The p-values test whether or not an observed relationship is statistically significant. The p-values in the deviance table are for the likelihood ratio tests. The likelihood ratio tests are more accurate for small samples than Wald approximation tests. You need to:

1    Identify the p-value at the top of the deviance table. This p-value tells you if there is a significant association between at least one predictor and the response by testing whether all slopes are equal to zero.

2    Compare this p-value to your a-level. If the p-value is less than or equal to the a-level you have selected, the association is significant. A commonly used a-level is 0.05.

·      If the p-value is less than or equal to the a-level, then the association is significant, and you can conclude that at least one predictor is significantly associated with the response.

·      If the p-value is greater than the a-level, then you can conclude that there is no significant association and the interpretation ends.

3    If you concluded in step 2 that there is at least one significant predictor, identify the p-value for each term in the model. These p-values tell you whether or not there is a statistically significant association between a particular predictor variable and the response.

4    Compare the individual p-values to your a-level: If a p-value is less than or equal to the a-level you have selected, the association is significant.

For the cereal data, the p-value for testing that all slopes are zero is 0.011. Assume an a-level of 0.05. Because 0.011 is less than 0.05, you conclude that there is a significant relationship between the response and at least one of the predictor variables.

Now look at the p-values for each predictor. If the a-level is 0.10, ViewAd (P = 0.066) and Children (P = 0.066) are both significant at the 90% confidence level. You would also conclude that there is no significant association between household income and purchase of the cereal.