Select the method or formula of your choice.

A commonly used measure of the center of a batch of numbers. The mean is also called the average. It is the sum of all observations divided by the number of (nonmissing) observations.

Term | Description |
---|---|

x_{i} | i^{th} observation |

N | number of nonmissing observations |

The sample standard deviation provides a measure of the spread of your data. It is equal to the square root of the sample variance.

If the column contains *x* _{1}, *x* _{2},..., *x* _{N}, with mean , then the standard deviation of the sample is:

Term | Description |
---|---|

x _{i} | i ^{th} observation |

mean of the observations | |

N | number of nonmissing observations |

The variance measures how spread out the data are about their mean. The variance is equal to the standard deviation squared.

Term | Description |
---|---|

x_{i} | i^{th} observation |

mean of the observations | |

N | number of nonmissing observations |

Term | Description |
---|---|

x _{i} | i ^{th} observation |

The smallest value in your data set.

The sample median is in the middle of the data: at least half the observations are less than or equal to it, and at least half are greater than or equal to it.

Suppose you have a column that contains N values. To calculate the median, first order your data values from smallest to largest. If N is odd, the sample median is the value in the middle. If N is even, the sample median is the average of the two middle values.

For example, when N = 5 and you have data x_{1}, x_{2}, x_{3}, x_{4}, and x_{5}, the median = x_{3}.

When N = 6 and you have ordered data x_{1}, x_{2}, x_{3}, x_{4}, x_{5},and x_{6}:

where x_{3} and x_{4} are the third and fourth observations.

The largest value in your data set.

Term | Description |
---|---|

mean of the i^{th} resample | |

B | number of resamples |

N | number of observations in the original sample |

Term | Description |
---|---|

mean of the resamples | |

B | number of resamples |

mean of the i^{th} resample |

The calculation of the p-value depends on the alternative hypothesis.

**Mean less than hypothesized value:****Mean not equal to hypothesized value:****Mean greater than hypothesized value:**

Term | Description |
---|---|

l | number of bootstrap means that are less than or equal to the sample mean |

u | number of bootstrap means that are greater than or equal to the sample mean |

β | number of resamples |

n_{l} | number of bootstrap means that are less than or equal to μ_{0} − d |

n_{u} | number of bootstrap means that are greater than or equal to μ_{0} + d |

μ_{0} | hypothesized value |

d | |

mean of the observed sample |