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Example sentences for: williams-

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The Watson-Williams-Stevens test returns an F-statistic for the comparison of vectors between two groups to determine whether they represent significantly different estimates of phase (see Figures 5, 6and [ 27 32 ] for further detail).
It's the WP that passes along the reward doctors received for participating--a bottle of Williams-Sonoma tomato sauce.
In this case two average vectors are compared, and an F-statistic (Watson-Williams-Stevens test in [ 63 ] ) is calculated to test whether the means are drawn from the same population or not.
The angle of the vector corresponds to the mean phase for the group of points, and the magnitude of the vector represents the variability in the phase estimates [ 32 ] . The Watson-Williams-Stevens statistic was applied to evaluate whether two such vectors are significantly different from one another [ 32 ] . Significant differences were evident in the phase of these two clock genes' cyclical expression under a light-dark cycle, for all tissues except isolated antennal pairs and the heads (see Figure 7) and 8.