Why We Remove Predictors with P-Values Greater Than Significance Level: Ensuring Statistical Robustness and Model Efficiency

Statistical hypothesis testing is a fundamental approach in data analysis. The significance level, commonly denoted as α, is often set at 0.05 to determine whether to reject the null hypothesis. Understanding the implications of P-values and their relation to the significance level is crucial for building robust and interpretable models. In this article, we explore why predictors with P-values greater than the significance level are typically removed from a model.

Understanding P-Values

A P-value indicates the probability of observing the data or something more extreme given that the null hypothesis is true. A low P-value (P ≤ α) suggests a low probability of observing the data under the null hypothesis, indicating strong evidence against the null hypothesis. Conversely, a high P-value (P > α) suggests that the observed data are not inconsistent with the null hypothesis, and thus, the null hypothesis cannot be rejected.

Model Simplicity and Interpretability

Incorporating predictors with P-values greater than the significance level can complicate the model unnecessarily, diluting the model's explanatory power. A simpler model with only statistically significant predictors is often easier to interpret and communicate. This approach not only simplifies the model but also enhances the clarity and understanding of the model's components.

Avoiding Overfitting

Overfitting occurs when a model learns noise in the training data rather than the underlying relationship, leading to poor generalization to new data. Including too many predictors, especially those that do not contribute meaningful information, can exacerbate this issue. By removing predictors with high P-values, we reduce the risk of overfitting and improve the model's ability to generalize to unseen data.

Focus on Relevant Variables

Retaining only predictors with low P-values (P ≤ α) helps focus the analysis on variables that have a meaningful relationship with the response variable. This selective process enhances the model's performance and reliability, reducing the noise and irrelevant information that can distort the relationship being studied.

Statistical Power

In regression analysis, a model with many predictors may have less power to detect the effects of those that are truly significant. Retaining non-significant predictors can dilute the model's statistical power, making it harder to identify the true underlying relationships. By removing these predictors, we enhance the model's power to detect significant effects, improving its overall predictive accuracy.

Conclusion

Removing predictors with P-values greater than the significance level is a critical step in building robust and interpretable models. This practice ensures that the final model is both statistically robust and practically useful. By focusing on only those variables that provide meaningful insights into the relationship being studied, we enhance the model's predictive accuracy and interpretability, making it more reliable for real-world applications.