# Question:problems with ChiSquareSuitableModelTest

## Question:problems with ChiSquareSuitableModelTest

Maple

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

 > restart:
 > with(Statistics):
 > randomize(): N := 100: S := Sample(Normal(0, 1), N):
 > infolevel[Statistics] := 1: # 0 parameter to fit from the sample S  CORRECT ANSWER ChiSquareSuitableModelTest(S, Normal(0, 1), level = 0.5e-1): print():
 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
 (1)
 > # 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():
 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
 (2)
 > # 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():
 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
 (3)
 > ChiSquareSuitableModelTest(S, Normal(a, 1), level = 0.5e-1, fittedparameters = 1):  #CORRECT ANSWER print(): # verification m := Mean(S); print():
 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
 (4)
 > ChiSquareSuitableModelTest(S, Normal(0, b), level = 0.5e-1, fittedparameters = 1):  #CORRECT ANSWER print(): # verification s := sqrt((add(S^~2) - 0^2) / N); print():
 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
 (5)
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