Compound probability distributions | Special functions | Continuous distributions | Location-scale family probability distributions | Normal distribution | Probability distributions with non-finite variance | Infinitely divisible probability distributions
In probability and statistics, Student's t-distribution (or simply the t-distribution) is any member of a family of continuous probability distributions that arise when estimating the mean of a normally distributed population in situations where the sample size is small and the population's standard deviation is unknown. It was developed by English statistician William Sealy Gosset under the pseudonym "Student". The t-distribution plays a role in a number of widely used statistical analyses, including Student's t-test for assessing the statistical significance of the difference between two sample means, the construction of confidence intervals for the difference between two population means, and in linear regression analysis. Student's t-distribution also arises in the Bayesian analysis of data from a normal family. If we take a sample of observations from a normal distribution, then the t-distribution with degrees of freedom can be defined as the distribution of the location of the sample mean relative to the true mean, divided by the sample standard deviation, after multiplying by the standardizing term . In this way, the t-distribution can be used to construct a confidence interval for the true mean. The t-distribution is symmetric and bell-shaped, like the normal distribution. However, the t-distribution has heavier tails, meaning that it is more prone to producing values that fall far from its mean. This makes it useful for understanding the statistical behavior of certain types of ratios of random quantities, in which variation in the denominator is amplified and may produce outlying values when the denominator of the ratio falls close to zero. The Student's t-distribution is a special case of the generalized hyperbolic distribution. (Wikipedia).
What is the t-distribution? An extensive guide!
See all my videos at http://www.zstatistics.com/videos/ 0:00 Introduction 2:17 Overview 6:06 Sampling RECAP 12:27 Visualising the t distribution 14:24 Calculating values from the t distribution (EXCEL and t-tables!)
From playlist Distributions (10 videos)
What is a t distribution? Overview of the t test, t score formula, and the t-table. Also, when to use a z score vs. t score.
From playlist Probability Distributions
Student's T Distribution - Confidence Intervals & Margin of Error
This statistics video tutorial provides a basic introduction into the student's t-distribution. It explains how to construct confidence intervals around a population mean using the student's t-distribution as well as calculating the margin of error or error bound of the mean. It's a good
From playlist Statistics
The Student's t-Distribution: Confidence Intervals
This lesson introduces the Student's t-distribution and shows how to determine a mean confidence interval. http://mathispower4u.com
From playlist Confidence Intervals
How to find a t critical value on the ti 83 AND how to find the area under a t distribution curve,
From playlist TI 83 for Statistics
The small sample is a 10-day series of Google's daily periodic returns. The question is, with 95% confidence, what is the true (population) average return? This is the essence of statistics, based on sample statistics (sample mean, sample variance) we are trying to infer population paramet
From playlist Statistics: Distributions
Intro to t Distributions for Mean Inference
Intro and overview of t distributions and how they relate to Z distributions for means. Confidence intervals for means and hypothesis tests for means are typically using t distributions.
From playlist Unit 9: t Inference and 2-Sample Inference
Hypothesis Testing - Difference of Two Means - Student's -Distribution & Normal Distribution
This statistics video explains how to perform hypothesis testing with two sample means using the t-test with the student's t-distribution and the z-test with the normal distribution table. My Website: https://www.video-tutor.net Patreon Donations: https://www.patreon.com/MathScienceTuto
From playlist Statistics
Level 1 Chartered Financial Analyst (CFA ®): Sampling and Estimation
In this video, I'm looking forward to sharing highlights with you from the CFA section, sampling and estimation. Sampling and estimation in statistics are theoretically essential and foundational, but in actual practice, it's very important. This is the practice of using samples to draw in
From playlist Level 1 Chartered Financial Analyst (CFA ®) Volume 1
From playlist STAT 200 Video Lectures
Statistics - 8.2 Student's t-Distribution
In this video, we explore a probability distribution model closely related to the normal model. It is called the student's t-distribution. We will use this in scenarios where we are trying to estimate a population mean but do not know the population standard deviation (sigma). Power Poin
From playlist Applied Statistics (Entire Course)
The t Distribution: A BREWER’S Solution for Small Samples (13-4)
In the early days of statistics, the lack of replicability created skepticism that statistics could be a science. When using small samples, the results were inconsistent. William Sealy Gosset, a scientist-brewer at Guinness Brewing Company solved the problem of small sample sizes by adjust
From playlist Estimating Intervals, Point Estimators, and Confidence Intervals (WK 13 - QBA 237)
Confidence Intervals using a t Distribution when Estimating Population (Week 13C)
Unfortunately, we rarely know the mean and SD of the population we are sampling. Yes, we can estimate population parameters from our sample statistics, but the SD estimations are biased when our sample sizes are small. Therefore, we need to adjust for that bias using a t distribution and a
From playlist Basic Business Statistics (QBA 237 - Missouri State University)
Guinness, Student, and the History of t Tests (10-1)
We concluded our lesson on z tests with the sad realization that z tests rarely get used in the real world. Instead of using a z test we compare samples to populations using a t test. William Sealy Gosset, a master brewer and a scientist at the Guinness brewery in Dublin, Ireland solved th
From playlist WK10 One Sample t Tests - Online Statistics for the Flipped Classroom
ANOVA.4.F Distribution Sums of Squares 4
This video is brought to you by the Quantitative Analysis Institute at Wellesley College. The material is best viewed as part of the online resources that organize the content and include questions for checking understanding: https://www.wellesley.edu/qai/onlineresources
From playlist ANOVA
07e Python Data Analytics: Hypothesis Testing Interactive
Interactive discussion of hypothesis testing with a short lecture and use of my interactive hypothesis testing based on Python in Jupyter Notebook. Teh code is available on my GitHub repository (GeostatsGuy) at https://github.com/GeostatsGuy/PythonNumericalDemos/blob/master/Interactive_Hyp
From playlist Data Analytics and Geostatistics