Date - time                : 15/10/2003 10:33:45

Data file name           : T°Alcoolisation.dta

 

Single Cosinor Test for one chosen period  

Studied period (T)          : 2.4700000E+01

 

1. Results by each series

Equation of the model : β  cos(2π t/T) + γ  sin(2π t/T) + α

 

Serie n°1

Solution model : 5.79E-02Cos(2π t/24.70)-3.97E-01Sin(2π t/24.70)+3.69E+01

Initial model      : 4.01E-01Cos((2π t/24.70)-4.86E+00)+3.69E+01

-  Model (ANOVA) is valid at the probability level     : 0.9500

 

1.1. Chronobiometric values :

- Amplitude                                                                       : 4.01E-01

  Amplitude Standard Error                                                  : 2.74E-02

  CI of Amplitude                                                                  : [3.46E-01 ; 4.57E-01]

- Dephasing -  Chronobiometric Acrophase (Radians)   : -4.86E+00

  Dephasing Standard Error                                                : 6.63E-02

  CI of Dephasing                                                                : [-4.99E+00 ; -4.73E+00]

- Dephasing -  Chronobiometric Acrophase (Degrees)  : -2.78E+02

  Dephasing Standard Error                                                : 3.80E+00

  CI of Dephasing                                                                : [-2.86E+02 ; -2.71E+02]

- Shifting  -  Chronobiometric MESOR                                : 3.69E+01

  Shifting Standard Error                                                      : 1.92E-02

  CI of Shifting                                                                      : [3.69E+01 ; 3.69E+01]

 

1.2. Chronobiometric parameters :

- Percent Rhythm                                                           : 72.47 %

- Percent Error                                                                : 27.53 %

- p-Value (H0: Amplitude=0)                                          : 0.0000

 

1.3. Chronobiometric test :

-  Ellipse Test (H0: β=0 And γ=0) for T =  2.4700000E+01 is significant at the probability level  : 0.9500

-  Area of the Confidence Ellipse  : 1.42E-02

 

1.4. Residuals distribution - Goodness of fit :

- Ajusted r² : 1.00E+00

- K-S Test (H0: Normal residuals distribution) is not significant at the probability level  : 0.9500

- k² Test (H0: Normal residuals distribution) is not significant at the probability level                               : 0.9500

- Average Test (H0: RS Average = 0) is not significant at the probability level                   : 0.9500

- Q Test (H0: Independent Residues) is significant at the probability level                                         : 0.9500

 

Serie n°2

Solution model : -4.42E-02Cos(2π t/24.70)-1.07E-01Sin(2π t/24.70)+3.70E+01

Initial model      : 1.16E-01Cos((2π t/24.70)-4.32E+00)+3.70E+01

-  Model (ANOVA) is valid at the probability level     : 0.9500

 

1.1. Chronobiometric values :

- Amplitude                                                                       : 1.16E-01

  Amplitude Standard Error                                                  : 2.71E-02

  CI of Amplitude                                                                  : [6.44E-02 ; 1.68E-01]

- Dephasing -  Chronobiometric Acrophase (Radians)   : -4.32E+00

  Dephasing Standard Error                                                : 2.16E-01

  CI of Dephasing                                                                : [-4.79E+00 ; -3.86E+00]

- Dephasing -  Chronobiometric Acrophase (Degrees)  : -2.48E+02

  Dephasing Standard Error                                                : 1.24E+01

  CI of Dephasing                                                                : [-2.74E+02 ; -2.21E+02]

- Shifting  -  Chronobiometric MESOR                                : 3.70E+01

  Shifting Standard Error                                                      : 1.86E-02

  CI of Shifting                                                                      : [3.69E+01 ; 3.70E+01]

 

1.2. Chronobiometric parameters :

- Percent Rhythm                                                           : 20.23 %

- Percent Error                                                                : 79.77 %

- p-Value (H0: Amplitude=0)                                          : 0.0001

 

1.3. Chronobiometric test :

-  Ellipse Test (H0: β=0 And γ=0) for T =  2.4700000E+01 is significant at the probability level  : 0.9500

-  Area of the Confidence Ellipse  : 1.33E-02

 

1.4. Residuals distribution - Goodness of fit :

- Ajusted r² : 1.00E+00

- K-S Test (H0: Normal residuals distribution) is not significant at the probability level  : 0.9500

- k² Test (H0: Normal residuals distribution) is not significant at the probability level                               : 0.9500

- Average Test (H0: RS Average = 0) is not significant at the probability level                   : 0.9500

- Q Test (H0: Independent Residues) is significant at the probability level                                         : 0.9500

 

Serie n°3

Solution model : -6.72E-02Cos(2π t/24.70)-1.10E-01Sin(2π t/24.70)+3.68E+01

Initial model      : 1.29E-01Cos((2π t/24.70)-4.17E+00)+3.68E+01

-  Model (ANOVA) is valid at the probability level     : 0.9500

 

1.1. Chronobiometric values :

- Amplitude                                                                       : 1.29E-01

  Amplitude Standard Error                                                  : 3.02E-02

  CI of Amplitude                                                                  : [7.22E-02 ; 1.86E-01]

- Dephasing -  Chronobiometric Acrophase (Radians)   : -4.17E+00

  Dephasing Standard Error                                                : 2.17E-01

  CI of Dephasing                                                                : [-4.63E+00 ; -3.70E+00]

- Dephasing -  Chronobiometric Acrophase (Degrees)  : -2.39E+02

  Dephasing Standard Error                                                : 1.24E+01

  CI of Dephasing                                                                : [-2.66E+02 ; -2.12E+02]

- Shifting  -  Chronobiometric MESOR                                : 3.68E+01

  Shifting Standard Error                                                      : 2.07E-02

  CI of Shifting                                                                      : [3.67E+01 ; 3.68E+01]

 

1.2. Chronobiometric parameters :

- Percent Rhythm                                                           : 20.56 %

- Percent Error                                                                : 79.44 %

- p-Value (H0: Amplitude=0)                                          : 0.0001

 

1.3. Chronobiometric test :

-  Ellipse Test (H0: β=0 And γ=0) for T =  2.4700000E+01 is significant at the probability level  : 0.9500

-  Area of the Confidence Ellipse  : 1.65E-02

 

1.4. Residuals distribution - Goodness of fit :

- Ajusted r² : 1.00E+00

- K-S Test (H0: Normal residuals distribution) is not significant at the probability level  : 0.9500

- k² Test (H0: Normal residuals distribution) is not significant at the probability level                               : 0.9500

- Average Test (H0: RS Average = 0) is not significant at the probability level                   : 0.9500

- Q Test (H0: Independent Residues) is significant at the probability level                                         : 0.9500

 

Serie n°4

Solution model : -5.28E-02Cos(2π t/24.70)-2.83E-01Sin(2π t/24.70)+3.69E+01

Initial model      : 2.88E-01Cos((2π t/24.70)-4.53E+00)+3.69E+01

-  Model (ANOVA) is valid at the probability level     : 0.9500

 

1.1. Chronobiometric values :

- Amplitude                                                                       : 2.88E-01

  Amplitude Standard Error                                                  : 2.82E-02

  CI of Amplitude                                                                  : [2.33E-01 ; 3.43E-01]

- Dephasing -  Chronobiometric Acrophase (Radians)   : -4.53E+00

  Dephasing Standard Error                                                : 9.19E-02

  CI of Dephasing                                                                : [-4.72E+00 ; -4.34E+00]

- Dephasing -  Chronobiometric Acrophase (Degrees)  : -2.59E+02

  Dephasing Standard Error                                                : 5.26E+00

  CI of Dephasing                                                                : [-2.70E+02 ; -2.49E+02]

- Shifting  -  Chronobiometric MESOR                                : 3.69E+01

  Shifting Standard Error                                                      : 1.95E-02

  CI of Shifting                                                                      : [3.69E+01 ; 3.70E+01]

 

1.2. Chronobiometric parameters :

- Percent Rhythm                                                           : 57.91 %

- Percent Error                                                                : 42.09 %

- p-Value (H0: Amplitude=0)                                          : 0.0000

 

1.3. Chronobiometric test :

-  Ellipse Test (H0: β=0 And γ=0) for T =  2.4700000E+01 is significant at the probability level  : 0.9500

-  Area of the Confidence Ellipse  : 1.46E-02

 

1.4. Residuals distribution - Goodness of fit :

- Ajusted r² : 1.00E+00

- K-S Test (H0: Normal residuals distribution) is not significant at the probability level  : 0.9500

- k² Test (H0: Normal residuals distribution) is not significant at the probability level                               : 0.9500

- Average Test (H0: RS Average = 0) is not significant at the probability level                   : 0.9500

- Q Test (H0: Independent Residues) is significant at the probability level                                         : 0.9500

 

Serie n°5

Solution model : 7.75E-02Cos(2π t/24.70)+4.76E-02Sin(2π t/24.70)+3.68E+01

Initial model      : 9.09E-02Cos((2π t/24.70)-5.51E-01)+3.68E+01

-  Model (ANOVA) is valid at the probability level     : 0.9500

 

1.1. Chronobiometric values :

- Amplitude                                                                       : 9.09E-02

  Amplitude Standard Error                                                  : 2.32E-02

  CI of Amplitude                                                                  : [4.71E-02 ; 1.35E-01]

- Dephasing -  Chronobiometric Acrophase (Radians)   : -5.51E-01

  Dephasing Standard Error                                                : 2.48E-01

  CI of Dephasing                                                                : [-1.09E+00 ; -1.63E-02]

- Dephasing -  Chronobiometric Acrophase (Degrees)  : -3.16E+01

  Dephasing Standard Error                                                : 1.42E+01

  CI of Dephasing                                                                : [-6.22E+01 ; -9.34E-01]

- Shifting  -  Chronobiometric MESOR                                : 3.68E+01

  Shifting Standard Error                                                      : 1.63E-02

  CI of Shifting                                                                      : [3.67E+01 ; 3.68E+01]

 

1.2. Chronobiometric parameters :

- Percent Rhythm                                                           : 17.78 %

- Percent Error                                                                : 82.22 %

- p-Value (H0: Amplitude=0)                                          : 0.0004

 

1.3. Chronobiometric test :

-  Ellipse Test (H0: β=0 And γ=0) for T =  2.4700000E+01 is significant at the probability level  : 0.9500

-  Area of the Confidence Ellipse  : 1.02E-02

 

1.4. Residuals distribution - Goodness of fit :

- Ajusted r² : 1.00E+00

- K-S Test (H0: Normal residuals distribution) is not significant at the probability level  : 0.9500

- k² Test (H0: Normal residuals distribution) is not significant at the probability level                               : 0.9500

- Average Test (H0: RS Average = 0) is not significant at the probability level                   : 0.9500

- Q Test (H0: Independent Residues) is significant at the probability level                                         : 0.9500

 

Serie n°6

Solution model : -1.07E-01Cos(2π t/24.70)-3.61E-01Sin(2π t/24.70)+3.68E+01

Initial model      : 3.76E-01Cos((2π t/24.70)-4.42E+00)+3.68E+01

-  Model (ANOVA) is valid at the probability level     : 0.9500

 

1.1. Chronobiometric values :

- Amplitude                                                                       : 3.76E-01

  Amplitude Standard Error                                                  : 2.87E-02

  CI of Amplitude                                                                  : [3.21E-01 ; 4.32E-01]

- Dephasing -  Chronobiometric Acrophase (Radians)   : -4.42E+00

  Dephasing Standard Error                                                : 7.09E-02

  CI of Dephasing                                                                : [-4.57E+00 ; -4.28E+00]

- Dephasing -  Chronobiometric Acrophase (Degrees)  : -2.53E+02

  Dephasing Standard Error                                                : 4.06E+00

  CI of Dephasing                                                                : [-2.62E+02 ; -2.45E+02]

- Shifting  -  Chronobiometric MESOR                                : 3.68E+01

  Shifting Standard Error                                                      : 1.97E-02

  CI of Shifting                                                                      : [3.68E+01 ; 3.69E+01]

 

1.2. Chronobiometric parameters :

- Percent Rhythm                                                           : 69.96 %

- Percent Error                                                                : 30.04 %

- p-Value (H0: Amplitude=0)                                          : 0.0000

 

1.3. Chronobiometric test :

-  Ellipse Test (H0: β=0 And γ=0) for T =  2.4700000E+01 is significant at the probability level  : 0.9500

-  Area of the Confidence Ellipse  : 1.50E-02

 

1.4. Residuals distribution - Goodness of fit :

- Ajusted r² : 1.00E+00

- K-S Test (H0: Normal residuals distribution) is not significant at the probability level  : 0.9500

- χ² Test (H0: Normal residuals distribution) is not significant at the probability level    : 0.9500

- k² Test (H0: Normal residuals distribution) is not significant at the probability level                               : 0.9500

- Average Test (H0: RS Average = 0) is not significant at the probability level                   : 0.9500

- Q Test (H0: Independent Residues) is significant at the probability level                                         : 0.9500

 

Serie n°7

Solution model : -1.92E-01Cos(2π t/24.70)-9.11E-02Sin(2π t/24.70)+3.66E+01

Initial model      : 2.13E-01Cos((2π t/24.70)-3.58E+00)+3.66E+01

-  Model (ANOVA) is valid at the probability level     : 0.9500

 

1.1. Chronobiometric values :

- Amplitude                                                                       : 2.13E-01

  Amplitude Standard Error                                                  : 2.67E-02

  CI of Amplitude                                                                  : [1.62E-01 ; 2.63E-01]

- Dephasing -  Chronobiometric Acrophase (Radians)   : -3.58E+00

  Dephasing Standard Error                                                : 1.24E-01

  CI of Dephasing                                                                : [-3.84E+00 ; -3.33E+00]

- Dephasing -  Chronobiometric Acrophase (Degrees)  : -2.05E+02

  Dephasing Standard Error                                                : 7.09E+00

  CI of Dephasing                                                                : [-2.20E+02 ; -1.91E+02]

- Shifting  -  Chronobiometric MESOR                                : 3.66E+01

  Shifting Standard Error                                                      : 1.88E-02

  CI of Shifting                                                                      : [3.65E+01 ; 3.66E+01]

 

1.2. Chronobiometric parameters :

- Percent Rhythm                                                           : 46.85 %

- Percent Error                                                                : 53.15 %

- p-Value (H0: Amplitude=0)                                          : 0.0000

 

1.3. Chronobiometric test :

-  Ellipse Test (H0: β=0 And γ=0) for T =  2.4700000E+01 is significant at the probability level  : 0.9500

-  Area of the Confidence Ellipse  : 1.37E-02

 

1.4. Residuals distribution - Goodness of fit :

- Ajusted r² : 1.00E+00

- K-S Test (H0: Normal residuals distribution) is not significant at the probability level  : 0.9500

- k² Test (H0: Normal residuals distribution) is not significant at the probability level                               : 0.9500

- Average Test (H0: RS Average = 0) is not significant at the probability level                   : 0.9500

- Q Test (H0: Independent Residues) is significant at the probability level                                         : 0.9500

 

Serie n°8

Solution model : 3.11E-02Cos(2π t/24.70)-1.76E-01Sin(2π t/24.70)+3.68E+01

Initial model      : 1.79E-01Cos((2π t/24.70)-4.89E+00)+3.68E+01

-  Model (ANOVA) is valid at the probability level     : 0.9500

 

1.1. Chronobiometric values :

- Amplitude                                                                       : 1.79E-01

  Amplitude Standard Error                                                  : 2.16E-02

  CI of Amplitude                                                                  : [1.35E-01 ; 2.23E-01]

- Dephasing -  Chronobiometric Acrophase (Radians)   : -4.89E+00

  Dephasing Standard Error                                                : 1.18E-01

  CI of Dephasing                                                                : [-5.12E+00 ; -4.65E+00]

- Dephasing -  Chronobiometric Acrophase (Degrees)  : -2.80E+02

  Dephasing Standard Error                                                : 6.76E+00

  CI of Dephasing                                                                : [-2.93E+02 ; -2.67E+02]

- Shifting  -  Chronobiometric MESOR                                : 3.68E+01

  Shifting Standard Error                                                      : 1.52E-02

  CI of Shifting                                                                      : [3.67E+01 ; 3.68E+01]

 

1.2. Chronobiometric parameters :

- Percent Rhythm                                                           : 45.49 %

- Percent Error                                                                : 54.51 %

- p-Value (H0: Amplitude=0)                                          : 0.0000

 

1.3. Chronobiometric test :

-  Ellipse Test (H0: β=0 And γ=0) for T =  2.4700000E+01 is significant at the probability level  : 0.9500

-  Area of the Confidence Ellipse  : 8.88E-03

 

1.4. Residuals distribution - Goodness of fit :

- Ajusted r² : 1.00E+00

- K-S Test (H0: Normal residuals distribution) is not significant at the probability level  : 0.9500

- k² Test (H0: Normal residuals distribution) is significant at the probability level                               : 0.9500

- Average Test (H0: RS Average = 0) is not significant at the probability level                   : 0.9500

- Q Test (H0: Independent Residues) is significant at the probability level                                         : 0.9500

 

Serie n°9

Solution model : 3.04E-02Cos(2π t/24.70)-3.61E-01Sin(2π t/24.70)+3.67E+01

Initial model      : 3.62E-01Cos((2π t/24.70)-4.80E+00)+3.67E+01

-  Model (ANOVA) is valid at the probability level     : 0.9500

 

1.1. Chronobiometric values :

- Amplitude                                                                       : 3.62E-01

  Amplitude Standard Error                                                  : 2.37E-02

  CI of Amplitude                                                                  : [3.15E-01 ; 4.10E-01]

- Dephasing -  Chronobiometric Acrophase (Radians)   : -4.80E+00

  Dephasing Standard Error                                                : 6.30E-02

  CI of Dephasing                                                                : [-4.92E+00 ; -4.67E+00]

- Dephasing -  Chronobiometric Acrophase (Degrees)  : -2.75E+02

  Dephasing Standard Error                                                : 3.61E+00

  CI of Dephasing                                                                : [-2.82E+02 ; -2.68E+02]

- Shifting  -  Chronobiometric MESOR                                : 3.67E+01

  Shifting Standard Error                                                      : 1.65E-02

  CI of Shifting                                                                      : [3.67E+01 ; 3.68E+01]

 

1.2. Chronobiometric parameters :

- Percent Rhythm                                                           : 74.45 %

- Percent Error                                                                : 25.55 %

- p-Value (H0: Amplitude=0)                                          : 0.0000

 

1.3. Chronobiometric test :

-  Ellipse Test (H0: β=0 And γ=0) for T =  2.4700000E+01 is significant at the probability level  : 0.9500

-  Area of the Confidence Ellipse  : 1.05E-02

 

1.4. Residuals distribution - Goodness of fit :

- Ajusted r² : 1.00E+00

- K-S Test (H0: Normal residuals distribution) is not significant at the probability level  : 0.9500

- k² Test (H0: Normal residuals distribution) is significant at the probability level                               : 0.9500

- Average Test (H0: RS Average = 0) is not significant at the probability level                   : 0.9500

- Q Test (H0: Independent Residues) is significant at the probability level                                         : 0.9500

 

2. Results for all data

Solution model : -2.96E-02Cos(2π t/24.70)-2.04E-01Sin(2π t/24.70)+3.68E+01

Initial model      : 2.06E-01Cos((2π t/24.70)-4.57E+00)+3.68E+01

-  Model (ANOVA) is valid at the probability level     : 0.9500

 

2.1. Chronobiometric values :

- Amplitude                                                                       : 2.06E-01

  Amplitude Standard Error                                                  : 1.24E-02

  CI of Amplitude                                                                  : [1.83E-01 ; 2.30E-01]

- Dephasing -  Chronobiometric Acrophase (Radians)    : -4.57E+00

  Dephasing Standard Error                                               : 5.62E-02

  CI of Dephasing                                                                : [-4.68E+00 ; -4.46E+00]

- Dephasing -  Chronobiometric Acrophase (Degrees)   : -2.62E+02

  Dephasing Standard Error                                                : 3.22E+00

  CI of Dephasing                                                                : [-2.68E+02 ; -2.55E+02]

- Shifting      -  Chronobiometric MESOR                           : 3.68E+01

  Shifting Standard Error                                                     : 8.53E-03

  CI of Shifting                                                                      : [3.68E+01 ; 3.68E+01]

 

2.2. Chronobiometric parameters :

- Percent Rhythm                                                           : 28.23 %

- Percent Error                                                                : 71.77 %

- p-Value for H0 (Amplitude=0)                                    : 0.0000

 

2.3. Chronobiometric test :

-  Ellipse Test (H0: β=0 And γ=0) for T =  2.4700000E+01 is significant at the probability level  : 0.9500

-  Area of the Confidence Ellipse  : 2.71E-03

 

2.4. Residuals distribution - Goodness of fit :

- Ajusted r²                                                                       : 1.00E+00

- Residual Sums of Squares                                         : 3.80E+01

- k² Test (H0: Normal residuals distribution) is significant at the probability level                               : 0.9500

- K-S Test (H0: Normal residuals distribution) is significant at the probability level                             : 0.9500

- Average Test (H0: RS Average = 0) is not significant at the probability level                    : 0.9500

- Q Test (H0: Independent Residues) is significant at the probability level                                          : 0.9500

 

- K-S Test is the Kolmogorov and Smirnov test  

- Average Test (H0: RS Average = 0) is a test of average on the average sum of residues  

- Q Test is the Ljung-Box Q-statistic lack-of-fit hypothesis test