Lecture

Hypothesis Testing: Statistics Overview

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Description

This lecture covers hypothesis testing, focusing on test statistics, critical regions, one-sided and two-sided tests, p-values, Wald test, power functions, and multiple testing methods like Bonferroni and False Discovery Rate control. It also delves into non-parametric statistics, empirical distribution functions, Glivenko-Cantelli theorem, and confidence intervals for distribution functions.

Official source

Ontological neighbourhood

Statistics

Statistical inference: Statistical hypothesis testing, Mathematical statistics

Related concepts (32)

Test statistic

A test statistic is a statistic (a quantity derived from the sample) used in statistical hypothesis testing. A hypothesis test is typically specified in terms of a test statistic, considered as a numerical summary of a data-set that reduces the data to one value that can be used to perform the hypothesis test. In general, a test statistic is selected or defined in such a way as to quantify, within observed data, behaviours that would distinguish the null from the alternative hypothesis, where such an alternative is prescribed, or that would characterize the null hypothesis if there is no explicitly stated alternative hypothesis.

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 .

Statistics

Statistics (from German: Statistik, () "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal".

Empirical distribution function

In statistics, an empirical distribution function (commonly also called an empirical cumulative distribution function, eCDF) is the distribution function associated with the empirical measure of a sample. This cumulative distribution function is a step function that jumps up by 1/n at each of the n data points. Its value at any specified value of the measured variable is the fraction of observations of the measured variable that are less than or equal to the specified value.

Multiple comparisons problem

In statistics, the multiple comparisons, multiplicity or multiple testing problem occurs when one considers a set of statistical inferences simultaneously or infers a subset of parameters selected based on the observed values. The more inferences are made, the more likely erroneous inferences become. Several statistical techniques have been developed to address that problem, typically by requiring a stricter significance threshold for individual comparisons, so as to compensate for the number of inferences being made.

Related lectures (64)

Describing Data: Statistics & Uncertainty

Introduces descriptive statistics, uncertainty quantification, and variable relationships, emphasizing the importance of statistical interpretation and critical analysis.

Hypothesis Testing in Statistics

Delves into hypothesis testing, covering test statistics, critical regions, power functions, p-values, multiple testing, and non-parametric statistics.

Statistical Theory: Inference and Optimality

Explores constructing confidence regions, inverting hypothesis tests, and the pivotal method, emphasizing the importance of likelihood methods in statistical inference.

Understanding Statistics & Experimental Design

Explores t-tests, confidence intervals, ANOVA, and hypothesis testing in statistics, emphasizing the importance of avoiding false discoveries and understanding the logic behind statistical tests.

Confidence Intervals and Hypothesis Testing

Explores confidence intervals, hypothesis testing, and decision-making using test statistics and p-values.

Related concepts (32)

Test statistic

Statistical hypothesis testing

Statistics

Empirical distribution function

Multiple comparisons problem