Yuanyuan Zhang
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Knowledge

Statistics is fantastic

How to read data — and make it less boring.

Data fundamentals

The basics of working with data: summarise a dataset, explore it, and structure a project from question to decision.

Descriptive Statistics: measures of central tendency, dispersion and position Descriptive statistics Descriptive statistics

How to read the story hidden in data: center, spread and position.

 MeanStd. deviationQuartiles IQR: a box plot showing the middle 50% of the data Descriptive statistics IQR

The middle 50% of your data: spread, outliers and box plots.

 QuartilesOutliersBox plot The PACE Framework: how to structure a data project that leads to reliable decisions, with the four stages Plan, Analyze, Construct and Execute Data fundamentals From Question to Decision: the PACE Framework

How Plan, Analyze, Construct and Execute structure a data project, up to the executive summary.

 PACEWorkflowExecutive summary Exploratory Data Analysis: distributions, group comparisons, relationships and outliers, with Python, pandas, NumPy and Matplotlib Exploratory analysis · Retail Exploratory Data Analysis

Systematic exploration of NordHome's retail data — distributions, group comparisons, relationships and outliers.

 PythonPandasNumPyMatplotlib One-Hot Encoding: a product category column turned into one yes/no column per category Data fundamentals One-Hot Encoding

How to turn categories into numbers a model can use, without inventing an order that isn't there.

 One-hot encodingCategorical dataDummy variables

Probability

From single events to distributions: the language of uncertainty.

Probability Basics: how likely is an event? A tumbling die in bold geometric shapes Probability Probability Basics

How likely is an event? Outcomes, events, and the complement, addition and multiplication rules.

 ProbabilityEventsP(A)Rules Conditional Probability and Independence: two overlapping circles A and B Probability Conditional Probability & Independence

When does one event change the probability of another? Dependent events and P(B | A).

 ConditionalP(B | A)Independence Bayes’ Theorem: a blue head for the prior, a yellow cone of evidence and a red head for the posterior Probability Bayes’ Theorem

How to update a belief with new evidence: prior, likelihood, posterior, and why an alert can still be wrong.

 PriorPosteriorP(A | B) Probability Distributions: three overlapping bell curves in red, blue and yellow Probability Random Variables & Probability Distributions

From a random variable to PMF, PDF and CDF: how to describe uncertainty in discrete and continuous data.

 PMFPDFCDF Four Common Discrete Distributions: uniform, Bernoulli, binomial and Poisson Probability Four Common Discrete Distributions

Uniform, Bernoulli, binomial and Poisson: what each one models and when to use it.

 BinomialPoissonBernoulli Normal Distribution: a bell curve with the areas within 1, 2 and 3 standard deviations marked as 68%, 95% and 99.7% Probability Normal Distribution

The bell curve and the 68-95-99.7 rule: what is typical, what is rare, and how to spot outliers.

 Empirical ruleZ-scoreBell curve Common Continuous Distributions: a flat uniform block, a bell curve, an exponential decay and skewed curves in red, yellow, blue and black Probability Common Continuous Distributions

Uniform, normal, exponential and log-normal: what each one models and when to use it.

 UniformExponentialLog-normal

Sampling

How to choose the data you analyze, and how to avoid bias.

Sampling: a population of colored shapes in a circle and a small sample picked from it Sampling Sampling Methods

Probability and non-probability sampling: how each method works and how it can bias your data.

 RandomStratifiedBias Central Limit Theorem: a population, repeated samples, and a bell-shaped distribution of sample means Sampling Central Limit Theorem

Sampling distributions, standard error, and why the means of repeated samples form a bell curve.

 Sampling distributionStandard errorNormal

Inference & experiments

Test whether a change really made a difference.

Confidence intervals: sample estimates with error bars around a true value, most of them crossing it Inference Confidence Intervals

Why a range beats a single estimate, how to read a 95% interval, and what it does not mean.

 Confidence intervalZ-scoreMargin of error Hypothesis testing: null and alternative hypothesis boxes above a bell curve with red rejection regions in both tails Inference Hypothesis Testing

Is a difference real or just luck? Significance level, p-value, t-test and power, shown on a checkout redesign example.

 Significance levelP-valuePower A/B testing: users randomly split into a control group and a treatment group Experimentation A/B Testing

How to design an experiment and tell whether a change really made things better.

 HypothesisRandomizationp-value T-Test vs. Z-Test: a standard normal curve in red and a wider t-distribution in blue Inference T-Test vs. Z-Test

How to choose the right test for averages and conversion rates with a simple decision tree.

 T-testZ-testDecision tree

Regression analysis

Model how an outcome depends on other variables, whatever type of outcome it is.

Simple Linear Regression: bold title next to a scatter plot of blue and red points with a fitted line, surrounded by yellow, blue and red geometric shapes Regression analysis Simple Linear Regression

Predict sales from advertising spend and learn what the intercept and slope of a fitted line really mean.

 SlopeInterceptFitted linePrediction Multiple Linear Regression: bold title next to three predictors X1, X2 and X3 feeding a fitted plane with data points above and below it, surrounded by blue, red, yellow and black geometric shapes Regression analysis Multiple Linear Regression

Predict a customer's net revenue from several drivers at once, and learn to read each coefficient on its own.

 CoefficientsAdjusted R²Multicollinearity Ordinary Least Squares: bold title next to a scatter plot with a red fitted line, dashed residuals and a squared-residual box, surrounded by yellow, red, blue and black geometric shapes Regression analysis OLS: Finding the Best-Fit Line

How residuals and the sum of squared residuals turn "fits well" into a number, and how OLS finds the best line.

 OLSResidualsSSR Regression Assumptions: four small charts labelled Linearity, Independence, Normality and Homoscedasticity next to a bold title, with yellow, red, blue and black geometric shapes Regression analysis The Four Assumptions of Simple Linear Regression

When can you trust a fitted line? Linearity, independence, normality and constant variance, and how to check them.

 LinearityNormalityHomoscedasticity Evaluating and interpreting a regression model: a blue circle with a fitted line for model fit, a red rectangle with a confidence band for uncertainty and a yellow triangle showing extrapolation beyond the observed data range Regression analysis Evaluating and Interpreting a Regression Model

How well does the model fit and how reliable are its estimates? R², error metrics, p-values and confidence intervals.

 Model fitR²Confidence intervals Overfitting and Underfitting: bold title above three scatter plots showing a straight line that is too simple, a smooth curve that fits well and a wiggly curve that is too complex, surrounded by red, yellow, blue and black geometric shapes Regression analysis Overfitting and Underfitting

Why a model can be too simple or too flexible, and how to tell the difference before it fails on new data.

 Bias-varianceOverfittingAdjusted R² Generalized Linear Models: a blue circle with a regression line, a red rectangle with an S-shaped logistic curve and a yellow triangle with rising bars Regression analysis Generalized Linear Models

One framework behind linear, logistic and Poisson regression: link functions for continuous, binary and count outcomes.

 GLMLogisticPoisson