### This post shows how to use the IDP statistical package to compare sport performance.

Climb | 2013 | 2014 |
---|---|---|

A | 29m16s | 29m14s |

B | 29m03s | 29m02s |

C | 23m28s | 23m01s |

D | 48m04s | 45m56s |

E | 28m51s | 30m43s |

F | 15m09s | 14m53s |

*Wilcoxon signed-rank test*. Our goal is to employ this test to assess whether my climbing performance on 2013 are worse (larger ascent time) than that on 2014. Therefore, we are going to perform a one-sided test.

In R this test can be performed by means of the function **wilcox.test** as follows:

T14 <- c(29*60+14, 29*60+02, 23*60+01, 45*60+56, 30*60+43, 14*60+53) T13 <- c(29*60+16, 29*60+03, 23*60+28, 48*60+04, 28*60+51, 15*60+09) wilcox.test(T13,T14,"greater", paired=TRUE)

**signrank**:

T14=[29*60+14, 29*60+02, 23*60+01, 45*60+56, 30*60+43, 14*60+53]; T13=[29*60+16, 29*60+03, 23*60+28, 48*60+04, 28*60+51, 15*60+09]; [p,h]=signrank(T13,T14,'tail','right')

*Imprecise Dirichlet Process*(IDP).

The details of the test can be found in this [paper] and to run the test you need to download and run the code [here].

In R, this test can be performed as follows

isignrank.test(T14,T13,"greater")

while in Matlab*:*

[prob,h]=isignrank(T13,T14,'tail','right','alpha',0.05);

*Wilcoxon signed-rank test*are: (i) the test is Bayesian and, thus, it returns the posterior probability of the hypothesis “T13 is larger than T14”; (ii) the test is imprecise, which means that it actually returns the lower and upper probabilities of the hypothesis “T13 is larger than T14”.

*IDP based test*and the

*Wilcoxon signed-rank test*agree in this case

*.*

__the posterior probabilities__. In fact, since the lower probability is about 0.75, we can actually declare that “T13 is larger than T14” with posterior probability 1-alpha=0.75.

In all the other cases, 0.75<1-alpha<0.93, we are in an indeterminate situation.

This means that the result of the hypothesis test is prior independent, i.e., it changes with the choice of the prior base measure of the Dirichlet process. In other words, this means that the evidence from the observations is not enough to declare either that the probability of the hypothesis being true is larger or smaller than the desired value 1 − alpha (the result is prior dependent); more measurements are necessary to take a decision.