The p-value is a probability that measures the evidence against the null hypothesis. Lower probabilities provide stronger evidence against the null hypothesis.
In a designed experiment, covariates account for variables that are measurable, but difficult to control. For example, members of a quality team at a hospital network design an experiment to study length of stay for patients admitted for total knee replacement surgery. For the experiment, the team can control factors like the format of pre-surgical instructions. To avoid bias, the team records data on covariates that they cannot control, such as the age of the patient.
To determine whether the association between the response and a covariate is statistically significant, compare the p-value for the covariate to your significance level to assess the null hypothesis. The null hypothesis is that the coefficient for the covariate is zero, which implies that there is no association between the covariate 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 different conditions between runs change the response when the conditions do not.
When you assess the statistical significance of terms for a model with covariates, consider the variance inflation factors (VIFs).
- P-value ≤ α: The association is statistically significant
- If the p-value is less than or equal to the significance level, you conclude that the association between the response and the covariate is statistically significant.
- P-value > α: The association is not statistically significant
- If the p-value is greater than the significance level, you cannot conclude that the association between the response and the covariate is statistically significant. You may want to fit a model without the covariate.
All the VIF values are 1 in most factorial designs, which simplifies the determination of statistical significance. The inclusion of covariates in the model and the occurrence of botched runs during data collection are two common ways that VIF values increase, which complicates the interpretation of statistical significance. VIF values are in the Coefficients table. For more information, go to Coefficients table for Analyze Factorial Design and click VIF.