Analysis of Variance table for Fit Cox Model in a Counting Process Form

The type of test in the ANOVA table depends on the specifications for the analysis. The interpretation of the statistics is the same whether the analysis uses the Wald test, the likelihood ratio test, or the score test.

In This Topic

DF
Chi-Square
P-Value

DF

Degrees of Freedom (DF) give information about the distribution of the associated chi-square test statistic. Continuous predictors use 1 degree of freedom. Categorical predictors use degrees of freedom equal to the number of levels minus 1. Higher-order terms use the product of the degrees of freedom for the component terms.

Chi-Square

Each term in the ANOVA table has a chi-square value. The chi-square value is the test statistic that determines whether a term or model has an association with the response.

Interpretation

Minitab uses the chi-square statistic to calculate the p-value, which you use to make a decision about the statistical significance of the terms and the model. The p-value is a probability that measures the evidence against the null hypothesis. Lower probabilities provide stronger evidence against the null hypothesis. A sufficiently large chi-square statistic results in a small p-value, which indicates that the term or model is statistically significant.

P-Value

The p-value is a probability that measures the evidence against the null hypothesis. Lower probabilities provide stronger evidence against the null hypothesis.

Interpretation

To determine whether the association between the response and each term in the model is statistically significant, compare the p-value for the term to your significance level to assess the null hypothesis. The null hypothesis is that the term's coefficient is equal to zero, which implies that there is no association between the term and the response. Usually, a significance level (denoted as α or alpha) of 0.05 works well. A significance level of 0.05 indicates a 5% risk of concluding that an association exists when there is no actual association.

Under the null hypothesis, the test statistic for each test has an asymptotic chi-square distribution with degrees of freedom equal to the number of coefficients in the model. The asymptotic distribution is valid when the number of observed events is large compared to the number of estimated parameters. For categorical predictors, the number of events in each level must be large enough for the asymptotic distribution to be valid.

P-value ≤ α: The association is statistically significant: If the p-value is less than or equal to the significance level, you can conclude that there is a statistically significant association between the response variable and the term.
P-value > α: The association is not statistically significant: If the p-value is greater than the significance level, you cannot conclude that there is a statistically significant association between the response variable and the term. You may want to refit the model without the term.; If there are multiple predictors without a statistically significant association with the response, you can reduce the model by removing terms one at a time. For more information on removing terms from the model, go to Model reduction.

If a model term is statistically significant, the interpretation depends on the type of term. The interpretations are as follows:

If a categorical factor is significant, you can conclude that the factor has an effect on the time to the event.
If an interaction term is significant, the relationship between a factor and the response depends on the level of the other factors in the term. In this case, you should not interpret the main effects without considering the interaction effect.
If a continuous predictor is significant, you can conclude that changes in the value of the predictor are associated with changes in the risk that the subject experiences the event.
If a coefficient for a polynomial term is significant, you can conclude that the data contain curvature.

Analysis of Variance

		Wald Test
Source	DF	Chi-Square	P-Value
Age	1	1.78	0.182
Stage	3	17.92	0.000

In these results, the p-value for stage is significant at an α-level of 0.05. Therefore, you can conclude that the stage of the cancer has a statistically significant effect on the survival of the patient. However, the p-value for age is 0.182, so the effect of age is not significant at an α-level of 0.05.