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. 2017 Feb 22;104(1):129–139. doi: 10.1093/biomet/asw071

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Fig. 2. — The powers of (black solid), (grey solid), Pearson correlation (grey circles), distance correlation (black dashed), the method of Heller et al. (2016) (black dotted) and (black circles) for testing independence between and when the underlying true functional relationships are linear, quadratic, cubic, radical, low-frequency sine, triangle, high-frequency sine, and piecewise constant. The horizontal axis represents , a monotone function of the signal-to-noise ratio, and the vertical axis is the power. We chose and performed 1000 replications for each relationship and each value.

Inline graphic — The powers of (black solid), (grey solid), Pearson correlation (grey circles), distance correlation (black dashed), the method of Heller et al. (2016) (black dotted) and (black circles) for testing independence between and when the underlying true functional relationships are linear, quadratic, cubic, radical, low-frequency sine, triangle, high-frequency sine, and piecewise constant. The horizontal axis represents , a monotone function of the signal-to-noise ratio, and the vertical axis is the power. We chose and performed 1000 replications for each relationship and each value.