Confidence Intervals and Test Assumptions › Confidence Intervals and Test Assumptions
Machine Learning from ScratchAll chapters Confidence Intervals and Test Assumptions › Confidence Intervals and Test AssumptionsOne section · Sections in this chapter1 / 9 ↓
Reading tools Definitions & inline links
Choose your expertise level to adjust how many terms are explained. Beginners see more tooltips, experts see fewer to maintain reading flow. Hover over underlined terms for instant definitions.
Article links
Make inline references clickable
In the previous chapter, we established the foundations of hypothesis testing: p-values, null and alternative hypotheses, and test statistics. Now we explore two complementary concepts that complete your understanding of statistical inference.
First, we'll discover that confidence intervals and hypothesis tests are mathematically equivalent. They're not two different methods for analyzing data; they're two perspectives on the same underlying calculation. Understanding this equivalence transforms how you interpret both tools.
Second, we'll examine the assumptions that make statistical tests work. Every test rests on mathematical assumptions, and when these assumptions are violated, tests can mislead you. Knowing what assumptions matter, when they matter, and what to do when they fail is essential for responsible data analysis.