Hi,
The procedure Statistics:-ChiSquareSuitableModelTest returns wrong or stupid results in some situations.
The stupid answer can easily be avoided if the user is careful enough.
The wrong answer is more serious: the standard deviation (in the second case below) is not correctly estimated.
PS: the expression "CORRECT ANSWER" is a short for "POTENTIALLY CORRECT ANSWER" given that what ChiSquareSuitableModelTest really does is not documented
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randomize():
N := 100:
S := Sample(Normal(0, 1), N):
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infolevel[Statistics] := 1:
# 0 parameter to fit from the sample S CORRECT ANSWER
ChiSquareSuitableModelTest(S, Normal(0, 1), level = 0.5e-1):
print():
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Chi-Square Test for Suitable Probability Model
----------------------------------------------
Null Hypothesis:
Sample was drawn from specified probability distribution
Alt. Hypothesis:
Sample was not drawn from specified probability distribution
Bins: 10
Degrees of freedom: 9
Distribution: ChiSquare(9)
Computed statistic: 15.8
Computed pvalue: 0.0711774
Critical value: 16.9189774487099
Result: [Accepted]
This statistical test does not provide enough evidence to conclude that the null hypothesis is false
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(1) |
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# 2 parameters (mean and standard deviation) to fit from the sample S INCORRECT ANSWER
ChiSquareSuitableModelTest(S, Normal(a, b), level = 0.5e-1, fittedparameters = 2):
print():
# verification
m := Mean(S);
s := StandardDeviation(S);
t := sqrt(add((S-~m)^~2) / (N-1));
print():
error "the estimation of the StandardDeviation ChiSquareSuitableModelTest is not correct";
print():
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Chi-Square Test for Suitable Probability Model
----------------------------------------------
Null Hypothesis:
Sample was drawn from specified probability distribution
Alt. Hypothesis:
Sample was not drawn from specified probability distribution
Model specialization: [a = -.2143e-1, b = .8489]
Bins: 10
Degrees of freedom: 7
Distribution: ChiSquare(7)
Computed statistic: 3.8
Computed pvalue: 0.802504
Critical value: 14.0671405764057
Result: [Accepted]
This statistical test does not provide enough evidence to conclude that the null hypothesis is false
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(2) |
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# ONLY 1 parameter (mean OR standard deviation ?) to fit from the sample S STUPID ANSWER
#
# A stupid answer: the parameter to fit not being declared, the procedure should return
# an error of the type "don(t know what is the paramater tio fit"
ChiSquareSuitableModelTest(S, Normal(a, b), level = 0.5e-1, fittedparameters = 1):
print():
WARNING("ChiSquareSuitableModelTest should return it can't fit a single parameter");
print():
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Chi-Square Test for Suitable Probability Model
----------------------------------------------
Null Hypothesis:
Sample was drawn from specified probability distribution
Alt. Hypothesis:
Sample was not drawn from specified probability distribution
Model specialization: [a = -.2143e-1, b = .8489]
Bins: 10
Degrees of freedom: 8
Distribution: ChiSquare(8)
Computed statistic: 3.8
Computed pvalue: 0.874702
Critical value: 15.5073130558655
Result: [Accepted]
This statistical test does not provide enough evidence to conclude that the null hypothesis is false
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(3) |
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ChiSquareSuitableModelTest(S, Normal(a, 1), level = 0.5e-1, fittedparameters = 1): #CORRECT ANSWER
print():
# verification
m := Mean(S);
print():
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Chi-Square Test for Suitable Probability Model
----------------------------------------------
Null Hypothesis:
Sample was drawn from specified probability distribution
Alt. Hypothesis:
Sample was not drawn from specified probability distribution
Model specialization: [a = -.2143e-1]
Bins: 10
Degrees of freedom: 8
Distribution: ChiSquare(8)
Computed statistic: 16.4
Computed pvalue: 0.0369999
Critical value: 15.5073130558655
Result: [Rejected]
This statistical test provides evidence that the null hypothesis is false
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(4) |
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ChiSquareSuitableModelTest(S, Normal(0, b), level = 0.5e-1, fittedparameters = 1): #CORRECT ANSWER
print():
# verification
s := sqrt((add(S^~2) - 0^2) / N);
print():
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Chi-Square Test for Suitable Probability Model
----------------------------------------------
Null Hypothesis:
Sample was drawn from specified probability distribution
Alt. Hypothesis:
Sample was not drawn from specified probability distribution
Model specialization: [b = .8492]
Bins: 10
Degrees of freedom: 8
Distribution: ChiSquare(8)
Computed statistic: 6.4
Computed pvalue: 0.60252
Critical value: 15.5073130558655
Result: [Accepted]
This statistical test does not provide enough evidence to conclude that the null hypothesis is false
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(5) |
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Download ChiSquareSuitableModelTest.mw
