# Inverts the regression-based TOST equivalence test

### Description

This function generates the TOST intervals for the intercept and the slope of the regression of y on x, and determines the smallest region of indifference in each case that would reject the null hypothesis of dissimilarity.

### Usage

1 | ```
equiv.p(x, y, alpha = 0.05)
``` |

### Arguments

`x` |
The predictor variable - perhaps the model predictions |

`y` |
The response variable - perhaps the observations |

`alpha` |
The size of the test |

### Details

The generated confidence intervals are corrected for experiment-level size of alpha using Bonferroni.

### Value

A list of two items:

`Intercept` |
The smallest half-length of the interval that leads to rejection of the null hypothesis of dissimilarity for the intercept, in the units of y. |

`Slope` |
The smallest half-length of the interval that leads to rejection of the null hypothesis of dissimilarity for the slope, in the units of the slope. |

### Note

The accuracy of the output of this function is contingent on the usual regression assumptions, which are not checked here. Caveat emptor!

### Author(s)

Andrew Robinson A.Robinson@ms.unimelb.edu.au

### References

Robinson, A.P., and R.E. Froese. 2004. Model validation using equivalence tests. Ecological Modelling 176, 349–358.

Robinson, A.P., R.A. Duursma, and J.D. Marshall. 2005. A regression-based equivalence test for model validation: shifting the burden of proof. Tree Physiology 25, 903-913.

### See Also

`tost.data`

### Examples

1 2 |