Stats and Cats Blog
Browse by topic →Statistics, data, and the cats who make us feel better about all of it.
Posts
The Base Rate Fallacy: When a Positive Test Isn't Good Evidence
A 99% accurate test for a rare condition still leaves you more likely than not to be healthy after a positive result. Bayes' theorem explains why the prior matters.
The Birthday Problem: Why 23 People Is Enough
In a room of 23 people, the probability that two share a birthday exceeds 50%. The math is clean; the intuition resists it. Here's what's actually being counted.
The Hot Hand
Streaks in basketball shooting data and whether they reflect genuine elevated performance or expected clustering in random sequences. A case study in what random actually looks like.
The Monty Hall Problem: Why You Should Always Switch
The conditional probability problem that has produced more confident wrong answers than almost any other. The correct answer is 2/3, and the host's knowledge is why.
Type I and Type II Errors: The Trade-Off You Can't Avoid
False positives and false negatives are not both minimizable at once. The threshold that reduces one will increase the other. Where it gets set is a choice, and it matters.
Variance and Standard Deviation: Why Spread Matters
Two distributions with identical means can behave entirely differently. Variance and standard deviation measure why, and understanding the mechanics behind them reveals what they actually capture.
What a p-value Actually Measures
A p-value is not the probability the null hypothesis is true, not a measure of effect size, and not a verdict on whether a finding is real. Here is what it is.
What Confidence Intervals Actually Tell You
A 95% confidence interval does not mean a 95% probability that the true value is inside it. Here is what the statement actually means, and why the distinction is worth getting right.
The Binomial Distribution: Counting Successes in Fixed Trials
How the binomial distribution models the number of successes in a fixed number of independent trials, and why the formula looks the way it does.
The Poisson Distribution: Modeling Rare Events at a Known Rate
The Poisson distribution models counts of independent events occurring at a constant rate. One parameter does everything, and that turns out to be enough.
Articles on probability distributions, statistical inference, and the concepts that undergraduate statistics courses introduce but don't always make time to explain well. The cats are load-bearing.