Learn Statistics & Biostatistics Data Analysis From Scratch

Learn how to install R from CRAN and set up R Studio on your system, choosing the right OS options and verifying integration by running a simple calculation.

Set the working directory in RStudio by selecting the Udemy folder on the desktop, then choose set as a working directory to ensure inputs and outputs stay there.

Explore the four data types R handles: vector, matrices, data frame, and list. Learn how to create them in R and upload from tab files, csv files, and excel files.

Explore vectors, the simplest one-dimensional data type in R, and learn how numeric, logical, and character vectors are created with concatenation, with appropriate quoting rules.

Explore matrices in R as two-dimensional arrays where all elements share the same type, and learn to create a 3x2 matrix using the matrix function with data 1 to 6.

Explore the data frame, the most important data type in R, a heterogeneous, columnar table that supports numeric and categorical data; learn to create it with data.frame and simple vectors.

Explore how to use R's list as a flexible container that holds a vector, a data frame, and a matrix, and learn to create lists with the list function.

Identify a variable as a storage for data in R, bound with an assignment operator. Use names that begin with a letter, avoid spaces and special characters, and allow underscores.

Discover the R base package and its automatically activated functions, including mean, median, and density plot, usable without calling a library in R Studio.

Learn how functions and packages in R work, install packages with install.packages, and use ggplot2 in RStudio to perform data analysis.

Explore Bioconductor, an open source project for rigorous, reproducible analysis of biological data, and learn to install Bioconductor in R using BiocManager to install packages like GenomicFeatures.

Learn the basic definition of statistics as a tool to analyze, interpret, and present data in a meaningful form.

Learn the two basic types of statistics: descriptive statistics describe and summarize data, while inferential statistics use a sample to infer the population mean.

Understand data distribution, including normal and skewed shapes, identify the central point and the two equal halves, and learn to apply statistics accordingly.

Explore four plots for viewing data distribution: density plots, box plots (box and whisker) with mean or median, histograms, and Q-Q plots, and learn how normality and skewness appear.

Build and interpret distribution plots in R to analyze a CSV clinical data set using histogram, box plot, density plot, and q-q plot.

Analyze central tendency by examining mean, median, and mode, learn the summation formula for the mean, and see how R helps compute it for large data.

Learn to find the median by sorting data and selecting the central value; for even data sets, average the two central values, and use R for large data sets.

Identify what outliers are and why they appear in data, from measurement errors to natural extremes, and learn why they heavily influence statistical analysis.

Identify outliers in data sets using box plots by examining dots above the upper whisker or below the lower whisker, and learn how to remove them in a future lesson.

Learn how mean is sensitive to outliers while median remains robust, illustrated with an outlier example. Understand when mean affords algebraic use and when median suits skewed data.

Determine when to use mean or median based on distribution shape, illustrated with a newborn serum bilirubin clinical example and jaundice, showing skewed data where the median is appropriate.

Learn the concept of the mode, the most frequent value in a data set, illustrated with a bar plot and a clinical example, and its suitability for categorical data.

Compute the mean, median, and mode of data sets in R using RStudio, highlighting central tendency and how to set working directory, load data, compute values, and interpret distributions.

Explain interquartile range (IQR) as the spread of the middle 50%, calculated by subtracting Q1 from Q3, and compute Q1, Q2 (median), and Q3 using a box plot.

Learn to calculate the interquartile range in R using the quantile function on the age variable, interpreting Q1, Q2, and Q3 to obtain the IQR.

Explore how variance measures data spread by calculating squared deviations from the mean, using the formula s^2, summing differences, and dividing by n-1, with a 1–5 example.

Learn to calculate variance in R using the var function on data$age in the loaded clinical data set, and view the result in the console.

Learn how standard deviation, the square root of variance, makes variability interpretable. Compare small and large deviations to gauge data spread.

Learn to calculate the standard deviation in R with the sd function on the data set's age, view the 10.85 result in the console, and compare it to variance.

Learn to compute all descriptive statistics for numeric variables at once using the psyche package, describe function, and interpret mean, median, sd, mad, min, max, skew, kurtosis, and range.

Discover how to analyze categorical data by using frequency tables, percentage proportions, mode, contingency tables, and visualizations.

Learn how to rectify R's misreading of categorical data by converting sex, diabetic status, smoking status, and exercise frequency to factors with as.factor, then verify changes using str(data).

Learn how to create frequency tables for categorical data, describing counts by category (sex, exercise, diabetes, smoking), and visualize with charts, using R's table function.

Learn how to build a frequency table for a categorical variable in R using the table function, with a walkthrough of the sex variable and interpreting the console output.

Learn to analyze categorical data by calculating percentages and proportions using frequency tables and prop.table in R, enabling comparison across datasets of different sizes.

Explore the mode as the main measure of central tendency for categorical data, including bimodal datasets, and learn how to calculate it in R.

Find the mode of a categorical variable in R with a custom function after loading the clinical data in RStudio, for exercise frequency (0–3 levels) showing 1 as the mode.

Explore contingency tables, or cross tabs, showing frequency distributions for variables, such as gender and pet type, with margins; learn to build them in R with table and add margin.

Learn to build a contingency table for two categorical variables in R using table and add margins, store it in a variable, and print the final table with margins.

Explore visualizations for categorical data, including bar plots, pie charts, and dot plots for single variables, and heatmaps, mosaic plots, and stacked bar plots for two variables, with R examples.

Build bar plots, pie plots, and dot plots from a single categorical variable in R by creating a frequency table and visualizing the gender data from the sex column.

Build heat maps, mosaic plots, and stacked bar charts to visualize the interaction of two categorical variables using a contingency table in R, with ggplot insights.

Learn the fundamentals of probability, including experiments, the sample space, and events, and apply the simple ratio of favorable outcomes to the total outcomes to assess likelihoods.

Explore the four basic types of probability—classical, empirical, subjective, and conditional—and how equal outcomes, from coin flips to genotype crosses, illustrate theoretical probability.

Explore empirical probability, the experimental probability based on real observations in clinical trials and population studies. Contrast it with subjective probability rooted in judgment when data is scarce.

Explore conditional probability by computing the chance of event a given b occurred, using joint probability and a positive probability of b, illustrated with red and blue balls.

Explore correlation as a statistical measure of the relationship between two variables, from -1 to 1, and interpret positive, negative, and zero correlations using Pearson, Spearman, and Kendall methods.

Examine parametric distributions such as normal, binomial, and Poisson, and contrast them with nonparametric distributions. Learn how data distribution guides the choice of statistical formulas in correlation analysis.

Apply Pearson correlation to continuous data with normal distribution and a linear relationship, using x_i, y_i, and their means. Compute it in R with the base function.

Learn to calculate Pearson correlation between systolic blood pressure and cholesterol in R, using a CSV dataset, with density and scatter plots and a regression line.

Discover the basics of ggplot, the R package for beautiful visualizations, and its three layers: data, aesthetics, and geometry, with a histogram example.

Learn to install and load ggplot2 in R, build a scatter plot with systolic blood pressure vs cholesterol, refine with themes, labels, and a linear trend line for publications.

Explore Spearman correlation and Spearman's rank correlation, learn when to apply it for monotonic, nonparametric data (and some parametric cases), and understand its formula using rho and d^2.

Explore how to apply Spearman correlation to data with a monotonic relationship by ranking math and science scores, computing rank differences, and using the formula, including an R calculation example.

Compute the spearman correlation in r with a practical workflow using a data set and ggplot visualizations, interpreting a weak negative relationship between systolic blood pressure and heart rate.

Explore Kendall tau correlation, a non-parametric measure of monotonic relationships for ordinal or continuous data, using concordant and discordant pairs and computing with cor(x, y, method = 'kendall').

Choose the right correlation method: Pearson for parametric data, Spearman for nonparametric, and assess linearity, outliers, and the fact that correlation does not imply causation.

Explore regression as the most decorated statistical concept that yields a quantitative relationship among variables, offering predictive power and informed decision making. It underpins machine learning models and scientific applications.

Define regression and model the relationship between the independent variable (explanatory) and the dependent variable (response), using nutrition and height as an example with x and y axes.

Explore the three main regression types: simple linear regression, multiple linear regression, and logistic regression for categorical outcomes, emphasizing when dependent variables are continuous or categorical.

Explore simple linear regression by modeling y from x with a regression line, using y = beta naught + beta one x + epsilon and minimizing sum of squared differences.

Apply the simple linear regression equation to predict BMI from cholesterol by interpreting the regression line, beta coefficients, and explanatory versus response variables.

Analyze the residual in regression, comparing observed values to predicted ones on the regression line. Relate the residuals to the sum of square error to judge model fit.

Understand the r square, or coefficient of determination, which measures how much the dependent variable's variability is explained by the independent variable; values span 0 to 1.

Build a simple linear regression model in R using the lm function from the stats package, specify dependent and independent variables, and view results with summary including coefficients and r-squared.

Build a simple linear regression model in R to explore how age affects heart rate, then visualize with ggplot and interpret the model outputs.

Visualize the regression line and interpret the intercept as about 72.68 beats per minute when age is zero, then compare the BMI-cholesterol model with slope 5.1358, p<0.001, and r-squared 0.5835.

Explore how multiple linear regression models the relationship between one numeric dependent variable and several explanatory variables, using the intercept and slope coefficients to show each variable's influence.

Learn to build a multiple linear regression model in R using lm and data variable, with heart rate as the response and age, systolic blood pressure, and cholesterol as predictors.

Visualize a four-variable multiple linear regression in R with ggplot, plotting heart rate against age, systolic blood pressure, and cholesterol on a single plot with regression lines from model coefficients.

Interpret a multiple linear regression model in R, examining residuals, coefficients, p-values, and R-squared while relating age, systolic blood pressure, and cholesterol to heart rate.

Ensure simple and multiple linear regression meet key assumptions—linearity, independence, normality of residuals, and no autocorrelation—by checking data before modeling, with a numeric response variable and numeric or categorical predictors.

Explore linearity in regression and how a proportional relationship between response and explanatory variables improves model predictability. See additive effects in categorical variables for better models in multiple linear regression.

Explain the independence assumption by ensuring observations are independent and how violations bias parameters and increase type one error. Illustrate with a 30-student example and random sampling to verify independence.

Learn why binary outcomes require logistic regression instead of linear regression. Explore an example where smoking and drinking intensity predict liver damage (0/1).

Explore why linear regression fails with a categorical variable and see how logistic regression models the data, emphasizing the shift from continuous to categorical prediction.

Explore the logistic regression formula, including the logit function and odds, and learn how beta naught and beta one estimate the pass probability from study hours.

Learn to implement logistic regression in R with glm and a binomial family for binary outcomes, adding independent variables and noting alternatives for multi-category outcomes.

Load the DB2 data into RStudio, convert diabetes_status to a factor, and build a logistic regression model with glm and binomial family to analyze age and BMI effects.

Explore interpreting logistic regression results in r-studio via the age coefficient, p-values, and null vs residual deviance, plus visualizing the sigmoid probability curve.

Build logistic regression probabilities in R by creating a probability column, using predict with your model and data, and visualize the sigmoidal curve with ggplot.

Interpret the logistic regression curve to read age-related diabetes probability from color-coded dots (red = non-diabetic, blue = diabetic). Learn estimating and converting a given age’s probability to a percentage.

Explore hypothesis testing by comparing two contradictory statements, define the hypothesis as a tentative statement, and learn how collecting and analyzing data leads to a decision.

Define null and alternative hypotheses as the default and opposite statements in hypothesis testing, with battery life and drug efficacy examples, and explain type one error and type two error.

Formulate null and alternative hypotheses from real statements, distinguishing claim from status quo. Explore examples: the mean weight in Georgetown equals £178 and whether a drug lowers blood pressure.

Set up the hypotheses and the alpha level, then choose an appropriate test—t, z, one-way ANOVA, or two-way ANOVA—based on data and design, and decide on the null.

Explore the level of significance, alpha, and how they set a threshold to reject the null hypothesis in hypothesis testing, balancing confidence, evidence, and risk.

Explore parametric and nonparametric hypothesis tests, learn when to use z, t, f tests and ANOVA, and identify chi-square, Mann–Whitney, and Wilcoxon tests for skewed data.

Explore traditional method and the p-value based method of hypothesis testing, decide on one- or two-tailed tests, and apply rules using critical values and acceptance or rejection of null hypothesis.

Master the p-value based decision method by comparing p values to alpha, calculate p values via z, t, and f tests, and plan future parametric and nonparametric analyses.

Determine which data require which statistical test by learning the basic assumptions of each test. We will start with the Z test.

Apply the z test to compare means under normal distribution with known population standard deviation. Distinguish one-sample and two-sample z tests and their key symbols x-bar, mu, sigma, and n.

Apply a one-sample z-test to evaluate if area frog weights differ from the population mean of 50 g, using a two-tailed test (n=40, x̄=52 g, s=5 g) at alpha 0.05.

Clarifies how to interpret z statistic scores with negative and positive values, comparing to left and right critical values in two-tailed tests to accept or reject the null hypothesis.

Learn to perform a one-sample z-test in R using the BSD library's z.test, specifying sample data, population mean and standard deviation, choosing one- or two-tailed tests, and interpreting p-values.

This lecture introduces the t test, contrasts it with the z test, and explains when to use it for n<30 samples, including one-sample and two-sample (independent and dependent) cases.

The one sample t test compares the sample mean with the population mean using the sample standard deviation, defining null and alternative hypotheses for a two-tailed test.

Learn to perform a one-sample t-test in R using the Bsda package's t.test, compare sample data to a population mean, and interpret p-values and confidence levels.

Learn to perform the two sample independent t test by comparing means of two independent groups, testing a two-tailed hypothesis for differences, and checking independence, normality, and variance homogeneity.

Execute a two-sample independent t-test in R using Bsda and t.test, compare groups, choose one- or two-tailed tests, and check variance homogeneity with Levene; reshape data with pivot_longer.

Learn to perform a two-sample t test in R on plant length data, from loading with read.csv to transforming with pivot_longer, checking normality, Levene test, and running t.test with var.equal.

Learn how to perform the two sample dependent (paired) t test, compute mean differences, set hypotheses, select one-tailed test, and interpret results using a weight-loss drug example.

Learn to perform a two-sample dependent (paired) t test in R with the BSD t.test function, including setting alternatives, conf level, and the correct variable order.

Learn to perform a paired two-sample t-test in R using before-and-after weight data, loading a CSV, running t.test, and interpreting a left-tailed result.

See how a minor misordering of input variables in a paired sample t-test can trigger type I and type II errors, altering p-values and alpha decisions.

Learn how the f-test, named for Ronald A. Fisher, compares variances between two groups, using an example with two dosages and a 0.05 significance level.

Compare the F test with t and z tests, showing why F handles two or more groups and variance homogeneity better, and guide R-based calculation.

Use the bsda library in R to perform an f-test with var.test, specifying the high-variance and low-variance variables in the correct order, a right-tailed test, and a chosen confidence level.

Perform an f-test in R to compare low and high drug dose groups, load csv data, compute variances, and interpret a p-value of 0.3916, concluding fail to reject the null.

Explore ANOVA, the analysis of variance, to compare means across three or more groups using between-group and within-group variance and F statistics; learn one-way and two-way types.

Explore how one-way ANOVA compares means across three or more groups and how to compute the F statistic from mean square between and within using a dose-level example.

Demonstrates R code for anova in RStudio by converting data from wide to long format and applying aov to compare BP across low, medium, and high dose groups.

Transform wide to long data in R with pivot_longer, convert the group to a factor, and perform a one-way ANOVA in R, interpreting p-values and significance stars.

Learn how two-way ANOVA extends one-way ANOVA to study two factors and their combined effects on multiple groups, using mean squares and f statistics.

Learn to run a two-way anova in R using bsda library's aov function, with data in long format, and specify two factors using tilde and the multiplication sign in RStudio.

Perform a two-way anova in R on a mouse weight dataset loaded from csv, converting diet and exercise to factors, and interpret the p-values for diet, exercise, and interaction.

Explore nonparametric hypothesis testing for categorical data with the chi-square test, including independence and goodness-of-fit, and learn how to perform calculations in R.

Apply the chi-square test of independence to assess association between two categorical variables, such as genotype and disease resistance, by comparing observed and expected frequencies with a 0.05 significance level.

Learn to compute chi square statistics in R using the base function chi squared dot test with sample data and no library, ready for use in RStudio.

Load genotype.csv in R and form a two-genotype data set for resistance and susceptibility. Apply the chi-square test of independence and interpret the small p-value to reject the null hypothesis.

Use the chi-square goodness of fit test to compare observed versus known population frequencies, set alpha 0.05 and degrees of freedom, and decide acceptance or rejection of the null hypothesis.

Master chi square goodness of fit with the R base function, provide the data variable name, and let R compute the statistics from your data.