Table 1 Significance of stride parameter

From: Coordinating limbs and spine: (Pareto-)optimal locomotion in theory, in vivo, and in robots

cluster

size

(\({\hat{\phi }}_{spine},{\hat{\phi }}_{leg},{\hat{\ell }}_{leg}\))

Hotelling p

Cuzick-Edwards p

family

  

\(\begin{array}{l}\quad\,{{{\rm{d}}}}\quad\,\,\,\, {{{\rm{g}}}}\qquad\;\, {{{\rm{s}}}}\qquad\,\,\, {{{\rm{v}}}}\\ \left(\begin{array}{lccc}1&* * * &* * * &* * * \\ &1&* * * &* * * \\ &&1&* * \\ &&&1\end{array}\right)\end{array}\)

\(\begin{array}{l}\quad{{{\rm{d}}}}\qquad\,\,\,\,\,\,\, {{{\rm{g}}}}\qquad {{{\rm{s}}}}\qquad {{{\rm{v}}}}\\ \left(\begin{array}{lccc}1&* * * &* * &* * * \\ * * * &1&* &* \\ * * &o&1&* \\ * * * &* * * &* &1\end{array}\right)\end{array}\)

 dragons [d]

74

(20.3, 80.2, 0.679)

 geckos [g]

154

(23.6, 103, 0.576)

 skinks [s]

21

(27.6, 93.3, 0.549)

 varanids [v]

71

(19.6, 98.1, 0.469)

direction

  

\(\begin{array}{l}\quad{{{\rm{u}}}}\quad\,\,\,\, {{{\rm{d}}}}\qquad\,\, {{{\rm{1}}}}\\ \left(\begin{array}{lcc}1&* * * &* * * \\ &1&* * * \\ &&1\end{array}\right)\end{array}\)

\(\begin{array}{l}\quad{{{\rm{u}}}}\qquad\,\,\,\,\,\, {{{\rm{d}}}}\qquad\,\,\, {{{\rm{1}}}}\\ \left(\begin{array}{lcc}1&* * * &* * * \\ * * * &1&* * \\ * * * &* &1\end{array}\right)\end{array}\)

 up [u]

218

(24.8, 94.7, 0.621)

 down [d]

51

(16.4, 93.1, 0.505)

 level [l]

51

(16.6, 105, 0.442)

habitat

  

\(\begin{array}{l}\quad{{{\rm{t}}}}\qquad {{{\rm{s}}}}\qquad\,\, {{{\rm{a}}}}\\ \left(\begin{array}{ccc}1&* * * &* * \\ &1&* * * \\ &&1\end{array}\right)\end{array}\)

\(\begin{array}{l}\quad\,\,\,\,\,{{{\rm{t}}}}\qquad\,\,\, {{{\rm{s}}}}\qquad\,\,\, {{{\rm{a}}}}\\ \left(\begin{array}{ccc}1&* * * &* * \\ * * * &1&* * * \\ * * * &* * * &1\end{array}\right)\end{array}\)

 terrestrial [t]

73

(21.3, 96.2, 0.55)

 semi-arboreal [s]

52

(17.4, 94.7, 0.611)

 arboreal [a]

102

(25.5, 100, 0.545)

speed

  

\(\begin{array}{l}\quad\,{{{\rm{s}}}}\quad {{{\rm{m}}}}\quad\,\, {{{\rm{f}}}}\\ \left(\begin{array}{ccc}1&* &* * * \\ &1&* * * \\ &&1\end{array}\right)\end{array}\)

\(\begin{array}{l}\quad\,\,\,\,\,{{{\rm{s}}}}\quad\,\,\,\, {{{\rm{m}}}}\quad\,\,\, {{{\rm{f}}}}\\ \left(\begin{array}{ccc}1&* * &* * \\ o&1&* * \\ * * * &* * &1\end{array}\right)\end{array}\)

 slow [s]

124

(22.7, 93.1, 0.574)

 medium [m]

105

(24, 95.8, 0.615)

 fast [f]

91

(19.4, 101, 0.528)

  1. Significant differences between clusters are examined by Hotelling’s p value for each pair of three-dimensional centres – consisting of mean spine ROM (\({\hat{\phi }}_{spine}\)), mean leg ROM (\({\hat{\phi }}_{leg}\)), and mean leg length (\({\hat{\ell }}_{leg}\)) normalised to TLS length – and by Cuzick-Edwards’ p value with respect to the k = 3 nearest neighbours. Values between 0.05 and 1, i.e., non-significant test statistics, are marked with ’o’, values below 0.05 with one asterisk (*), values below 0.01 with two (**), and values below 10−4 with three (***). Note that while Hotelling’s tests are symmetric, Cuzick-Edwards’ are not. Abbreviations (behind the groups) are given also above the p-matrices for a better overview.
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