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Figure 2 | Theoretical Biology and Medical Modelling

Figure 2

From: Cosinor-based rhythmometry

Figure 2

Single-component single cosinor: hypothesis testing and parameter estimation. A cosine curve with a given period is fitted to the data (top) by least squares. This approach consists of minimizing the sum of squared deviations between the data and the fitted cosine curve. The larger this residual sum of squares is, the greater the uncertainty of the estimated parameters is. This is illustrated by the elliptical 95% confidence region for the amplitude-acrophase pair (bottom). When the error ellipse does not cover the pole, the zero-amplitude (no-rhythm) test is rejected and the alternative hypothesis holds that a rhythm with the given period is present in the data (left). Conservative 95% confidence limits for the amplitude and acrophase can then be obtained by drawing concentric circles and radii tangent to the error ellipse, respectively. When the error ellipse covers the pole, the null hypothesis of no-rhythm (zero amplitude) is accepted (right). Results (P-value from the zero-amplitude test, percentage rhythm or proportion of the overall variance accounted for by the fitted model, MESOR ± SE, amplitude and 95% confidence limits, acrophase and 95% confidence limits) are listed in each case. © Halberg Chronobiology Center.

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