# Verification of results

## Reproduce a trajectory

    cerw <- reproduce.track.3d(niclas, DEM = dem)

The simulated trajectories result should be tested statistically. The first argument of the `test.verification.3d()` function is the original track to be tested against. The second argument is either a single track or a list of multiple tracks.

## Kolmogorov-Smirnov test

By setting `test = "ks"` a two-sample Kolmogorov-Smirnov test is carried out on the distributions of turn angles, lift angles and step lengths of the two tracks.

    tests <- test.verification.3d(niclas, cerw, test = "ks", plot = FALSE)
    #>   |*** Two-sample Kolmogorov-Smirnov test ***
    #>   |H0: Probability distributions do not differ significantly
    #>   |H1: Probability distributions differ significantly
    #>   |Turn angle  - p-value: 0.958 > 0.05, *H0*, autodifferences - p-value: 0.951 > 0.05, *H0*
    #>   |Lift angle  - p-value: 0.239 > 0.05, *H0*, autodifferences - p-value: 0.03 < 0.05, *H1*
    #>   |Step length - p-value: 0.958 > 0.05, *H0*, autodifferences - p-value: 0.998 > 0.05, *H0*

## One-sample t-test

By choosing `test = "ttest"` a random sample, without replacement is taken from the longer track, to shorten it to the length of the longer track. The order of the shorter track is also sampled randomly. Then the two randomly ordered vectors of turn angles, lift angles and step lengths are substracted from each other. If the both tracks stem from the same distributions the the mean deviatio should tend to towards zero, therefore the difference is tested two-sided against mu = 0 with a one-sample t-test.

    tests <- test.verification.3d(niclas, cerw, test = "ttest", plot = FALSE)
    #>   |*** One Sample t-test ***
    #>   |H0: Difference between tracks does not differ significantly from 0
    #>   |H1: Difference between tracks differs significantly from 0
    #>   |Turn angle  - p-value: 0.527 > 0.05, *H0*
    #>   |Lift angle  - p-value: 0.898 > 0.05, *H0*
    #>   |Step length - p-value: 0.704 > 0.05, *H0*