Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Section 14.2: Inference with Two Way Tables We will have to start by creating a two way table and then the c2 test for Homogeneity (do different categories yield the same results?) OR Association (is there a relationship between the two variables?) The dimensions of a two way table are given by the number of rows and columns (without the totals). This is referred to as a r x c table. Example: Is there is a difference in their responses? In these cases, the H0 is the distribution of the response variable is the same for all populations OR p1 = p2 = p3= … and Ha is the distribution is not all the same OR p1 ≠ p2 ≠ p3 ≠ … Expected count = row total x column total n We will, however do this with the calculator!! • Enter the observed data as a MATRIX • Do the test (Yes this is totally backwards) • It will enter the expected counts into matrix B for you to view Conditions: Check these AFTER the test • All individual expected counts are at least 1 • No more than 20% of expected counts are ≤ 5 Test Statistic and Conclusion c2 (O E ) 2 E (r – 1) (c – 1) degrees of freedom. Use the table to find the P-value Be sure that your conclusion is in context and make note of any largest component, if applicable. c2 test for Association H0: there is no association between the two categorical variables (IN CONTEXT) Ha: there is some association between the categorical variables (IN CONTEXT) The rest of the procedure is IDENTICAL (expected counts, c2 statistic, p-value) to the homogeneity test EXCEPT the conclusion would indicate There was sufficient/ insufficient evidence of an association between _________ and ________. Keep in mind that this test only determines IF there is a relationship between the variables in the table, not what is effecting the relationship. Example: Is student smoking effected by parents smoking? Example: Market researchers know that background music influences mood and purchasing behaviors of customers. A supermarket in Northern Ireland conducted a study comparing three treatments: no music, French accordion music, and Italian string music. The number of bottles of each type of wine sold was recorded (French, Italian, other). Will different music yield a different distribution of wine sales?