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− | == $t$ Tests == | + | == Family of $t$ Tests == |

− | $t$-tests is a family of [[Hypothesis Testing|Statistical tests]] that use $t$-statistics | + | $t$-tests is a family of [[Hypothesis Testing|Statistical tests]] that use $t$-statistics |

+ | * critical values come from the [[t Distribution|$t$-distribution]] - used for calculating $p$-values | ||

+ | == $t$ Tests == | ||

The following tests are $t$-tests: | The following tests are $t$-tests: | ||

− | * | + | * [[One-Sample t-test|One-Sample $t$-test]] - for comparing the mean of a sample against some given mean |

− | * | + | * [[Two-Sample t-test|Two-Sample $t$-test]] - for comparing the means of two samples |

− | * | + | * [[Paired t-test|Paired $t$-test]] - for Matching Pairs setup |

− | * | + | * [[Pairwise t-test|Pairwise $t$-test]] - for comparing the means of more than two samples |

− | |||

=== Assumptions === | === Assumptions === | ||

Assumptions for $t$ tests are similar to the assumptions of the [[z-tests|$z$-tests]] | Assumptions for $t$ tests are similar to the assumptions of the [[z-tests|$z$-tests]] | ||

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− | === vs [[z-tests|$z$-tests]] === | + | === $t$-tests vs [[z-tests|$z$-tests]] === |

Sample Size | Sample Size | ||

* the sample size can be smaller than for $z$-tests | * the sample size can be smaller than for $z$-tests | ||

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* this is exactly the correction we need to account for poorly estimated [[Standard Error]] when the sample size is not big | * this is exactly the correction we need to account for poorly estimated [[Standard Error]] when the sample size is not big | ||

− | + | == Alternatives to $t$-Tests == | |

− | + | * http://stats.stackexchange.com/questions/183456/have-the-reports-of-the-death-of-the-t-test-been-greatly-exaggerated | |

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* http://projectile.sv.cmu.edu/research/public/talks/t-test.htm | * http://projectile.sv.cmu.edu/research/public/talks/t-test.htm | ||

+ | [[Category:T-Test]] | ||

[[Category:Statistics]] | [[Category:Statistics]] | ||

[[Category:Statistical Tests]] | [[Category:Statistical Tests]] | ||

[[Category:R]] | [[Category:R]] |

$t$-tests is a family of Statistical tests that use $t$-statistics

- critical values come from the $t$-distribution - used for calculating $p$-values

The following tests are $t$-tests:

- One-Sample $t$-test - for comparing the mean of a sample against some given mean
- Two-Sample $t$-test - for comparing the means of two samples
- Paired $t$-test - for Matching Pairs setup
- Pairwise $t$-test - for comparing the means of more than two samples

Assumptions for $t$ tests are similar to the assumptions of the $z$-tests

- Observations are independent (if less than 10% of population is sampled, then we can make sure it's satisfied)
- Sample size is sufficiently large so C.L.T. holds
- Moderate skew, few outliers (not too extreme)

Sample Size

- the sample size can be smaller than for $z$-tests
- so it can be smaller than 30 - after 30 we can safely use $z$-tests with almost the same outcomes

$t$-distribution:

- the tails are thicker than for $N(0,1)$ and observations are more likely to fall within 2$\sigma$ from the mean
- this is exactly the correction we need to account for poorly estimated Standard Error when the sample size is not big