uncertainty 10 min
When a 99% Accurate Alert Is Only Half Right
Even a strong detector can produce a surprising share of false alerts when the event it seeks is rare. The missing ingredient is the base rate.
Twelve field guides
Read the claim. Inspect the assumptions.
Each guide starts with a common misconception, works through a synthetic example, and ends with the boundary conditions that make the result useful.
How these are reviewed
Definitions are checked against primary teaching or standards sources. Examples, calculations, figures, and prose are created for this publication.
Not sure where to begin?
Follow a three-lesson route
Four ordered routes connect every guide to its interactive experiment, practice prompt, and checked answer.
01Describe before you summarizeWhat does one headline number leave out?02Samples, bias, and uncertaintyWhen does more data fail to mean better evidence?03Compare like with likeWhich hidden structure can reverse or weaken a comparison?04Evaluate a statistical claimWhat context must travel with a striking result?
See lessons, self-checks, and concept index relationships 10 min
When Every Group Improves but the Total Gets Worse
A combined rate can reverse the comparison inside every subgroup when the groups appear in different proportions.
sampling 8 min
Why Sample Means Become Bell-Shaped
A skewed population can produce nearly normal averages. The change belongs to repeated sampling, not to the original observations.
sampling 8 min
A Bigger Biased Sample Is Still Biased
More responses can tighten an estimate around the wrong answer when the people who can respond differ from the people you want to describe.
communication 7 min
A Two-Point Increase Can Be a 50% Increase
From 4% to 6% is an increase of two percentage points and a relative increase of 50%. Both are correct, but they answer different questions.
uncertainty 7 min
Bootstrap Resampling Explained With a Simple Example
Bootstrap resampling explained through an everyday example: see how repeated samples estimate uncertainty without a complicated formula.
relationships 10 min
Four Patterns a Correlation Can and Cannot Describe
Positive, negative, near-zero, and nonlinear patterns show what Pearson's coefficient summarizes and what only a scatterplot reveals.
foundations 7 min
The Average Is Not the Middle
A single delayed delivery can pull the mean away from every ordinary experience. Learn what mean, median, and trimmed mean actually summarize.
communication 10 min
The Same Data, Two Stories: What a Truncated Axis Changes
A narrow vertical scale can reveal small changes or visually magnify them. The right choice depends on the graphical encoding and honest context.
uncertainty 11 min
Twenty Tests, One Discovery
At a 5% threshold, testing twenty independent null effects creates about a 64% chance of at least one false alarm. A small p-value needs its full search context.
uncertainty 8 min
What 95% Confidence Really Covers
A confidence interval is a procedure with a long-run success rate. Watch many intervals succeed and a few fail even when every calculation is correct.
relationships 8 min
Why Extreme Results Move Back Toward Average
Selecting the highest first scores also selects unusually favorable noise. A second measurement often looks less extreme without any intervention.
foundations 8 min
Why Random Sequences Contain Suspicious-Looking Streaks
Fair coin sequences naturally produce clusters and long runs. A pattern can look designed without changing the probability of the next independent outcome.
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