Mathematics · Beginner

Statistics

What a p-value actually means, and why so much published research turns out to be wrong.

Lessons
30 lessons
Total runtime
19 hours of video
Modules
7 modules
Optional lessons
13 optional
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About this course

Statistics is the subject people are most confidently wrong about. A p-value is not the probability that your hypothesis is false. A confidence interval is not the range the true value is 95% likely to be in. Almost everyone who has taken a statistics course will get both of those wrong under mild pressure, because both were taught as procedures to execute rather than as claims to understand.

This course is built around Josh Starmer's StatQuest, which is the rare statistics teaching that leads with the idea and lets the formula follow. The sequence is deliberate and mostly conventional: describe data, then model the noise in it, then test claims against it. The unconventional part is how much time module four spends on the ways the testing goes wrong.

That module — p-hacking, statistical power, and Veritasium's account of the replication crisis — is the reason to take this course rather than a textbook. Understanding what a p-value means is worth something. Understanding why a literature full of correct p-values can still be substantially false is worth considerably more, and it is what turns statistical knowledge into actual judgement about evidence.

Around five hours in the core sequence, in ten-minute pieces, and about nineteen once the optional lessons are included, and the two 3Blue1Brown lessons are there as visual counterpoints at the two hardest moments. There is no mathematics beyond algebra anywhere in it. This is a course about reasoning under uncertainty, not about computation.

What you'll be able to do

  • Describe a dataset properly: distribution, spread, and what the mean hides
  • State correctly what a p-value is and what it is not
  • Explain a confidence interval without the usual mistake
  • Recognise p-hacking, underpowered studies, and the difference between significant and important
  • Fit and interpret a linear regression, including what R-squared does and does not tell you
  • Read a study's statistics section and form your own view of whether it shows anything

Curriculum

30 lessons · 19 hours

Describing Data

3 lessons · 24m

  1. 01CompletedHistograms, Clearly ExplainedStatQuest with Josh StarmerVideoWhere every statistical analysis should begin and where almost none of them do. Look at the data first; a surprising number of statistical mistakes are visible in a histogram.4m
  2. 02CompletedCalculating the Mean, Variance and Standard DeviationStatQuest with Josh StarmerVideoThe three numbers everything else is built from, including the awkward business of why you divide by n minus one. Worth understanding rather than accepting.15m
  3. 03CompletedStandard Deviation vs Standard ErrorStatQuest with Josh StarmerVideoTwo numbers that look alike, measure different things, and get swapped constantly in published figures. Five minutes to stop making that mistake.5m

Distributions

5 lessons · 1h 19m

  1. 04CompletedThe Normal Distribution, Clearly ExplainedStatQuest with Josh StarmerVideoThe curve everything defaults to. Note what it assumes — a great deal of real data is not this shape, and pretending otherwise is a common source of nonsense.5m
  2. 05CompletedThe Binomial Distribution and TestStatQuest with Josh StarmerVideoCounting successes out of trials — the right model for anything with a yes-or-no outcome, which covers most of what people actually measure.16m
  3. 06CompletedBinomial distributions | Probabilities of probabilitiesOptional3Blue1BrownVideoOptional. The same distribution approached through a genuinely useful question: how confident should a 10-out-of-10 review score make you? A good bridge into Bayesian thinking.19m
  4. 07CompletedThe Central Limit Theorem, Clearly ExplainedStatQuest with Josh StarmerVideoWhy the normal distribution turns up even when the underlying data is nothing like normal. This is the theorem that licenses most of the tests in the next module.8m
  5. 08CompletedBut what is the Central Limit Theorem?Optional3Blue1BrownVideoOptional, and the deeper treatment. Half an hour on why this happens rather than merely that it does — take it if the previous lesson felt like a fact you were asked to accept.31m

Testing Claims

6 lessons · 1h 25m

  1. 09CompletedHypothesis Testing and The Null HypothesisStatQuest with Josh StarmerVideoThe odd backwards logic of the whole enterprise: you never confirm your hypothesis, you only fail to reject its opposite. Everything confusing about p-values starts here.15m
  2. 10Completedp-values: What they are and how to interpret themStatQuest with Josh StarmerVideoThe most misunderstood number in science, defined carefully. If you take one lesson from this course, take this one — and note precisely what it is not saying.12m
  3. 11CompletedHow to calculate p-valuesOptionalStatQuest with Josh StarmerVideoWhere the number comes from, worked through. Optional if you only need to read statistics; essential if you intend to produce any.25m
  4. 12CompletedConfidence Intervals, Clearly ExplainedStatQuest with Josh StarmerVideoMore informative than a p-value and far less often reported. Also the second most misinterpreted object in statistics, so read the definition carefully.7m
  5. 13CompletedWhat Is a P-Value? Clearly ExplainedOptionalSteven BradburnVideoEight minutes, aimed at researchers rather than statisticians, and stronger than most on what a p-value does not mean. Worth it as a second framing of the hardest idea in this course.8m
  6. 14CompletedThe P-Value Method for Hypothesis TestingOptionalThe Organic Chemistry TutorVideoThe arithmetic rather than the interpretation — actually computing a test statistic and reading a table. Necessary if you are being examined on this.18m

How It Goes Wrong

3 lessons · 42m

  1. 15Completedp-hacking: What it is and how to avoid itStatQuest with Josh StarmerVideoHow to obtain a significant result from data containing nothing, without lying at any point. Mostly done by accident, which is what makes it dangerous.13m
  2. 16CompletedPower Analysis, Clearly ExplainedStatQuest with Josh StarmerVideoHow large a sample needs to be before the study could have detected anything. An underpowered study that finds nothing has told you nothing, and this is how you tell the difference.17m
  3. 17CompletedIs Most Published Research Wrong?VeritasiumVideoThe previous two lessons applied to the actual scientific literature, with the arithmetic of how a field full of valid p-values ends up substantially false. The most important twelve minutes here.12m

Relationships Between Variables

3 lessons · 1h

  1. 18CompletedCovariance, Clearly ExplainedStatQuest with Josh StarmerVideoThe raw measure of two things moving together, and why its units make it awkward to interpret directly. Correlation is this, tidied up.22m
  2. 19CompletedLinear Regression, Clearly ExplainedStatQuest with Josh StarmerVideoFitting a line, and — more importantly — how the fit gets tested. The workhorse of applied statistics and the foundation of most machine learning.27m
  3. 20CompletedR-squared, Clearly ExplainedStatQuest with Josh StarmerVideoHow much of the variation your model accounts for. Widely quoted as a score out of one hundred, which is not what it is.11m

Another View of Probability

6 lessons · 2h 53m

  1. 21CompletedBayes' Theorem, Clearly ExplainedStatQuest with Josh StarmerVideoUpdating a belief when evidence arrives. Everything before this module treated probability as frequency; this treats it as confidence, and both are legitimate.15m
  2. 22CompletedBayes theorem, the geometry of changing beliefs3Blue1BrownVideoThe same theorem as a picture, with the medical-test example that shows why a 99% accurate test can still be wrong most of the time it fires. Worth the repetition.15m
  3. 23CompletedMaximum Likelihood, clearly explainedOptionalStatQuest with Josh StarmerVideoOptional, and a good closing idea: choosing the model that makes the observed data least surprising. It is what almost every fitting procedure is quietly doing, including the training in the neural networks course.6m
  4. 24CompletedThe Medical Test ParadoxOptional3Blue1BrownVideoWhy a positive result on a highly accurate test for a rare disease usually means nothing. The single most useful application of Bayes' theorem to ordinary life.21m
  5. 25CompletedBayesian Statistics — An IntroductionOptionalzedstatisticsVideoBayesian and frequentist statistics as two different answers to the same question, explained without partisanship. Everything above this point in the course has been frequentist.38m
  6. 26CompletedBayesian Statistics — MIT 18.650OptionalMIT OpenCourseWareVideoThe formal version, with the mathematics the rest of this course avoids. The hardest item here and the most complete.1h 18m

The Full Courses

4 lessons · 11h 18m

  1. 27CompletedTeach Me Statistics in Half an HourOptionalzedstatisticsVideoThe whole subject in one sitting, built around a single running example. Excellent revision once the short lessons above have landed.42m
  2. 28CompletedAll of Statistics in 1 HourOptionalJensenMathVideoA study-guide format aimed at exams — every formula, worked once. Different purpose from the rest of this course and useful for it.1h 3m
  3. 29CompletedIntroduction to Statistics — MIT 18.650OptionalMIT OpenCourseWareVideoWhat statistics is as a discipline, from a mathematics department rather than a data-science one. The framing is noticeably more careful about what inference can and cannot deliver.1h 18m
  4. 30CompletedStatistics — A Full University CourseOptionalfreeCodeCamp.orgVideoEight hours covering the standard syllabus with the computation included. The reference version, for when a specific technique needs working through properly.8h 15m

Credits

Every lesson in this course was made by one of these channels. Tubeversity sequenced them; it did not make them. If a course is useful to you, the people below are the ones who earned it.