Date - time :
16/10/2003 09:18:59
Data file name :
triang.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 : -1.93E-02Cos(2π t/6.28)+9.95E-01Sin(2π t/6.28)-3.51E-03
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°2
Solution
model : -1.61E-02Cos(2π t/6.28)+1.01E+00Sin(2π t/6.28)+2.72E-03
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°3
Solution
model : -4.76E-02Cos(2π t/6.28)+9.94E-01Sin(2π t/6.28)-1.40E-04
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°4
Solution
model : -4.97E-02Cos(2π t/6.28)+1.00E+00Sin(2π t/6.28)-2.49E-03
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°5
Solution
model : -7.33E-02Cos(2π t/6.28)+9.91E-01Sin(2π t/6.28)+1.65E-05
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°6
Solution
model : -9.62E-02Cos(2π t/6.28)+1.00E+00Sin(2π t/6.28)+2.27E-03
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°7
Solution
model : -9.91E-02Cos(2π t/6.28)+9.89E-01Sin(2π t/6.28)+5.54E-04
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°8
Solution
model : -1.31E-01Cos(2π t/6.28)+1.00E+00Sin(2π t/6.28)-3.02E-03
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°9
Solution
model : -1.27E-01Cos(2π t/6.28)+9.86E-01Sin(2π t/6.28)+3.52E-03
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°10
Solution
model : -1.59E-01Cos(2π t/6.28)+9.87E-01Sin(2π t/6.28)+3.40E-05
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°11
Solution
model : -1.67E-01Cos(2π t/6.28)+9.90E-01Sin(2π t/6.28)-5.38E-04
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°12
Solution
model : -1.90E-01Cos(2π t/6.28)+9.72E-01Sin(2π t/6.28)-3.14E-03
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°13
Solution
model : -2.02E-01Cos(2π t/6.28)+9.94E-01Sin(2π t/6.28)+3.87E-03
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°14
Solution
model : -2.15E-01Cos(2π t/6.28)+9.66E-01Sin(2π t/6.28)-2.15E-03
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°15
Solution
model : -2.34E-01Cos(2π t/6.28)+9.78E-01Sin(2π t/6.28)-1.29E-03
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°16
Solution
model : -2.44E-01Cos(2π t/6.28)+9.66E-01Sin(2π t/6.28)-1.01E-04
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°17
Solution
model : -2.75E-01Cos(2π t/6.28)+9.61E-01Sin(2π t/6.28)+3.27E-03
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°18
Solution
model : -2.72E-01Cos(2π t/6.28)+9.65E-01Sin(2π t/6.28)-1.64E-03
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°19
Solution
model : -3.05E-01Cos(2π t/6.28)+9.53E-01Sin(2π t/6.28)-1.11E-03
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°20
Solution
model : -3.02E-01Cos(2π t/6.28)+9.54E-01Sin(2π t/6.28)+3.07E-03
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°21
Solution
model : -3.28E-01Cos(2π t/6.28)+9.39E-01Sin(2π t/6.28)-9.86E-05
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°22
Solution
model : -3.46E-01Cos(2π t/6.28)+9.44E-01Sin(2π t/6.28)-1.59E-03
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°23
Solution
model : -3.52E-01Cos(2π t/6.28)+9.26E-01Sin(2π t/6.28)-1.71E-03
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°24
Solution
model : -3.82E-01Cos(2π t/6.28)+9.39E-01Sin(2π t/6.28)+3.69E-03
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°25
Solution
model : -3.77E-01Cos(2π t/6.28)+9.17E-01Sin(2π t/6.28)-3.34E-03
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°26
Solution
model : -4.08E-01Cos(2π t/6.28)+9.16E-01Sin(2π t/6.28)-3.33E-04
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°27
Solution
model : -4.13E-01Cos(2π t/6.28)+9.12E-01Sin(2π t/6.28)+1.45E-04
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°28
Solution
model : -4.37E-01Cos(2π t/6.28)+8.91E-01Sin(2π t/6.28)+3.49E-03
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°29
Solution
model : -4.46E-01Cos(2π t/6.28)+9.08E-01Sin(2π t/6.28)-3.37E-03
- Model (ANOVA) is valid at the probability
level : 0.9500
Serie
n°30
Solution
model : -4.61E-01Cos(2π t/6.28)+8.79E-01Sin(2π t/6.28)+1.09E-03
- 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 : 1.84E-02
Variance Sy² : 1.27E-03
Correlation : 9.45E-01
2.2
Parameters values of the Confidence Ellipse:
Confidence Ellipse Inclination
(Geometrical) : -2.46E-01
Confidence Ellipse Inclination
(Algebraical) : -1.82E+00
Major axis (Geometrical) : 1.34E-01
Major axis (Algebraical) : 1.34E-01
Minor axis (Geometrical) : 1.09E-02
Minor axis (Algebraical) : 1.09E-02
Area of the confidence ellipse
(Geometrical) : 1.15E-03
2.3
Main values of the global model(Chronobiometric values) :
- Amplitude :
9.90E-01
Confidence Interval of the Amplitude
(Geometrical) : [9.84E-01 ; 9.96E-01]
Confidence Interval of the Amplitude
(Algebraical) : [8.86E-01 ; 1.09E+00]
- Dephasing - Chronobiometric Acrophase (Radians) : -1.81E+00
Confidence Interval of the Phase
(Radians) (Geometrical) : [-1.87E+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 ; -1.01E+02]
Confidence Interval of the Phase
(Degrees) (Algebraical) : [-1.04E+02 ; -1.04E+02]
- Shifting - Chronobiometric MESOR : 6.14E-05
Confidence Interval of the Shifting
(Statistical)
: [-7.74E-04 ; 6.51E-04]
Confidence Interval of the Shifting
(Algebraical)
: [-2.14E-02 ; 2.13E-02]
2.4
Chronobiometric parameters :
- Percent Rhythm :
98.64 %
- Percent
Error :
1.36 %
- 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 : 8.17E+02
Limit of confidence : 2.49E-02
- Ellipse Test (H0: β=0 And γ=0) for T = 6.2800000E+00 is significant at the
probability level : 0.9500
- 0rigin (O) is outside of
the confidence ellipse
- Bartlett Test (H0: s²1 = … = s²i) is not significant at the probability level : 0.9500
- KW Test (H0:
Samples from same population) is not significant at the probability level : 0.9500
- Global model : -2.39E-01Cos(2π t/6.28E+00)+9.61E-01Sin(2π t/6.28E+00)-6.14E-05
- Initial model : 9.90E-01Cos((2π t/6.28E+00)-1.81E+00)-6.14E-05
2.6
Residuals distribution - Goodness of fit :
- Ajusted r²
: 9.67E-01
- K-S Test (H0:
Normal residuals distribution) is significant at the probability level : 0.9500
- χ² Test (H0: Normal
residuals distribution) is significant at the probability level : 0.9500
- Average Test
(H0: Residuals Average=0) is not significant at the probability level : 0.9500
- Q Test (H0:
Independent Residues) is significant at the probability level : 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