Date - time :
19/11/2004 06:42:15
Data file name :
rectang.dta
Seriel
Cosinor Test for one chosen period - Population Mean Cosinor generalized
Studied
period (T) : 6.2800000E+00
1.
Results by each series
Model
equation : β cos(2π t/T) + γ sin(2π t/T) + α
Serie
n°1
Solution
model : -3.39E-02Cos(2π t/6.28)+1.02E+00Sin(2π
t/6.28)+8.76E-03
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°2
Solution
model : -2.50E-03Cos(2π t/6.28)+9.81E-01Sin(2π
t/6.28)-1.44E-02
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°3
Solution
model : -4.74E-02Cos(2π t/6.28)+9.55E-01Sin(2π
t/6.28)-1.30E-02
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°4
Solution
model : -8.44E-02Cos(2π t/6.28)+1.06E+00Sin(2π
t/6.28)+2.37E-02
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°5
Solution
model : -7.55E-02Cos(2π t/6.28)+9.48E-01Sin(2π
t/6.28)+1.54E-03
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°6
Solution
model : -6.31E-02Cos(2π t/6.28)+1.07E+00Sin(2π
t/6.28)-2.53E-02
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°7
Solution
model : -9.67E-02Cos(2π t/6.28)+9.50E-01Sin(2π
t/6.28)+1.24E-02
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°8
Solution
model : -1.40E-01Cos(2π t/6.28)+9.75E-01Sin(2π
t/6.28)+1.44E-02
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°9
Solution
model : -1.12E-01Cos(2π t/6.28)+1.01E+00Sin(2π
t/6.28)-6.58E-03
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°10
Solution
model : -2.32E-01Cos(2π t/6.28)+9.71E-01Sin(2π
t/6.28)-2.35E-02
- Model (ANOVA) is valid at the probability level : 0.9500
Serie
n°11
Solution
model : -9.14E-02Cos(2π t/6.28)+1.03E+00Sin(2π
t/6.28)+2.92E-02
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°12
Solution
model : -2.11E-01Cos(2π t/6.28)+9.59E-01Sin(2π
t/6.28)-2.12E-03
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°13
Solution
model : -1.93E-01Cos(2π t/6.28)+9.78E-01Sin(2π
t/6.28)-1.42E-02
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°14
Solution
model : -1.93E-01Cos(2π t/6.28)+9.41E-01Sin(2π
t/6.28)-8.26E-03
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°15
Solution
model : -3.12E-01Cos(2π t/6.28)+1.01E+00Sin(2π
t/6.28)+2.96E-02
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°16
Solution
model : -1.90E-01Cos(2π t/6.28)+9.48E-01Sin(2π
t/6.28)-1.43E-02
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°17
Solution
model : -2.87E-01Cos(2π t/6.28)+1.01E+00Sin(2π t/6.28)-1.53E-02
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°18
Solution
model : -2.52E-01Cos(2π t/6.28)+9.36E-01Sin(2π
t/6.28)+1.43E-02
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°19
Solution
model : -3.03E-01Cos(2π t/6.28)+9.15E-01Sin(2π
t/6.28)+1.41E-02
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°20
Solution
model : -3.27E-01Cos(2π t/6.28)+1.00E+00Sin(2π
t/6.28)-1.81E-02
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°21
Solution
model : -3.51E-01Cos(2π t/6.28)+8.93E-01Sin(2π
t/6.28)-1.05E-02
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°22
Solution
model : -3.10E-01Cos(2π t/6.28)+1.02E+00Sin(2π
t/6.28)+2.87E-02
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°23
Solution
model : -3.51E-01Cos(2π t/6.28)+8.90E-01Sin(2π
t/6.28)-9.81E-03
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°24
Solution
model : -3.82E-01Cos(2π t/6.28)+9.18E-01Sin(2π
t/6.28)-1.42E-02
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°25
Solution
model : -3.56E-01Cos(2π t/6.28)+9.26E-01Sin(2π
t/6.28)+3.89E-04
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°26
Solution
model : -4.90E-01Cos(2π t/6.28)+9.00E-01Sin(2π
t/6.28)+2.80E-02
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°27
Solution
model : -3.43E-01Cos(2π t/6.28)+9.50E-01Sin(2π
t/6.28)-2.58E-02
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°28
Solution
model : -4.62E-01Cos(2π t/6.28)+8.93E-01Sin(2π
t/6.28)-3.74E-03
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°29
Solution
model : -4.26E-01Cos(2π t/6.28)+8.93E-01Sin(2π
t/6.28)+1.43E-02
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°30
Solution
model : -4.38E-01Cos(2π t/6.28)+8.48E-01Sin(2π
t/6.28)+1.14E-02
- Model (ANOVA) is valid at the probability
level : 0.9500
2.
Global results - Seriel Cosinor Test
Number of series : 30
Number of observations : 32
Number of models : 30
Level probability of tests : 0.9500
Tested period : 6.2800000E+00
2.1 Characteristic values of the Harmonic Regression :
Variance Sx² : 1.91E-02
Variance Sy² : 2.84E-03
Correlation : 6.61E-01
2.2 Parameters values of the Confidence Ellipse:
Confidence Ellipse Inclination
(Geometrical) : -2.69E-01
Confidence Ellipse Inclination
(Algebraical) : -1.84E+00
Major axis (Geometrical) : 1.37E-01
Major axis (Algebraical) : 1.37E-01
Minor axis (Geometrical) : 3.71E-02
Minor axis (Algebraical) : 3.71E-02
Area of the confidence ellipse
(Geometrical) : 4.01E-03
2.3 Main values of the global model(Chronobiometric values) :
- Amplitude :
9.89E-01
Confidence Interval of the Amplitude
(Geometrical) : [9.68E-01 ; 1.01E+00]
Confidence Interval of the Amplitude
(Algebraical) : [6.34E-01 ; 1.34E+00]
- Dephasing - Chronobiometric Acrophase (Radians) : -1.81E+00
Confidence Interval of the Dephasing
(Radians) (Geometrical) : [-1.88E+00 ; -1.75E+00]
Confidence Interval of the Dephasing
(Radians) (Algebraical) : [-1.81E+00 ; -1.81E+00]
- Dephasing -
Chronobiometric Acrophase (Degrees)
: -1.04E+02
Confidence Interval of the Dephasing
(Degrees) (Geometrical) : [-1.07E+02 ; -1.00E+02]
Confidence Interval of the Dephasing
(Degrees) (Algebraical) : [-1.04E+02 ; -1.04E+02]
- Shifting - Chronobiometric MESOR : 3.85E-04
Confidence Interval of the Shifting
(Statistical)
: [-4.85E-03 ; 5.62E-03]
Confidence Interval of the Shifting
(Algebraical)
: [-1.56E-01 ; 1.57E-01]
2.4 Chronobiometric parameters :
- Percent Rhythm :
49.43 %
- Percent
Error :
50.57 %
- p-Value (H0:
Amplitude=0) : 0.0000
2.5 Test parameters and results of the Seriel Cosinor test :
F Snedecor (2, 28) : 3.34
T² Hotelling : 6.92
Confidence area : 3.69E+02
Limit of confidence : 1.30E-01
- Ellipse Test (H0: β=0 And γ=0) for T = 6.2800000E+00 H0 rejected
: 0.9500
- 0rigin (O) is outside of the
confidence ellipse
- Bartlett Test (H0: s²1 = … = s²i) H0 accepted : 0.9500
- KW Test (H0:
Samples from same population) H0 accepted : 0.9500
- Global model : -2.39E-01Cos(2p t/6.28E+00)+9.60E-01Sin(2π
t/6.28E+00)+3.85E-04
- Initial model : 9.89E-01Cos((2π
t/6.28E+00)-1.81E+00)+3.85E-04
2.6 Residuals distribution - Goodness of fit :
- Ajusted r²
: 4.80E-01
- K-S Test (H0:
Normal residuals distribution) H0 rejected :
0.9500
- χ² Test (H0: Normal residuals distribution) H0 rejected : 0.9500
- Average Test
(H0: SResiduals Average=0) H0 accepted
: 0.9500
- Q Test (H0:
Independent Residues) H0 rejected : 0.9500
- KW Test is the Kruskall and Wallis test
- 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