CHI2TEST: Single sample Pearson Chi Square goodness-of-fit hypothesis test.
H=CHI2TEST(X,ALPHA) performs the particular case of Pearson Chi Square test to determine whether the null hypothesis of composite normality PDF is a reasonable assumption regarding the population distribution of a random sample X with the desired significance level ALPHA.
H indicates the result of the hypothesis test according to the MATLAB rules of conditional statements:
H=1 => Do not reject the null hypothesis at significance level ALPHA.
H=0 => Reject the null hypothesis at significance level ALPHA.
The Chi Square hypotheses and test statistic in this particular case are:
Null Hypothesis: X is normal with unknown mean and variance.
Alternative Hypothesis: X is not normal.
The random sample X is shifted by its estimated mean and normalized by its
estimated standard deviation. The tested bins XP of the assumed normal distribution are chosen [-inf, -1.6:0.4:1.6, inf] to avoid unsufficient statistics.
Let E(x) be the expected frequency of X falls into XP according to the normal distribution and O(x) be the observed frequency. The Pearson statistics
X2=SUM((E(x)-O(x))^2/E(x)) distributes Chi Square with length(XP)-3 degrees of freedom.
The decision to reject the null hypothesis is taken when the P value (probability that Chi2 random value with length(XP)-3 degrees of freedom is greater than X2)is less than significance level ALPHA.
X must be a row vector representing a random sample. ALPHA must be a scalar.
The function doesn't check the formats of X and ALPHA, as well as a number of the input and output parameters.
The asymptotic limit of the Chi Square Test presented is reached when
LENGTH(X)>90.
Acknowledge: Dr. S. Loyka
Author: G. Levin, May, 2003.
References:
W. T. Eadie, D. Drijard, F. E. James, M Roos and B. Sadoulet, "Statistical Methods in Experimental Physics", North-Holland, Sec. Reprint, 1982. |
