What is a 'TTest'
A ttest is an analysis framework used to determine the difference between two sample means from two normally distributed populations with unknown variances. A ttest is an analysis of two populations means through the use of statistical examination; analysts commonly use a ttest with two samples with small sample sizes, testing the difference between the samples when they do not know the variances of two normal distributions.
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 the tstatistic. To conduct a test with three or more variables, one must use an analysis of variance.
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 and tests 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 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 the standard error of the difference. To compute this part of the ratio, one must determine the variance for each sample and divide by the number of individuals comprising the sample or group. These two values are then added together, and a square root is taken of the result.
Example of a TTest
For example, consider that an analyst wants to study the amount that Pennsylvanians and Californians spend on clothing per month. 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, and the average amount for Californians is $1,000. The ttest questions whether the difference between the groups represents a true difference between people in Pennsylvania and people in California or if it is likely a meaningless statistical difference. In this example, if all Pennsylvanians spent $500 per month on clothing and all Californians spent $1,000 per month, 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 indicates a significant difference between the populations of each state.

Sampling
Sampling is a process used in statistical analysis in which a ... 
Sampling Distribution
A sampling distribution is a probability distribution of a statistic ... 
T Distribution
A T distribution is a type of probability function that is appropriate ... 
Simple Random Sample
A simple random sample is a subset of a statistical population ... 
Analysis Of Variances  ANOVA
Analysis of variances (ANOVA) is a statistical examination of ... 
Frequency Of Exclusion
Frequency of exclusion refers to the rate of occurrence of a ...

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 ... 
Personal Finance
Birch Box Review: Is It Worth It?
Learn more about the convenience of the subscription beauty box industry, and discover why the Birchbox company in particular has become so popular. 
Personal Finance
Jump Start Your Financial Career With The BAT
The BAT is quickly becoming known in the job market as a tool to provide a window into the minds of those seeking financial jobs. 
Investing
CPA Exam Tips
Tips for the CPA exam  how to approach it, what to expect, and the time it takes to complete. 
Investing
Most Common Probability Distributions
In this article, we'll go over a few of the most popular probability distributions and show you how to calculate them. 
Investing
Two Approaches to Building a LowRisk Portfolio
Building a portfolio consisting of lowrisk assets is achieved primarily by using one of two principal lowvolatility strategies. 
Investing
Bet Smarter With the Monte Carlo Simulation
This technique can reduce uncertainty in estimating future outcomes.

What assumptions are made when conducting a ttest?
Learn what a ttest is and discover the five standard assumptions made regarding the validity of sampling and data used in ... 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 >> 
When is it better to use systematic over simple random sampling?
Learn when systematic sampling is better than simple random sampling, such as in the absence of data patterns and when there ... Read Answer >> 
What are the disadvantages of using a simple random sample to approximate a larger ...
Learn here what a simple random sample is, how researchers use it as a statistical tool and the disadvantages it carries ... 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's an example of stratified random sampling?
Stratified random sampling divides a population into subgroups or strata, whereby the members in each of the stratum formed ... Read Answer >>