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Lecture

Confidence Intervals and Hypothesis Tests

In course

MATH-232: Probability and statistics (for IC)

Cours d'introduction à la théorie des probabilités et aux statistiques. ...

Description

This lecture covers the construction of confidence intervals based on pivots, using the central limit theorem to approximate the distribution of an estimator. It explains how to build confidence intervals and conduct hypothesis tests, illustrating with examples. The instructor discusses the importance of standard errors, unknown variances, and statistical models. The lecture also delves into the concepts of likelihood, Bayesian inference, and the ROC curve for tests. Additionally, it explores the Pearson statistic, goodness of fit tests, and the power of tests. The presentation concludes with a discussion on the null and alternative hypotheses, emphasizing the significance of the ROC curve in testing.

Instructors (2)

Raphaël Jean Berthier

Emmanuel Abbé

Official source

Ontological neighbourhood

Statistics

Statistical inference: Statistical hypothesis testing, Mathematical statistics

Related concepts (32)

Pearson's chi-squared test

Pearson's chi-squared test () is a statistical test applied to sets of categorical data to evaluate how likely it is that any observed difference between the sets arose by chance. It is the most widely used of many chi-squared tests (e.g., Yates, likelihood ratio, portmanteau test in time series, etc.) – statistical procedures whose results are evaluated by reference to the chi-squared distribution. Its properties were first investigated by Karl Pearson in 1900.

Merge sort

In computer science, merge sort (also commonly spelled as mergesort) is an efficient, general-purpose, and comparison-based sorting algorithm. Most implementations produce a stable sort, which means that the relative order of equal elements is the same in the input and output. Merge sort is a divide-and-conquer algorithm that was invented by John von Neumann in 1945. A detailed description and analysis of bottom-up merge sort appeared in a report by Goldstine and von Neumann as early as 1948.

Null hypothesis

In scientific research, the null hypothesis (often denoted H0) is the claim that no relationship exists between two sets of data or variables being analyzed. The null hypothesis is that any experimentally observed difference is due to chance alone, and an underlying causative relationship does not exist, hence the term "null". In addition to the null hypothesis, an alternative hypothesis is also developed, which claims that a relationship does exist between two variables.

Merge algorithm

Merge algorithms are a family of algorithms that take multiple sorted lists as input and produce a single list as output, containing all the elements of the inputs lists in sorted order. These algorithms are used as subroutines in various sorting algorithms, most famously merge sort. The merge algorithm plays a critical role in the merge sort algorithm, a comparison-based sorting algorithm.

Statistical hypothesis testing

A statistical hypothesis test is a method of statistical inference used to decide whether the data at hand sufficiently support a particular hypothesis. Hypothesis testing allows us to make probabilistic statements about population parameters. While hypothesis testing was popularized early in the 20th century, early forms were used in the 1700s. The first use is credited to John Arbuthnot (1710), followed by Pierre-Simon Laplace (1770s), in analyzing the human sex ratio at birth; see .

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