When is the x2 test robust

EDA Techniques 1. Quantitative Techniques 1. Purpose: Test for distributional adequacy. The chi-square test Snedecor and Cochran, is used to test if a sample of data came from a population with a specific distribution.

An attractive feature of the chi-square goodness-of-fit test is that it can be applied to any univariate distribution for which you can calculate the cumulative distribution function.

The chi-square goodness-of-fit test is applied to binned data i. This is actually not a restriction since for non-binned data you can simply calculate a histogram or frequency table before generating the chi-square test. However, the value of the chi-square test statistic are dependent on how the data is binned. Another disadvantage of the chi-square test is that it requires a sufficient sample size in order for the chi-square approximation to be valid.

The chi-square test is an alternative to the Anderson-Darling and Kolmogorov-Smirnov goodness-of-fit tests. The chi-square goodness-of-fit test can be applied to discrete distributions such as the binomial and the Poisson. The Kolmogorov-Smirnov and Anderson-Darling tests are restricted to continuous distributions.

Additional discussion of the chi-square goodness-of-fit test is contained in the product and process comparisons chapter chapter 7. The chi-square test is defined for the hypothesis: H 0 :. One of the limitations is that all participants measured must be independent, meaning that an individual cannot fit in more than one category.

If a participant can fit into two categories a chi-square analysis is not appropriate. Keeping in line with our tomato plant example, if a tomato plant, when measured, can be put in more than one box, a chi-square statistic is not appropriate. So the plant must be either resistant or susceptible and show just one banding pattern A, B or H.

Another limitation with using chi-square is that the data must be frequency data. For example if you are just counting how many tomato plants show resistance to bacterial spot versus how many show susceptiblity, than a chi-square is appropriate.

Also when calculating the number of expected individuals for each class, there should be greater than 5 for each class for the most appropriate use of chi-square. Another consideration one must make is that the chi-square statistic is sensitive to sample size.

Purchase Products Training Support Company. How do the ML estimation commands e. Title Chi-squared test for models estimated with robust standard errors Author William Sribney, StataCorp When you specify vce robust , specify vce cluster clustvar , or use pweight s for a maximum likelihood estimation command that allows these options, the model chi-squared test is a Wald test rather than a likelihood-ratio test.

Reference Korn, E. Simultaneous testing of regression coefficients with complex survey data: Use of Bonferroni t statistics. American Statistician — Stata New in Stata Why Stata? Order Stata.