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Environmental Modeling Basic Testing Methods - Statistics II

Environmental Modeling Basic Testing Methods - Statistics II. 4. C 2 Test. Test for goodness of fit between the distribution of a sample and a predefined distribution can be used for nominal and ordinal data, i.e. count data divide a distribution into k categories

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Environmental Modeling Basic Testing Methods - Statistics II

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  1. Environmental ModelingBasic Testing Methods - Statistics II

  2. 4. C2 Test • Test for goodness of fit between the distribution of a sample and a predefined distribution • can be used for nominal and ordinal data, i.e. count data • divide a distribution into k categories • can be used for nonparametric statistics

  3. C2 Test • Null hypothesis: the sample has a known distribution k  (Oj - Ej)2 Oj- number of observed  X2 = S -------------   Ej- number of expected 1 Ej

  4. If X2 value > critical value, reject the null hypothesis • Check whether p<a, if so, reject the null Hyp • Otherwise accept the null that the sample has an expected distribution

  5. Null hypothesis: the sample has a normal distribution • Standardize the data:       Xi - X         Zi = --------               S

  6. C2 Test - normal distribution • Divide the normal distribution evenly into n categories • Assign the sample into the n categories • Compare the computed C2 value to the C2 critical values (one-tailed) for specified degrees of freedom and level of significance

  7. t Calculation

  8. If X2 value > critical value, reject the null hypothesis, check whether p<a • otherwise accept the null that the sample has a normal distribution

  9. 5. Kolmogorov-Smirnov Test • Nonparametric substitute for X2 test • It does not group data into categories • It is more sensitive to deviations in the tails

  10. Fit a sample to a normal distribution of unspecified m and s • Null hypothesis: the sample has a normal distribution • Standardize the data:      Xi - X         Zi = ---------               S

  11. Plot a normal distribution and the sample in cumulative form • Find the maximum absolute difference between the two curves         K-S = |normal - sample|

  12. :

  13. Compare the computed K-S value to K-S critical values (one/two-tailed) for specified sample size and level of significance • If the K-S value > critical value, reject the null hypothesis • Check whether p<a, if so, reject the null hypothesis

  14. t Calculation

  15. C2 Test

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