Learn Statistics with Phoebe

Is this real, or is it noise? Statistics and probability, the foundation under all of it.

Two tracks, one running brand. The 6-session leader track teaches executives, PMs, and marketers to read statistics without being fooled - mean vs median, what a confidence interval and a p-value actually claim, and the fallacies that sink smart rooms - with no code. The 10-session builder track takes practitioners from descriptive stats and probability, through distributions, random variables, sampling and the Central Limit Theorem, estimation and maximum likelihood, confidence intervals, hypothesis testing, chi-square and ANOVA, to correlation and regression - built from scratch in Python with numpy, scipy, and statsmodels. This is the foundation the experimentation and machine-learning courses assume you already have. Learn it on Lumen Skincare, then walk straight into A/B testing.

16sessions, 2 tracks
10topic areas, descriptive to regression
3live in-browser stat tools
1running brand: Lumen

The leader track 🤝 · for execs, PMs & marketers · 6 x 45 min · no code

A statistic is only as good as the reading you give it. This track teaches you to interpret the numbers in any report - the center, the spread, the error bars, and the verdict - and to spot the fallacies that fool smart people, without opening a notebook. A friendly on-ramp for LinkedIn readers, too.

📊 Leader session 1 · start here

Reading the data

Mean, median, spread, and shape - and why the average is the most over-trusted number in business. Read a boxplot and a "typical customer" claim without being fooled.

▶ Start hereNo code 🎲 Leader session 2

Thinking in odds

Probability in plain language - independence, conditional probability, base rates and Bayes - and why a 99%-accurate test can still be wrong most times it fires.

Read the odds 🔔 Leader session 3

The bell and its cousins

The normal curve and the 68-95-99.7 rule, plus the binomial (counts of yes/no) and the Poisson (events per period) - what each shape tells you at a glance.

Distributions 🎯 Leader session 4

What a sample can say

Why a sample of thousands can speak for millions - sampling error, the Central Limit Theorem, and the margin-of-error intuition behind every poll and dashboard.

Sampling & CLT 📏 Leader session 5

The number and its error bars

Point vs interval estimates, and what a 95% confidence interval really means - plus the three things people wrongly think it means. Why "3.2% ± 0.5" beats "3.2%".

Confidence intervals ⚖️ Leader session 6

Real or noise?

The logic of a test, the p-value (defined correctly), significance vs importance, and the fallacy gauntlet - p-hacking, Simpson's paradox, correlation vs causation. Capstone: read a Lumen A/B result like an exec.

Capstone

The builder track 🛠️ · for practitioners · 10 x 45 min · Python

For DA, DE, DS, and anyone who needs the statistics under machine learning and experimentation. One running brand - Lumen Skincare - carried across every session: describe it, simulate it, fit distributions to it, sample from it, estimate its parameters, and test hypotheses on it - all from scratch with numpy, scipy, and statsmodels.

📊 Builder session 1 · start here

Describe the data

Build the Lumen dataset once (seed 42), then center, spread, and shape in numpy/pandas - and why .describe() can quietly mislead you on skewed money.

▶ Start herePython 🎲 Builder session 2

Probability and simulation

Sample spaces, conditional probability and Bayes in code, and Monte Carlo simulation - watch the law of large numbers converge on Lumen's conversion rate.

Simulate it 🔢 Builder session 3

Random variables, E and Var

Discrete vs continuous random variables, expectation and variance, covariance, and the pmf/pdf/cdf trio - expected revenue per session, from first principles.

Expectation 🔔 Builder session 4

Distributions in scipy

Normal, binomial, Poisson (and uniform, exponential, lognormal) via scipy.stats - pdf/pmf/cdf/ppf, Q-Q plots, and fitting the right shape to Lumen's data.

scipy.stats 🎯 Builder session 5

Sampling and the CLT

Sampling distributions, standard error, and the Central Limit Theorem demonstrated by resampling - watch skewed order values average into a normal. Plus the bootstrap.

The money demo 🎛️ Builder session 6

Estimation and MLE

Estimators, bias and consistency, why we divide by N-1, and maximum likelihood - derive it, then let scipy find the parameter that makes Lumen's data most probable.

Maximum likelihood 📏 Builder session 7

Confidence intervals

z and t intervals for a mean, Wald and Wilson for a proportion, and the bootstrap CI - build the interval on Lumen's conversion rate that sets up the A/B test.

Error bars in code ⚖️ Builder session 8

Hypothesis testing

Null vs alternative, the test statistic, p-value, Type I/II error and power - the one and two-sample t-test and the two-proportion z-test. Is 3.6% really above 3.2%?

The verdict 🧮 Builder session 9

Chi-square and ANOVA

Chi-square goodness-of-fit and independence (channel vs convert), one-way ANOVA across product categories, and the nonparametric fallback when assumptions break.

More tests 📈 Builder session 10

Correlation, regression & fallacies

Pearson and Spearman, simple and multiple OLS, R-squared and residuals - then the fallacy capstone: p-hacking simulated, multiple comparisons corrected, Simpson's paradox in code.

Capstone
start here - foundations building up - the core craft getting real - inference hardest - regression & fallacies

Choose your path 🗺️

Leaders start at Leader session 1; practitioners start at Builder session 1. The fast-tracks fit a specific gap.

🤝 Leader journey (no code) A1→ A2→ A3→ A4→ A5→ A6→ curious? Builder session 1
🛠️ Full builder journey 1→ 2→ 3→ 4→ 5→ 6→ 7→ 8→ 9→ 10
⚡ Inference fast-track (feeds A/B testing) 1→ 5→ 7→ 8
🎲 Probability fast-track 2→ 3→ 4
👔 Leader crash course (60 min) A1→ A4→ A6

Try the statistics playground 🎛️

Three live tools, no install, seeded from Lumen's real numbers. Drag the dials and watch the math move - the same tools are embedded in the sessions that teach them.

One brand, both tracks. Every session works on Lumen Skincare - a synthetic $18M direct-to-consumer skincare label. Its numbers are the teaching examples: order values average ~$74 (median $63, right-skewed), checkout converts at ~3.2%, ~4,000 sessions a day, and prior spend correlates ~0.6 with order value. Leaders learn to read those numbers honestly; builders compute, simulate, and test them from scratch - and every figure lines up with the experimentation course, so this is the prequel that makes A/B testing click.
Honest about scope. Sessions distill the leading foundational material - OpenIntro Statistics (the structural spine), Google's "The Power of Statistics", 365 Data Science's Statistics, Khan Academy, StatQuest, and Coursera's Basic Statistics (Amsterdam). Certificates, graded exams, and lecture videos stay with their official sources. Deeper Bayesian inference, full regression modelling, and causal inference are pointed to their own courses. Content verified July 2026.

The knowledge map 🧠

The builder track at a glance - hover a session to spotlight its concepts, click any node to jump in.

The whole course on one sheet 📐

Seven modules: both tracks, the three shapes almost every business number takes, what an honest error bar actually claims, the builder ladder from describing data to regression, which test to reach for, the six fallacies that fool smart rooms, and the Lumen checkout claim worked end to end.

Download for print (2800px) Every word here is real selectable text, so it stays sharp however far you zoom.

learn statistics
with phoebe

Is this real, or is it noise?
16 sessions - two tracks - one running brand, Lumen - no math you have to do

SEC-01 TWO TRACKS

LEADER TRACK
read it without being fooled, no code

  1. a1Reading the data
  2. a2Thinking in odds
  3. a3The bell and its cousins
  4. a4What a sample can say
  5. a5The number and its error bars
  6. a6Real, or noise?

BUILDER TRACK
run it yourself in scipy

  1. b1Describe the data
  2. b2Probability and simulation
  3. b3Random variables
  4. b4Distributions in scipy
  5. b5Sampling and the CLT
  6. b6Estimation and MLE
  7. b7Confidence intervals
  8. b8Hypothesis testing
  9. b9Chi-square and ANOVA
  10. b10Correlation and regression
Both tracks read the same numbers off the same brand.
16sessions
6leader
10builder
45min each

SEC-02 THE THREE SHAPES

Almost every number a business tracks falls into one of three shapes. Name the shape and you can read the number properly.

normalbell

  • heights, errors
  • averages of anything
  • typical: the centre
  • swings: symmetric

binomialtries

  • successes out of
  • a fixed set of tries
  • typical: rate x tries
  • swings: widest at 50%

poissonrate

  • events per stretch
  • of time
  • typical: the rate
  • swings: grow with count
Why the shape comes first

The shape tells you what is typical, what is surprising, and how wide the swings should be. Read a count as if it were a bell and every unusual week looks like a crisis.

SEC-03 THE HONEST NUMBER

A single number is a best guess. The honest version carries its margin of error, and the margin is the part people drop.
Point estimate against interval
point estimate 3.2% small sample [2.0% 4.4%] large sample [3.0% 3.4%]

Same best guess, very different confidence. Bigger samples make the interval tighter: more data, more certainty, narrower error bar.

3.2% +/- 0.5pp is the same claim as [2.7%, 3.7%]. If two error bars overlap, "different" is probably just noise.
The one rule that governs it

Bigger samples make the interval tighter. Same best guess, more certainty, narrower bar. Every confidence interval on the sheet is that one rule applied.

SEC-04 THE BUILDER LADDER

1
mean, median, spread, shape describe what you already have
b1
2
simulation run it when the formula is harder than the loop
b2
3
expectation, variance the two numbers that summarise any variable
b3
4
scipy.stats one API for every shape of randomness
b4
5
CLT why sample means go normal whatever the source
b5
6
MLE fit a shape to the data you observed
b6
7
confidence intervals the honest error bar
b7
8
hypothesis tests is the difference real
b8
9
chi-square, ANOVA counts, and more than two groups
b9
10
correlation, regression association, then prediction
b10
How to climb it

Rungs 1 to 4 are description. Rung 5 is the hinge: once sample means go normal, every error bar and test above it becomes available.

SEC-05 WHICH TEST, WHICH TOOL

b10
PearsonLinear association between two numbers. Blind to curves.
b10
SpearmanMonotonic association. Survives a curve that Pearson reads as zero.
b9
chi-squareCounts falling into categories. Are these proportions different?
b9
ANOVAMore than two groups at once, without testing every pair.
b10
regressionPredict a number from others. Simple and multiple, fitted to Lumen order value.
Session b8 runs the tests in scipy and statsmodels; b9 and b10 pick the right one.

SEC-06 THE FALLACY GAUNTLET

p-hackingTest twenty noise features and one clears the bar by luck. Ask: how many things were tested before this one?
Correlation is not causationThe line fits and still explains nothing. Ask: what else moved at the same time?
Simpson's paradoxGrouping the same rows can reverse the verdict outright. Ask: does this hold inside every segment?
Base-rate neglectA test that is 99 percent accurate is still mostly wrong on a rare event. Ask: how common is the thing being detected?
The over-trusted averageThe mean is the most over-trusted number in business, and one outlier moves it. Ask: what does the median say?
Two bars that overlapTwo error bars touching is not two different results. Ask: do the intervals overlap?
A correlation of zero can hide a perfect curve. Pearson measures straight lines only; Spearman catches anything monotonic.
Why this is the capstone, not the footnote

Every fallacy here is an honest calculation. Nobody lied, nobody mistyped a formula. The number is right and the reading is wrong, which is exactly why the fallacy survives a review that only checks the arithmetic.

SEC-07 IS IT REAL, OR LUCK?

The claim on the table, from session a6
Lumen checkout old 3.2% -> new 3.6% +0.4 points, a 12.5% relative gain

The room is already celebrating. With a small sample a jump that size happens by pure luck more often than you would guess.

1
NAME THE SHAPEcounts out of tries, so binomial, not a bell
2
GET THE INTERVALthe point estimate alone cannot answer the question
3
CHECK THE OVERLAPif the two intervals overlap, hold the champagne
4
ASK WHAT ELSE WAS TESTEDone winner out of twenty is not a winner
5
SIZE THE NEXT TEST FIRSTwhich is where the experimentation course starts
learn statistics with phoebe 16 sessions - 3 shapes - 6 fallacies - 1 honest error bar by Phoebe Fu