# Multivariate regression: MANOVA table

## Simultaneous confidence intervals

Sometimes, we want to look at the differences between the means of a variable, for two different subsets. For example, we may want to test whether the mean age of male patients or female patients is different. One way to do this — to test the equality, according to two different types — is to look at the confidence interval for the difference between the respect means. In other words, we can look at a null hypothesis and hypothesis,

Or, alternatively,

To calculate the confidence interval, our multiplier will be the univariate t-statistic. However, we have to take into consideration the number of variables and the number of groupings,

Parameter | Description |
---|---|

t-multiplier | t for probability |

For example, for a 95% significance level, then our | |

m | |

t-multiplier probability | |

t-multiplier degrees of freedom | |

Spreadsheet formula | = ABS (T.INV ( |

So for example, if we have a sample with 4 variables, 3 groupings, and 516 observations, then, we have =T.INV(0.05/(4*3*2),513) which gives us a t-multiplier of 2.878. | |

p | Number of variables. |

g | Number of groupings. We calculate g as the number of groupings (subsets) that exist. For example, if we are testing a generic version of a drug, then we may have samples for a placebo, the brand name version, and the generic version. In that case, the number of groupings is |

n | Number of observations across all groupings being considered. If we are looking at just two groupings, then our n is the number of observations for those two groupings, rather than the total number of observations for all groupings. |

The number of observations in subgrouping | |

Once we have these components figured out, we can calculate the standard error for the confidence interval. | |

Standard error | |

W | To calculate W, we need the covariance matrix In other words, the separate covariances are pooled together according to the respective numbers of observations. |

When we are comparing the means for a variable | |

mean difference of variable | The mean difference is calculated as, |

Confidence interval | The confidence interval for the difference between the means between two groupings (subsets) within the sample, with one grouping called |