For each parameter in the model, Prism makes a comparison between a model in which this parameter is excluded and one in which it is included. The null hypothesis being tested is that the true population value of the parameter is 0.0. What this means is that the corresponding variable simply has no impact on the outcome variable, or that the difference between the models in which the term was included or excluded is zero. The P value answers the question:
If that null hypothesis were true, what is the chance that analysis of a randomly selected data sample will result in a parameter as far, or further, from zero than reported from this analysis?
For each parameter, Prism reports:
•The P value which is computed from the t ratio and the number of degrees of freedom (equal to the number of rows of data minus the number of columns of data).
•A P value summary, as ns or one or more asterisks.
Note that these P values test individual terms. For continuous variables (or interactions of continuous variables), the P values reported in this section will match the P values reported in the ANOVA table as these terms require only one degree of freedom.
Categorical parameters with more than two levels
For categorical variables with more than two levels, or interaction terms requiring multiple degrees of freedom, the P values reported in this section are different than P values reported in the ANOVA table. Parameter estimates are calculated for each level of a categorical variable (except for the reference level), and a P value is calculated for each parameter estimate. These P values result from a test comparing the specific level of a categorical variable with its reference level. In contrast, the P values reported in the ANOVA table compare the model with and without the entire categorical variable.
Consider a categorical variable with three levels: A, B, and C. In the ANOVA table, a single P value is given for the overall effect of the categorical variable on the model (are the models with and without the categorical variable the same). In the parameter estimates section, two P values will be reported. If the reference level of this categorical variable is A, one P value will be given for the parameter for level [B] and one for the parameter for level [C]. The P value for [B] represents a comparison between the model for the reference level [A] (included in the intercept term) and the model for the specific level [B]. Similarly, the P value for [C] represents a comparison of [A] and [C]. There is no information on a comparison between a model with [B] and [C]! This is just one reason why it’s important to understand how reference levels affect a regression model and its interpretation, and why you should carefully consider which level is being used as the reference level.
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