Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Introduction to t tests

In course

MICRO-110: Probability & statistics for engineers

Description

This lecture introduces the concept of t tests, starting with a general methodology for hypothesis testing and the importance of the null hypothesis. It covers the calculation of probabilities, the significance level, and tests that do not make the normality assumption. The lecture also explains the logic of statistical inference, the basics of t tests, and the t distribution. Additionally, it includes information on P-values, Z-tests, and how to quickly look up values using standardized t-tables. The instructor provides insights on how to conduct different types of t tests, such as the two-sample t-test and the paired t-test, along with practical examples and online resources for calculating p values.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Instructor

Vivek Subramanian

Official source

Ontological neighbourhood

Statistics

Statistical inference: Statistical hypothesis testing

Related concepts (29)

Student's t-test

A t-test is a type of statistical analysis used to compare the averages of two groups and determine if the differences between them are more likely to arise from random chance. It is any statistical hypothesis test in which the test statistic follows a Student's t-distribution under the null hypothesis. It is most commonly applied when the test statistic would follow a normal distribution if the value of a scaling term in the test statistic were known (typically, the scaling term is unknown and therefore a nuisance parameter).

Z-test

A Z-test is any statistical test for which the distribution of the test statistic under the null hypothesis can be approximated by a normal distribution. Z-tests test the mean of a distribution. For each significance level in the confidence interval, the Z-test has a single critical value (for example, 1.96 for 5% two tailed) which makes it more convenient than the Student's t-test whose critical values are defined by the sample size (through the corresponding degrees of freedom).

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.

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 significance

In statistical hypothesis testing, a result has statistical significance when a result at least as "extreme" would be very infrequent if the null hypothesis were true. More precisely, a study's defined significance level, denoted by , is the probability of the study rejecting the null hypothesis, given that the null hypothesis is true; and the p-value of a result, , is the probability of obtaining a result at least as extreme, given that the null hypothesis is true. The result is statistically significant, by the standards of the study, when .

Related lectures (31)

Hypothesis Testing and Confidence Intervals: An Overview

Covers hypothesis testing, confidence intervals, and their applications in statistics.

Statistics & Experimental Design

Explores conditional probability, Framingham studies, effect size, t-test, and sampling error in statistics.

Statistics Essentials: The t-test

Introduces the t-test for assessing categorical effects on quantitative outcomes, covering hypothesis testing, assumptions, and alternative tests.

Hypothesis Testing and Confidence Intervals: Key Concepts

Provides an overview of hypothesis testing and confidence intervals in statistics, including practical examples and key concepts.

Understanding Statistics & Experimental Design