One-Sample t-Test
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An One-Sample t-Test is a student's t-test based on a single sample and used to test whether a population mean differs from the observed sample mean.
- AKA: t-Value Test, Single-Sample t-Test, One-Sample Location Test.
- Context:
- It is based on an One-Sample t-Statistic.
- It is described by an One-Sample t-Test Task and solved by an One-Sample t-Test System.
- It is used when population mean is unknown. A Z-Test replaces an one-sample t-test when the population mean is known.
- It is based on numerical data (i. e. interval data and ratio data) from a single sample drawn from a single population.
- It is a parametric statistical test for which the population mean ([math]\displaystyle{ \mu }[/math]) and population variance ([math]\displaystyle{ \sigma^2 }[/math]) are parameter estimations based on the sample data.
- It can range being One-Tailed Hypothesis Test to being a Two-Tailed Hypothesis Test.
- Example(s)
- Counter-Example(s):
- See: Statistical Significance, Sample Average, Sample Variance.
References
2017
- (Stat Trek, 2017) ⇒ http://stattrek.com/statistics/dictionary.aspx?definition=One-sample%20t-test
- A one-sample t-test is used to test whether a population mean is significantly different from some hypothesized value.
(...) The test statistic is a t statistic (t) defined by the following equation.
- A one-sample t-test is used to test whether a population mean is significantly different from some hypothesized value.
- [math]\displaystyle{ t = \frac{(x - M )}{s \sqrt{n}} }[/math]
- where [math]\displaystyle{ x }[/math] is the observed sample mean, [math]\displaystyle{ M }[/math] is the hypothesized population mean (from the null hypothesis), and [math]\displaystyle{ s }[/math] is the standard deviation of the sample.
2011
- (Wikipedia, 2016) ⇒ http://en.wikipedia.org/wiki/Student%27s_t-test#One-sample_t-test
- In testing the null hypothesis that the population mean is equal to a specified value μ0, one uses the statistic
- [math]\displaystyle{ t = \frac{\overline{x} - \mu_0}{s/\sqrt{n}} }[/math]
- where [math]\displaystyle{ \overline{x} }[/math] is the sample mean, s is the sample standard deviation of the sample and n is the sample size. The degrees of freedom used in this test are n − 1. Although the parent population does not need to be normally distributed, the distribution of the population of sample means, [math]\displaystyle{ \overline {x} }[/math], is assumed to be normal. By the central limit theorem, if the sampling of the parent population is independent then the sample means will be approximately normal.[1] (The degree of approximation will depend on how close the parent population is to a normal distribution and the sample size, n.)
- ↑ George Box, William Hunter, and J. Stuart Hunter, Statistics for Experimenters, ISBN 978-0471093152, pp. 66–67.