Goodness-of-Fit Chi-Square Test: 1- Select intervals, k=number of intervals 2- Count number of observations in each interval O i 3- Guess the fitted distribution 4- Decide on p = number of parameters of this distribution (if values of parameters are calculated from the sample data), otherwise p = Calculate expected number in each interval e i 6- Calculate Then X has a Chi-square distribution. Jan 2007

Hypothesis Testing H0: Data has estimated distribution H1: Data does not have estimated distribution Find P-value related to this X, P-value = Fail to reject Ho if either the following conditions hold: Level of significance is less than P-value Or Jan 2007

P-value < 0.01 generally leads to rejection of H 0 P-value > 0.1 generally leads to acceptance of H 0 If 0.01 < P-value < 0.1 we need to have significance level to make a decision Larger P-value is better for accepting H0. Arena uses “min square error” for best fit and provides information On Chi-square test and Kolmogorov-Smirnov test. Jan 2007

Points of Subjective Decisions for Goodness-of-Fit Test Number of collected observations Quality of collected data Number of cells for histogram Cell width for histogram Cell range for histogram Estimation of distribution and its parameters Selections of Confidence level for Chi-square test Jan 2007