What is a 'T Distribution'
A T distribution is a type of probability distribution that is appropriate for estimating population parameters for small sample sizes and unknown population variances. A T distribution resembles a normal distribution, but it differs from the normal distribution by its degrees of freedom. A T distribution has a smaller number of independent observations. However, the higher the degrees of freedom, the closer that distribution will resemble a standard normal distribution with a mean of 0, and a standard deviation of 1. The T distribution is also known as the "Student's T Distribution."
BREAKING DOWN 'T Distribution'
When a sample of a population is sufficiently large, the sample will follow a normal distribution. A zscore can be calculated with a known population standard deviation. But when a sample is not large enough, or the population standard deviation is unknown, a tscore must be calculated as a basis for the T distribution.
The tscore (or tstatistic or tvalue) formula is the sample mean minus the population mean divided by the quotient of the standard deviation of the sample and the square root of the sample size.
Application Example of a T Distribution
The Centers for Disease Control and Prevention (CDC) regularly conducts studies on the prevalence of diseases or chronic conditions. The methodology is consistently applied for each study. According to the current methodology, "when sample sizes ... are less than 50, as they are in some of the subgroup tables, the standard error may be large relative to the prevalence value, leading to a wide 95% confidence interval," in which case "it is appropriate to use values of the tdistribution to compute confidence intervals." A confidence interval is the probability that a value will fall between an upper and lower bound of a probability distribution. For example, the CDC calculated that at a 95% confidence interval 6.5% to 11.6% of children in New York suffered from asthma in 2014. The sample size was only 752 children, which made use of the T distribution suitable.

Sampling
A process used in statistical analysis in which a predetermined ... 
Central Limit Theorem  CLT
A statistical theory that states that given a sufficiently large ... 
Probability Distribution
A statistical function that describes all the possible values ... 
Sample Size Neglect
Sample size neglect occurs when an individual infers too much ... 
Attribute Sampling
Attribute sampling is a statistical method typically used in ... 
Stratified Random Sampling
Stratified random sampling is a method of sampling that involves ...

Investing
How to Use Stratified Random Sampling
Stratified random sampling is a technique best used with a sample population easily broken into distinct subgroups. Samples are then taken from each subgroup based on the ratio of the subgroupâ€™s ... 
Investing
Optimize your portfolio using normal distribution
Normal or bell curve distribution can be used in portfolio theory to help portfolio managers maximize return and minimize risk. 
Investing
Lognormal and normal distribution
When and why do you use lognormal distribution or normal distribution for analyzing securities? Lognormal for stocks, normal for portfolio returns. 
Investing
Hypothesis testing in finance: Concept and examples
When you're indecisive about an investment, the best way to keep a cool head might be test various hypotheses using the most relevant statistics. 
Investing
Computing Historical Volatility in Excel
We examine how annualized historical volatility is computed from daily log returns, variance and standard deviation. 
Retirement
Top 3 T. Rowe Funds for Retirement Diversification in 2016
Find out which T. Rowe Price funds to use to create a diversified retirement income portfolio for current income, income growth and capital preservation. 
Financial Advisor
4 Best T. Rowe Price Mutual Funds
Learn about four of the best T. Rowe Price mutual funds that have shown strong performance with reasonable net expense ratios, outperforming most peers. 
Financial Advisor
PRDGX, PRSIX, TRREX: T. Rowe Price Funds for Income Seekers
Find out which T. Rowe Price mutual funds to use to create a diversified income portfolio for current income, income growth and capital preservation. 
Investing
Expect Big Capital Gains Distributions from These Funds (AGTHX, ACRNX)
The steady rise in the markets since 2009 has led to some outsized gains in a few funds that are finally being realized as longterm winning holdings. 
Investing
Why Standard Deviation Should Matter to Investors
Think of standard deviation as a thermometer for risk, or better yet, anxiety.

What is the difference between systematic sampling and cluster sampling?
Learn about the differences between systematic sampling and cluster sampling, including how the samples are created for each ... Read Answer >> 
What's the difference between a representative sample and a random sample?
Explore the differences between representative samples and random samples, and discover how they are often used in tandem ... Read Answer >> 
What are the advantages and disadvantages of using systematic sampling?
Learn about the primary advantages and disadvantages of using a systematic sampling method when conducting research of a ... Read Answer >> 
How do I calculate the standard error using Matlab?
Learn how to calculate the standard error for a sample statistical measure, such as the sample mean, using standard Matlab ... Read Answer >> 
What are the advantages of using a simple random sample to study a larger population?
Learn how simple random sampling works and what advantages it offers over other sampling methods when selecting a research ... Read Answer >> 
What is the difference between a simple random sample and a stratified random sample?
Learn about the differences between simple random sampling and stratified random sampling, and the advantages of each method. Read Answer >>