Date - time                : 24/09/2005 15:00:39

Data file name           : Triang.dta

 

Single Cosinor Tests for one chosen period  

Studied period (T)          : 6.2800000E+00

 

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 : -1.93E-02Cos(2π t/6.28)+9.95E-01Sin(2π t/6.28)-3.51E-03

Initial model      : 9.95E-01Cos((2π t/6.28)-1.59E+00)-3.51E-03

-  Model (ANOVA) is valid at the probability level   p =0.9500, α =0.0500

 

1.1. Chronobiometric values :

- Amplitude                                                                       : 9.95E-01

  Amplitude Standard Error                                                  : 2.15E-02

  CI of Amplitude                                                                  : [9.51E-01 ; 1.04E+00]

- Dephasing -  Chronobiometric Acrophase (Radians)   : -1.59E+00

  Dephasing Standard Error                                                : 2.17E-02

  CI of Dephasing                                                                : [-1.63E+00 ; -1.55E+00]

- Dephasing -  Chronobiometric Acrophase (Degrees)  : -9.11E+01

  Dephasing Standard Error                                                : 1.24E+00

  CI of Dephasing                                                                : [-9.36E+01 ; -8.86E+01]

- Shifting  -  Chronobiometric MESOR                                : -3.51E-03

  Shifting Standard Error                                                      : 1.52E-02

  CI of Shifting                                                                      : [-3.47E-02 ; 2.76E-02]

- AESOR[0, T] -  Chronobiometric AESOR                         : -2.20E-02

  AESOR Standard Error                                                     : 9.56E-02

  CI of AESOR                                                                     : [-2.18E-01 ; 1.74E-01]

 

1.2. Chronobiometric parameters :

- Percent Rhythm                                                           : 98.66 %

- Percent Error                                                                : 1.34 %

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

 

1.3. Chronobiometric test : p =0.9500, α =0.0500

-  Ellipse Test (H0: β=0 And γ=0) for T =  6.2800000E+00 H0 rejected            

-  Area of the Confidence Ellipse  : 9.70E-03

 

1.4. Residuals distribution - Goodness of fit : p =0.9500, α =0.0500

- Ajusted r²                     : 9.85E-01

- K-S Test (H0: Normal residuals distribution) H0 accepted                

- k² Test (H0: Normal residuals distribution) H0 accepted                  

- Average Test (H0: RS Average = 0) H0 accepted                                 

- Q Test (H0: Independent Residues) H0 rejected                                          

 

Serie n°2

Solution model : -1.61E-02Cos(2π t/6.28)+1.01E+00Sin(2π t/6.28)+2.72E-03

Initial model      : 1.01E+00Cos((2π t/6.28)-1.59E+00)+2.72E-03

-  Model (ANOVA) is valid at the probability level   p =0.9500, α =0.0500

 

1.1. Chronobiometric values :

- Amplitude                                                                       : 1.01E+00

  Amplitude Standard Error                                                  : 2.26E-02

  CI of Amplitude                                                                  : [9.62E-01 ; 1.05E+00]

- Dephasing -  Chronobiometric Acrophase (Radians)   : -1.59E+00

  Dephasing Standard Error                                                : 2.28E-02

  CI of Dephasing                                                                : [-1.63E+00 ; -1.54E+00]

- Dephasing -  Chronobiometric Acrophase (Degrees)  : -9.09E+01

  Dephasing Standard Error                                                : 1.31E+00

  CI of Dephasing                                                                : [-9.36E+01 ; -8.82E+01]

- Shifting  -  Chronobiometric MESOR                                : 2.72E-03

  Shifting Standard Error                                                      : 1.61E-02

  CI of Shifting                                                                      : [-3.03E-02 ; 3.57E-02]

- AESOR[0, T] -  Chronobiometric AESOR                         : 1.71E-02

  AESOR Standard Error                                                     : 1.01E-01

  CI of AESOR                                                                     : [-1.90E-01 ; 2.24E-01]

 

1.2. Chronobiometric parameters :

- Percent Rhythm                                                           : 98.57 %

- Percent Error                                                                : 1.43 %

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

 

1.3. Chronobiometric test : p =0.9500, α =0.0500

-  Ellipse Test (H0: β=0 And γ=0) for T =  6.2800000E+00 H0 rejected            

-  Area of the Confidence Ellipse  : 1.09E-02

 

1.4. Residuals distribution - Goodness of fit : p =0.9500, α =0.0500

- Ajusted r²                     : 9.84E-01

- K-S Test (H0: Normal residuals distribution) H0 accepted                

- k² Test (H0: Normal residuals distribution) H0 accepted                  

- Average Test (H0: RS Average = 0) H0 accepted                                 

- Q Test (H0: Independent Residues) H0 rejected                                          

 

Serie n°3

Solution model : -4.76E-02Cos(2π t/6.28)+9.94E-01Sin(2π t/6.28)-1.40E-04

Initial model      : 9.95E-01Cos((2π t/6.28)-1.62E+00)-1.40E-04

-  Model (ANOVA) is valid at the probability level   p =0.9500, α =0.0500

 

1.1. Chronobiometric values :

- Amplitude                                                                       : 9.95E-01

  Amplitude Standard Error                                                  : 2.06E-02

  CI of Amplitude                                                                  : [9.53E-01 ; 1.04E+00]

- Dephasing -  Chronobiometric Acrophase (Radians)   : -1.62E+00

  Dephasing Standard Error                                                : 2.10E-02

  CI of Dephasing                                                                : [-1.66E+00 ; -1.58E+00]

- Dephasing -  Chronobiometric Acrophase (Degrees)  : -9.27E+01

  Dephasing Standard Error                                                : 1.20E+00

  CI of Dephasing                                                                : [-9.52E+01 ; -9.03E+01]

- Shifting  -  Chronobiometric MESOR                                : -1.40E-04

  Shifting Standard Error                                                      : 1.47E-02

  CI of Shifting                                                                      : [-3.02E-02 ; 2.99E-02]

- AESOR[0, T] -  Chronobiometric AESOR                         : -8.81E-04

  AESOR Standard Error                                                     : 9.22E-02

  CI of AESOR                                                                     : [-1.89E-01 ; 1.88E-01]

 

1.2. Chronobiometric parameters :

- Percent Rhythm                                                           : 98.77 %

- Percent Error                                                                : 1.23 %

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

 

1.3. Chronobiometric test : p =0.9500, α =0.0500

-  Ellipse Test (H0: β=0 And γ=0) for T =  6.2800000E+00 H0 rejected            

-  Area of the Confidence Ellipse  : 9.00E-03

 

1.4. Residuals distribution - Goodness of fit : p =0.9500, α =0.0500

- Ajusted r²                     : 9.86E-01

- K-S Test (H0: Normal residuals distribution) H0 accepted                

- k² Test (H0: Normal residuals distribution) H0 accepted                  

- Average Test (H0: RS Average = 0) H0 accepted                                 

- Q Test (H0: Independent Residues) H0 rejected                                          

.

.

.

.

.

Serie n°30

Solution model : -4.61E-01Cos(2π t/6.28)+8.79E-01Sin(2π t/6.28)+1.09E-03

Initial model      : 9.92E-01Cos((2π t/6.28)-2.05E+00)+1.09E-03

-  Model (ANOVA) is valid at the probability level   p =0.9500, α =0.0500

 

1.1. Chronobiometric values :

- Amplitude                                                                       : 9.92E-01

  Amplitude Standard Error                                                  : 2.04E-02

  CI of Amplitude                                                                  : [9.51E-01 ; 1.03E+00]

- Dephasing -  Chronobiometric Acrophase (Radians)   : -2.05E+00

  Dephasing Standard Error                                                : 2.02E-02

  CI of Dephasing                                                                : [-2.10E+00 ; -2.01E+00]

- Dephasing -  Chronobiometric Acrophase (Degrees)  : -1.18E+02

  Dephasing Standard Error                                                : 1.16E+00

  CI of Dephasing                                                                : [-1.20E+02 ; -1.15E+02]

- Shifting  -  Chronobiometric MESOR                                : 1.09E-03

  Shifting Standard Error                                                      : 1.43E-02

  CI of Shifting                                                                      : [-2.81E-02 ; 3.03E-02]

- AESOR[0, T] -  Chronobiometric AESOR                         : 6.85E-03

  AESOR Standard Error                                                     : 8.98E-02

  CI of AESOR                                                                     : [-1.77E-01 ; 1.90E-01]

 

1.2. Chronobiometric parameters :

- Percent Rhythm                                                           : 98.83 %

- Percent Error                                                                : 1.17 %

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

 

1.3. Chronobiometric test : p =0.9500, α =0.0500

-  Ellipse Test (H0: β=0 And γ=0) for T =  6.2800000E+00 H0 rejected            

-  Area of the Confidence Ellipse  : 8.54E-03

 

1.4. Residuals distribution - Goodness of fit : p =0.9500, α =0.0500

- Ajusted r²                     : 9.87E-01

- K-S Test (H0: Normal residuals distribution) H0 accepted                

- k² Test (H0: Normal residuals distribution) H0 accepted                  

- Average Test (H0: RS Average = 0) H0 accepted                                 

- Q Test (H0: Independent Residues) H0 rejected                                          

 

2. Results for all data

Solution model : -2.39E-01Cos(2π t/6.28)+9.61E-01Sin(2π t/6.28)+1.65E-05

Initial model      : 9.90E-01Cos((2π t/6.28)-1.81E+00)+1.65E-05

-  Model (ANOVA) is valid at the probability level      p =0.9500, α =0.0500

 

2.1. Chronobiometric values :

- Amplitude                                                                       : 9.90E-01

  Amplitude Standard Error                                                  : 5.91E-03

  CI of Amplitude                                                                  : [9.79E-01 ; 1.00E+00]

- Dephasing -  Chronobiometric Acrophase (Radians)    : -1.81E+00

  Dephasing Standard Error                                               : 5.97E-03

  CI of Dephasing                                                                : [-1.83E+00 ; -1.80E+00]

- Dephasing -  Chronobiometric Acrophase (Degrees)   : -1.04E+02

  Dephasing Standard Error                                                : 3.42E-01

  CI of Dephasing                                                                : [-1.05E+02 ; -1.03E+02]

- Shifting      -  Chronobiometric MESOR                           : 1.65E-05

  Shifting Standard Error                                                     : 4.18E-03

  CI of Shifting                                                                      : [-8.18E-03 ; 8.22E-03]

- AESOR[0, T] -  Chronobiometric AESOR                         : 1.04E-04

  AESOR Standard Error                                                     : 2.62E-02

  CI of AESOR                                                                     : [-5.14E-02 ; 5.16E-02]

 

2.2. Chronobiometric parameters :

- Percent Rhythm                                                           : 96.71 %

- Percent Error                                                                : 3.29 %

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

 

2.3. Chronobiometric test : p =0.9500, α =0.0500

-  Ellipse Test (H0: β=0 And γ=0) for T =  6.2800000E+00 H0 rejected              

-  Area of the Confidence Ellipse  : 6.59E-04

 

2.4. Residuals distribution - Goodness of fit : p =0.9500, α =0.0500

- Ajusted r²                                                                       : 9.67E-01

- Residual Sums of Squares                                         : 1.60E+01

- χ² Test (H0: Normal residuals distribution) H0 rejected                    :

- K-S Test (H0: Normal residuals distribution) H0 rejected                    

- Average Test (H0: RS Average = 0) H0 accepted                        

- Q Test (H0: Independent Residues) H0 rejected                                

 

- 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