Statistics 201: distributions, correlation and tests
You answer "is this difference real?" with probability, distributions, confidence intervals, hypothesis tests and correlation.
Level 201 · 16 lessons · 12 practice labs
Lessons
Probability
- Probability basics: events, odds, independence
- Conditional probability and Bayes: how much to trust an alert
- Count data and the Poisson distribution
- Quick task: work out the base-rate fallacy
Estimation and uncertainty
- Sampling distributions and the central limit
- Confidence intervals
- Uncertainty with the bootstrap
- Quick task: a confidence interval for a phishing click rate
Tests
- Hypothesis testing and the p-value
- Tests comparing means and proportions
- Chi-square: association between categories
- Multiple testing and false discoveries
- Quick task: account takeovers before and after MFA
Relationships
- Pearson and Spearman correlation
- Trends with simple regression
- Capstone: did the new firewall rule work
Practice labs
- Probability of independent events: Compute from the logged rates the probability that two separate backup systems fail on the same night and interpret it.
- How far to trust a positive alert: Use Bayes to work out the chance that an alert is real for a malware signature with a given sensitivity and false-positive rate.
- An unexpected day under Poisson: Compute Poisson probabilities from the average daily admin logins and find which days are too busy to be explained by chance.
- A confidence interval for a mean: Compute a 95 per cent confidence interval for the mean after-hours session length of Kestrel Logistics' 60 drivers.
- A confidence interval for a proportion: Compute a confidence interval for the missing-patch rate in a small audit sample and show how it narrows as the sample grows.
- Uncertainty of a median with the bootstrap: Produce a bootstrap confidence interval for the median of skewed incident resolution times and compare it with a formula-based result.
- Is there a difference between two means: Compare the response times of the old and new server configuration with a t-test and write the p-value and the decision.
- Category association with chi-square: Test whether device type and malware detection are associated with a chi-square test and write the expected counts into a table.
- The multiple-testing trap: Test twenty departments one by one and re-evaluate the “significant” ones with Bonferroni and Benjamini-Hochberg corrections.
- Pearson or Spearman: Compute Pearson and Spearman coefficients for two measurements with outliers and write which one describes the relationship better.
- A trend with simple regression: Fit a linear regression to monthly phishing report counts and interpret the slope and next month's estimate.
- Did the change work: Test account lockouts before and after a new password policy while accounting for seasonal differences and write an evidence-based decision.
About this course
You answer "is this difference real?" with probability, distributions, confidence intervals, hypothesis tests and correlation.
What you will learn
- Probability
- Estimation and uncertainty
- Tests
- Relationships
Prerequisites
Finishing the level 101 courses of the same path, or knowing those topics, is enough.
Lab environment
Lessons run in your own Kali Linux terminal that opens in the browser. Nothing to install; the lab starts clean in every lesson.
Frequently asked questions
- Is this course right for my level?
- The course is at level 201; it assumes you know the topics of the lower-level courses.
- Is there anything to install?
- No. Every lesson runs in your own lab environment that opens in the browser.
- How do lessons work?
- Each lesson has 8 to 10 steps and a short quiz. Early steps show the command to type, later steps give less help; if two attempts fail, the solution opens.
- Can I try it for free?
- Yes. The first three lessons of every course are free.