Date - time                : 09/03/2006 13:11:08

Data file name           : T°Placebo.dta

 

Single Cosinor Tests for one chosen period  

Studied period (T)          : 2.4400000E+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 : -1.11E-01Cos(2π t/24.40)-3.98E-01Sin(2π t/24.40)+3.66E+01

Initial model      : 4.13E-01Cos((2π t/24.40)-4.44E+00)+3.66E+01

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

 

1.1. Chronobiometric values :

- Amplitude                                                                       : 4.13E-01

  Amplitude Standard Error                                                  : 2.00E-02

  CI of Amplitude                                                                  : [3.74E-01 ; 4.51E-01]

- Dephasing -  Chronobiometric Acrophase (Radians)   : -4.44E+00

  Dephasing Standard Error                                                : 4.47E-02

  CI of Dephasing                                                                : [-4.53E+00 ; -4.35E+00]

- Dephasing -  Chronobiometric Acrophase (Degrees)  : -2.54E+02

  Dephasing Standard Error                                                : 2.56E+00

  CI of Dephasing                                                                : [-2.60E+02 ; -2.49E+02]

- Shifting  -  Chronobiometric MESOR                                : 3.66E+01

  Shifting Standard Error                                                      : 1.37E-02

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

- AESOR[0, T] -  Chronobiometric AESOR                         : 8.93E+02

  AESOR Standard Error                                                     : 3.33E-01

  CI of AESOR                                                                     : [8.93E+02 ; 8.94E+02]

 

1.2. Chronobiometric parameters :

- Percent Rhythm                                                           : 85.22 %

- Percent Error                                                                : 14.78 %

- 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 =  2.4400000E+01 H0 rejected            

-  Area of the Confidence Ellipse  : 7.21E-03

 

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

- Ajusted r²                     : 1.00E+00

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

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

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

- Q Test (H0: Independent Residues) H0 rejected                                          

 

Serie n°2

Solution model : -2.72E-01Cos(2π t/24.40)-4.07E-01Sin(2π t/24.40)+3.68E+01

Initial model      : 4.90E-01Cos((2π t/24.40)-4.12E+00)+3.68E+01

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

 

1.1. Chronobiometric values :

- Amplitude                                                                       : 4.90E-01

  Amplitude Standard Error                                                  : 3.29E-02

  CI of Amplitude                                                                  : [4.28E-01 ; 5.52E-01]

- Dephasing -  Chronobiometric Acrophase (Radians)   : -4.12E+00

  Dephasing Standard Error                                                : 6.21E-02

  CI of Dephasing                                                                : [-4.25E+00 ; -3.99E+00]

- Dephasing -  Chronobiometric Acrophase (Degrees)  : -2.36E+02

  Dephasing Standard Error                                                : 3.56E+00

  CI of Dephasing                                                                : [-2.44E+02 ; -2.29E+02]

- Shifting  -  Chronobiometric MESOR                                : 3.68E+01

  Shifting Standard Error                                                      : 2.25E-02

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

- AESOR[0, T] -  Chronobiometric AESOR                         : 8.97E+02

  AESOR Standard Error                                                     : 5.49E-01

  CI of AESOR                                                                     : [8.96E+02 ; 8.98E+02]

 

1.2. Chronobiometric parameters :

- Percent Rhythm                                                           : 75.93 %

- Percent Error                                                                : 24.07 %

- 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 =  2.4400000E+01 H0 rejected            

-  Area of the Confidence Ellipse  : 1.96E-02

 

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

- Ajusted r²                     : 1.00E+00

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

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

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

- Q Test (H0: Independent Residues) H0 rejected                                          

 

Serie n°3

Solution model : -1.54E-01Cos(2π t/24.40)-3.83E-01Sin(2π t/24.40)+3.68E+01

Initial model      : 4.13E-01Cos((2π t/24.40)-4.33E+00)+3.68E+01

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

 

1.1. Chronobiometric values :

- Amplitude                                                                       : 4.13E-01

  Amplitude Standard Error                                                  : 1.42E-02

  CI of Amplitude                                                                  : [3.86E-01 ; 4.41E-01]

- Dephasing -  Chronobiometric Acrophase (Radians)   : -4.33E+00

  Dephasing Standard Error                                                : 3.16E-02

  CI of Dephasing                                                                : [-4.40E+00 ; -4.26E+00]

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

  Dephasing Standard Error                                                : 1.81E+00

  CI of Dephasing                                                                : [-2.52E+02 ; -2.44E+02]

- Shifting  -  Chronobiometric MESOR                                : 3.68E+01

  Shifting Standard Error                                                      : 9.70E-03

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

- AESOR[0, T] -  Chronobiometric AESOR                         : 8.97E+02

  AESOR Standard Error                                                     : 2.37E-01

  CI of AESOR                                                                     : [8.97E+02 ; 8.98E+02]

 

1.2. Chronobiometric parameters :

- Percent Rhythm                                                           : 92.12 %

- Percent Error                                                                : 7.88 %

- 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 =  2.4400000E+01 H0 rejected            

-  Area of the Confidence Ellipse  : 3.64E-03

 

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

- Ajusted r²                     : 1.00E+00

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

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

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

- Q Test (H0: Independent Residues) H0 rejected                                          

 

Serie n°4

Solution model : -1.31E-01Cos(2π t/24.40)-4.27E-01Sin(2π t/24.40)+3.66E+01

Initial model      : 4.47E-01Cos((2π t/24.40)-4.41E+00)+3.66E+01

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

 

1.1. Chronobiometric values :

- Amplitude                                                                       : 4.47E-01

  Amplitude Standard Error                                                  : 3.13E-02

  CI of Amplitude                                                                  : [3.87E-01 ; 5.07E-01]

- Dephasing -  Chronobiometric Acrophase (Radians)   : -4.41E+00

  Dephasing Standard Error                                                : 6.45E-02

  CI of Dephasing                                                                : [-4.55E+00 ; -4.28E+00]

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

  Dephasing Standard Error                                                : 3.70E+00

  CI of Dephasing                                                                : [-2.61E+02 ; -2.45E+02]

- Shifting  -  Chronobiometric MESOR                                : 3.66E+01

  Shifting Standard Error                                                      : 2.14E-02

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

- AESOR[0, T] -  Chronobiometric AESOR                         : 8.92E+02

  AESOR Standard Error                                                     : 5.21E-01

  CI of AESOR                                                                     : [8.91E+02 ; 8.93E+02]

 

1.2. Chronobiometric parameters :

- Percent Rhythm                                                           : 73.53 %

- Percent Error                                                                : 26.47 %

- 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 =  2.4400000E+01 H0 rejected            

-  Area of the Confidence Ellipse  : 1.76E-02

 

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

- Ajusted r²                     : 1.00E+00

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

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

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

- Q Test (H0: Independent Residues) H0 rejected                                          

 

Serie n°5

Solution model : 7.75E-02Cos(2π t/24.40)-2.85E-01Sin(2π t/24.40)+3.67E+01

Initial model      : 2.95E-01Cos((2π t/24.40)-4.98E+00)+3.67E+01

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

 

1.1. Chronobiometric values :

- Amplitude                                                                       : 2.95E-01

  Amplitude Standard Error                                                  : 1.33E-02

  CI of Amplitude                                                                  : [2.68E-01 ; 3.22E-01]

- Dephasing -  Chronobiometric Acrophase (Radians)   : -4.98E+00

  Dephasing Standard Error                                                : 4.41E-02

  CI of Dephasing                                                                : [-5.06E+00 ; -4.89E+00]

- Dephasing -  Chronobiometric Acrophase (Degrees)  : -2.85E+02

  Dephasing Standard Error                                                : 2.53E+00

  CI of Dephasing                                                                : [-2.90E+02 ; -2.80E+02]

- Shifting  -  Chronobiometric MESOR                                : 3.67E+01

  Shifting Standard Error                                                      : 9.33E-03

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

- AESOR[0, T] -  Chronobiometric AESOR                         : 8.96E+02

  AESOR Standard Error                                                     : 2.28E-01

  CI of AESOR                                                                     : [8.95E+02 ; 8.96E+02]

 

1.2. Chronobiometric parameters :

- Percent Rhythm                                                           : 85.53 %

- Percent Error                                                                : 14.47 %

- 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 =  2.4400000E+01 H0 rejected            

-  Area of the Confidence Ellipse  : 3.37E-03

 

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

- Ajusted r²                     : 1.00E+00

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

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

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

- Q Test (H0: Independent Residues) H0 rejected                                          

 

Serie n°6

Solution model : -6.72E-02Cos(2π t/24.40)-4.55E-01Sin(2π t/24.40)+3.68E+01

Initial model      : 4.60E-01Cos((2π t/24.40)-4.57E+00)+3.68E+01

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

 

1.1. Chronobiometric values :

- Amplitude                                                                       : 4.60E-01

  Amplitude Standard Error                                                  : 2.05E-02

  CI of Amplitude                                                                  : [4.20E-01 ; 5.00E-01]

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

  Dephasing Standard Error                                                : 4.14E-02

  CI of Dephasing                                                                : [-4.65E+00 ; -4.48E+00]

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

  Dephasing Standard Error                                                : 2.37E+00

  CI of Dephasing                                                                : [-2.66E+02 ; -2.57E+02]

- Shifting  -  Chronobiometric MESOR                                : 3.68E+01

  Shifting Standard Error                                                      : 1.40E-02

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

- AESOR[0, T] -  Chronobiometric AESOR                         : 8.99E+02

  AESOR Standard Error                                                     : 3.43E-01

  CI of AESOR                                                                     : [8.98E+02 ; 9.00E+02]

 

1.2. Chronobiometric parameters :

- Percent Rhythm                                                           : 86.93 %

- Percent Error                                                                : 13.07 %

- 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 =  2.4400000E+01 H0 rejected            

-  Area of the Confidence Ellipse  : 7.63E-03

 

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

- Ajusted r²                     : 1.00E+00

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

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

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

- Q Test (H0: Independent Residues) H0 rejected                                          

 

Serie n°7

Solution model : -3.03E-03Cos(2π t/24.40)-4.56E-01Sin(2π t/24.40)+3.67E+01

Initial model      : 4.56E-01Cos((2π t/24.40)-4.71E+00)+3.67E+01

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

 

1.1. Chronobiometric values :

- Amplitude                                                                       : 4.56E-01

  Amplitude Standard Error                                                  : 2.03E-02

  CI of Amplitude                                                                  : [4.16E-01 ; 4.96E-01]

- Dephasing -  Chronobiometric Acrophase (Radians)   : -4.71E+00

  Dephasing Standard Error                                                : 4.21E-02

  CI of Dephasing                                                                : [-4.79E+00 ; -4.62E+00]

- Dephasing -  Chronobiometric Acrophase (Degrees)  : -2.70E+02

  Dephasing Standard Error                                                : 2.41E+00

  CI of Dephasing                                                                : [-2.74E+02 ; -2.65E+02]

- Shifting  -  Chronobiometric MESOR                                : 3.67E+01

  Shifting Standard Error                                                      : 1.40E-02

  CI of Shifting                                                                      : [3.66E+01 ; 3.67E+01]

- AESOR[0, T] -  Chronobiometric AESOR                         : 8.94E+02

  AESOR Standard Error                                                     : 3.42E-01

  CI of AESOR                                                                     : [8.94E+02 ; 8.95E+02]

 

1.2. Chronobiometric parameters :

- Percent Rhythm                                                           : 86.50 %

- Percent Error                                                                : 13.50 %

- 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 =  2.4400000E+01 H0 rejected            

-  Area of the Confidence Ellipse  : 7.61E-03

 

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

- Ajusted r²                     : 1.00E+00

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

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

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

- Q Test (H0: Independent Residues) H0 rejected                                          

 

Serie n°8

Solution model : -8.69E-02Cos(2π t/24.40)-4.11E-01Sin(2π t/24.40)+3.67E+01

Initial model      : 4.20E-01Cos((2π t/24.40)-4.50E+00)+3.67E+01

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

 

1.1. Chronobiometric values :

- Amplitude                                                                       : 4.20E-01

  Amplitude Standard Error                                                  : 1.65E-02

  CI of Amplitude                                                                  : [3.88E-01 ; 4.52E-01]

- Dephasing -  Chronobiometric Acrophase (Radians)   : -4.50E+00

  Dephasing Standard Error                                                : 3.64E-02

  CI of Dephasing                                                                : [-4.58E+00 ; -4.43E+00]

- Dephasing -  Chronobiometric Acrophase (Degrees)  : -2.58E+02

  Dephasing Standard Error                                                : 2.09E+00

  CI of Dephasing                                                                : [-2.62E+02 ; -2.54E+02]

- Shifting  -  Chronobiometric MESOR                                : 3.67E+01

  Shifting Standard Error                                                      : 1.13E-02

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

- AESOR[0, T] -  Chronobiometric AESOR                         : 8.96E+02

  AESOR Standard Error                                                     : 2.76E-01

  CI of AESOR                                                                     : [8.95E+02 ; 8.96E+02]

 

1.2. Chronobiometric parameters :

- Percent Rhythm                                                           : 89.61 %

- Percent Error                                                                : 10.39 %

- 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 =  2.4400000E+01 H0 rejected            

-  Area of the Confidence Ellipse  : 4.95E-03

 

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

- Ajusted r²                     : 1.00E+00

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

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

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

- Q Test (H0: Independent Residues) H0 rejected                                          

 

Serie n°9

Solution model : -1.86E-01Cos(2π t/24.40)-3.84E-01Sin(2π t/24.40)+3.67E+01

Initial model      : 4.26E-01Cos((2π t/24.40)-4.26E+00)+3.67E+01

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

 

1.1. Chronobiometric values :

- Amplitude                                                                       : 4.26E-01

  Amplitude Standard Error                                                  : 2.58E-02

  CI of Amplitude                                                                  : [3.77E-01 ; 4.75E-01]

- Dephasing -  Chronobiometric Acrophase (Radians)   : -4.26E+00

  Dephasing Standard Error                                                : 5.57E-02

  CI of Dephasing                                                                : [-4.38E+00 ; -4.15E+00]

- Dephasing -  Chronobiometric Acrophase (Degrees)  : -2.44E+02

  Dephasing Standard Error                                                : 3.19E+00

  CI of Dephasing                                                                : [-2.51E+02 ; -2.38E+02]

- Shifting  -  Chronobiometric MESOR                                : 3.67E+01

  Shifting Standard Error                                                      : 1.76E-02

  CI of Shifting                                                                      : [3.66E+01 ; 3.67E+01]

- AESOR[0, T] -  Chronobiometric AESOR                         : 8.95E+02

  AESOR Standard Error                                                     : 4.29E-01

  CI of AESOR                                                                     : [8.94E+02 ; 8.96E+02]

 

1.2. Chronobiometric parameters :

- Percent Rhythm                                                           : 79.26 %

- Percent Error                                                                : 20.74 %

- 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 =  2.4400000E+01 H0 rejected            

-  Area of the Confidence Ellipse  : 1.20E-02

 

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

- Ajusted r²                     : 1.00E+00

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

- χ² 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 : -1.04E-01Cos(2π t/24.40)-4.01E-01Sin(2π t/24.40)+3.67E+01

Initial model      : 4.14E-01Cos((2π t/24.40)-4.46E+00)+3.67E+01

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

 

2.1. Chronobiometric values :

- Amplitude                                                                       : 4.14E-01

  Amplitude Standard Error                                                  : 9.73E-03

  CI of Amplitude                                                                  : [3.95E-01 ; 4.33E-01]

- Dephasing -  Chronobiometric Acrophase (Radians)    : -4.46E+00

  Dephasing Standard Error                                               : 2.17E-02

  CI of Dephasing                                                                : [-4.50E+00 ; -4.42E+00]

- Dephasing -  Chronobiometric Acrophase (Degrees)   : -2.55E+02

  Dephasing Standard Error                                                : 1.24E+00

  CI of Dephasing                                                                : [-2.58E+02 ; -2.53E+02]

- Shifting      -  Chronobiometric MESOR                           : 3.67E+01

  Shifting Standard Error                                                     : 6.65E-03

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

- AESOR[0, T] -  Chronobiometric AESOR                         : 8.96E+02

  AESOR Standard Error                                                     : 1.62E-01

  CI of AESOR                                                                     : [8.95E+02 ; 8.96E+02]

 

2.2. Chronobiometric parameters :

- Percent Rhythm                                                           : 72.42 %

- Percent Error                                                                : 27.58 %

- 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 =  2.4400000E+01 H0 rejected              

-  Area of the Confidence Ellipse  : 1.65E-03

 

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

- Ajusted r²                                                                       : 1.00E+00

- Residual Sums of Squares                                         : 2.32E+01

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

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

- 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