hyptestingchisquaretests.ppt

Presentation Hypothesis Testing Chi-Square Tests Module Objectives By the end of this module the participant will be able to Formulate appropriate hypotheses for Chi-Square Tests for Association Apply Chi-Square Tests for Association to practical problems Why Learn Chi-Square Test for Association? Make data driven decisions with defined confidence Determine if two attribute variables are related. What is the Chi-Square of Association? Chi-Square Test for Association To test if a relationship between two attribute variables exists The Chi-Square Distribution Measure of difference between observed counts and expected counts Observations must be independent Works best with 5 or more observations in each cell Cells may be combined to pool observations Test For Association What Is Chi-Square Test For Association? Tests the hypothesis of independence between two attribute variables Tests if the probabilities of items or subjects being classified for one variable depends upon the classification of the other variable Degrees of Freedom (df): Given we have a (r x c) contingency table, df = (r-1) * (c-1) Why Chi-square Test For Independence? Tests the hypothesis of independence between two variables Probabilities of items or subjects being classified for one variable are tested for dependence on the classifications of the other variable Random and Independent Sampling If expected frequencies are 5, sample size is sufficient Non-parametric test Does not require assumption of normality Used for attribute data Test For Independence Procedure State the practical problem: “Is the Y variable independent of the X variable?” Each combination has equal probability State the statistical problem: Ho : Y independent of X (no difference) Ha : Y dependent of X (at least one combination is different) Calculate the test statistic ?2 observed Determine the critical value of ?2 test statistic Reject the null hypothesis if ?2 observed ?2 critical or Reject the