# Student's t-Test

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A Student's t-Test is a parametric statistical test whose test statistic follows a Student's t-distribution under the null hypothesis.

**AKA:**t-Value Test.**Context:**- It can range from being a Paired t-Test to being an Unpaired t-Test.
- It can (typically) be applied when the Test Statistic follows a Normal Distribution.
- It can range from being a One Sample t-Test, to being a Two-Sample t-Test, to being an n-Sample t-Test.
- It can be used as a Paired Difference Test, such as a Paired Difference Test with Equal Variance and Unequal Sample Size.
- It can (typically) assume that the distribution of Sample Means will approximate a Normal Distribution (parametric data) and Equal Variances.

**Example(s):****Counter-Example(s):**- a Chi-Squared Test.
- a Z-Value Test.
- an ANOVA.
- a Welch's t-Test.
- a Treatment-Controlled Experiment.

**See:**Statistical Significance, Sample Average, Sample Variance.

## References

### 2011

- (Wikipedia, 2011) ⇒ http://en.wikipedia.org/wiki/Student%27s_t-test
- A
is any statistical hypothesis test in which the test statistic follows a Student's*t*-test*t*distribution if the null hypothesis is supported. 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. When the scaling term is unknown and is replaced by an estimate based on the data, the test statistic (under certain conditions) follows a Student's*t*distribution.

- A
- http://en.wikipedia.org/wiki/Student%27s_t-test#Assumptions
- Most
*t*-test statistics have the form [math]\displaystyle{ T=\frac{Z}{s} }[/math], where Z*and*s*are functions of the data. Typically,*Z*is designed to be sensitive to the alternative hypothesis (i.e. its magnitude tends to be larger when the alternative hypothesis is true), whereas*s*is a scaling parameter that allows the distribution of*T to be determined.The assumptions underlying a

*t*-test are that*Z*follows a standard normal distribution under the null hypothesis.*ps*^{2}follows a χ^{2}distribution with*p*degrees of freedom under the null hypothesis, where*p*is a positive constant*Z*and*s*are independent.

- Most

### 2008

- http://www.introductorystatistics.com/escout/main/Glossary.htm
- t test: A special hypothesis test about the population mean used when the population is known to be normally distributed, the sample size is small, and the population standard deviation is unknown.