differences.

Explore the paired t test for dependent samples by analyzing before-and-after measurements, computing differences, and testing whether the mean difference significantly deviates from zero.

Explore how to perform a paired t test in R using bp.before and bp.after, interpret a p-value of 0.53, and visualize differences with a bp.diff box plot.

Use a two-sample variance f-test to test sigma1^2 equals sigma2^2; compute f from the variances and compare to the f critical value; reject when f falls in the rejection region.

Perform a two-sample variance test in R using F distribution to compare two machines' variances via raw data and var.test, rejecting equal variances at 90% confidence.

Visualize two-sample variance test by plotting F distribution with degrees of freedom and comparing f calculated to f critical, compare machine A and B variances with a box plot.

Explains what ANOVA is, as analysis of variance using the f-test to assess equality of several means, and why it replaces multiple t-tests when comparing more than two groups.

Grasp the intuition behind ANOVA by comparing machine groups, using box and whisker plots, and learning how variation between and within drives mean differences.

Explore ANOVA by defining variance and sum of squares, separating between and within variation (treatment and error), and using mean squares with degrees of freedom to form the F value.

Explore manual anova across three machines, computing within and between sum of squares, mean sum of squares, and f value; reject the null hypothesis with a critical value.

Perform a complete ANOVA in R by reshaping data into volume and machine columns, running aov, interpreting the summary, and planning a Tukey HSD post-hoc test.

Following a one-way anova, TukeyHSD post-hoc tests compare pairs and show that machine 3 differs from 1 and 2, with adjusted p-values indicating significance, while 1 and 2 do not.

Apply the chi-square goodness-of-fit test to decide if data fit a specified distribution, using a coin-toss example. Compare observed and expected counts and understand null and alternative hypotheses.

Apply a chi-square goodness-of-fit test in R to assess a 40/60 coin flip, using observed versus expected counts, p-value, and the decision to reject the null of an unbiased coin.

Apply a chi-square goodness-of-fit test in R to compare expected and observed shirt-size distributions. The example uses 0.2, 0.4, 0.3, 0.1 with observed counts and visualizes the result.

Explore contingency tables to test relationships between two discrete variables using chi-square, by formulating null and alternative hypotheses and interpreting observed versus expected counts.

Build a three-by-three contingency table in R from operator production across three shifts, perform a chi-square test, and reject the null of independence based on the p-value.

Generate and interpret a contingency table in R using the gmodels crossTable with nycflights13 data, comparing airlines by month and performing Pearson chi-square.