1. 12.The Chi-square Test and the Analysis of the Contingency Tables 12.1Contingency Table 12.2A Words of Caution about Chi-Square Test

2. 12.1Contingency Tables General Form of a Contingency Tables Analysis: A Test for Independence Where,

3. Rejection region: Assumption: 1.The n observed counts are a random sample from the population of interest. We may then consider this to be a multinomial experiment with r c possible outcomes 2.The sample size, n, will be large enough so that, for every cell, the expected count,, will be equal to 5 or more.

4. 12.2A Words of Caution about Chi- Square Test The use of x 2 probability as an approximation to the sampling distribution should be avoided when the expected counts are very small. An expected cell count of at least 5 means that the x 2 probability distribution can be used to determine an approximate critical value.

5. If the x 2 value does not exceed the established critical value of x 2, do not accept the hypothesis of independence. (you would be risking Type II error and the probability of committing such an error is unknown. The usual alternative hypothesis is that the classifications are dependent.

6. If the a contingency table x 2 does exceed the critical value, we must be careful to avoid inferring that a causal relationship exists between the classification. The alternative hypothesis states that the two classification are statistically dependent – and statistically dependence does not imply causality. Therefore, the existence of a causal relationship cannot be established by a contingency table analysis.