What is a 'TTest'
A ttest is an analysis of two populations means through the use of statistical examination; a ttest with two samples is commonly used with small sample sizes, testing the difference between the samples when the variances of two normal distributions are not known.
A ttest looks at the tstatistic, the tdistribution and degrees of freedom to determine the probability of difference between populations; the test statistic in the test is known as the tstatistic. To conduct a test with three or more variables, an analysis of variance (ANOVA) must be used.
BREAKING DOWN 'TTest'
A form of hypothesis testing, the ttest is just one of many tests used for this purpose. Statisticians must use tests other than the ttest to examine more variables, as well as for test with larger sample sizes. For a large sample size, statisticians use a ztest. Other testing options include the chisquare test and the ftest.Statistical Analysis of the TTest
The formula used to calculate the test is a ratio: The top portion of the ratio is the easiest portion to calculate and understand, as it is simply the difference between the means or averages of the two samples. The lower half of the ratio is a measurement of the dispersion, or variability, of the scores. The bottom part of this ratio is known as the standard error of the difference. To compute this part of the ratio, the variance for each sample is determined and is then divided by the number of individuals the compose the sample, or group. These two values are then added together, and a square root is taken of the result.
Example
For example, consider that an analyst wants to study the amount that Pennsylvanians and Californians spend, per month, on clothing. It would not be practical to record the spending habits of every individual (or family) in both states, thus a sample of spending habits is taken from a selected group of individuals from each state. The group may be of any small to moderate size — for this example, assume that the sample group is 200 individuals.
The average amount for Pennsylvanians comes out to $500; the average amount for Californians is $1,000. The ttest questions whether the different between the groups is representative of a true difference between people in Pennsylvania and people in California in general or if it is likely a meaningless statistical difference. In this example, if, theoretically, all Pennsylvanians spent $500 per month on clothing and all Californians spent $1,000 per month on clothing, it is highly unlikely that 200 randomly selected individuals all spent that exact amount, respective to state. Thus, if an analyst or statistician yielded the results listed in the example above, it is safe to conclude that the difference between sample groups is indicative of a significant difference between the populations, as a whole, of each state.

Sampling Distribution
A sampling distribution is a probability distribution of a statistic ... 
ZTest
A ztest is a statistical test used to determine whether two ... 
Sample
A sample is a smaller, manageable version of a larger group. ... 
Central Limit Theorem  CLT
A statistical theory that states that given a sufficiently large ... 
Systematic Sampling
Systematic sampling is a probability sampling method in which ... 
T Distribution
A T distribution is a type of probability function that is appropriate ...

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 subgroup’s ... 
Investing
Using Historical Volatility To Gauge Future Risk
Use these calculations to uncover the risk involved in your investments. 
Investing
How Vanguard Index Funds Work
Learn how Vanguard index funds work. See how the index sampling technique allows Vanguard to charge low expense ratios that can save investors money. 
Trading
Exploring the Exponentially Weighted Moving Average
Learn how to calculate a metric that improves on simple variance. 
Insights
Which Consumer Genetic Tests Are FDAApproved?
Now you can get some genetic tests without going to a doctor. Should you? 
Financial Advisor
5 Powerful Website Tools Every Advisor Needs
Topperforming financial advisor websites have these five features in common. 
Managing Wealth
An Investor's Guide To Bank StressTesting
Just how are bank stress tests performed and what is the logic behind them? And is a stress test useful for evaluating a bank's stock? 
Investing
Find the right fit with probability distributions
Discover a few of the most popular probability distributions and how to calculate them. 
Personal Finance
8 Signs Your Neighborhood Is On The Upswing
If you were hardhit by the real estate crash, you may be wondering when things will get better for you. We show you how to keep tabs.

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 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 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 >> 
What are the disadvantages of using a simple random sample to approximate a larger ...
Learn what a simple random sample is, how researchers use it as a statistical tool and the disadvantages it carries when ... Read Answer >> 
What are the pros and cons of stratified random sampling?
Stratified random sampling provides a more accurate sampling of a population, but can be disadvantageous when researchers ... Read Answer >> 
What is the difference between the standard error of means and standard deviation?
Learn about the difference between the standard error of the mean and the standard deviation and how standard deviation is ... Read Answer >>