Determining the Chi-Square Test P-Value Cutoff for Logistic Regression

In logistic regression, the chi-square test is often utilized to assess the significance of categorical predictors before their inclusion in the model. While there isn't a strict cutoff point, a commonly recommended practice is to use a significance level of

Interpreting P-Values in Chi-Square Tests

Let's delve into the criteria for interpreting the p-values from the chi-square test in the context of logistic regression.

P-Value

If the p-value from the chi-square test is less than 0.05, it suggests that the categorical predictor is statistically associated with the binary outcome. Such predictors are often considered for inclusion in the logistic regression model as they contribute significantly to explaining the variability in the outcome.

P-Value ≥ 0.05

On the other hand, if the p-value from the chi-square test is greater than or equal to 0.05, it may indicate that the predictor is not significantly associated with the outcome. In this case, the predictor may be excluded from the model, particularly if it lacks other theoretical or practical significance. However, the decision to exclude a predictor should also consider the model's overall fit, potential confounding variables, and research goals.

It's important to note that other factors such as the theoretical relevance of the predictors and potential confounding variables should also be taken into account when deciding on model inclusion. These factors can provide additional insights that may influence the final model selection.

Understanding Chi-Square and Logistic Regression

It's often unclear whether a chi-square test should precede or be replaced by logistic regression in certain situations. To address this, it's helpful to distinguish between the two statistical methods:

A chi-square test is a descriptive test that examines the strength of the relationship between categorical variables. It is not a modeling technique and does not have a dependent variable. Instead, it is used to determine the association between two categorical variables.

In contrast, logistic regression is a modeling technique used for predicting a binary outcome. It explicitly defines a dependent variable and provides a way to estimate the risk or odds of the outcome occurring based on the predictors.

According to a discussion on the differences between the chi-square test and logistic regression:

"A Chi-square test is really a descriptive test akin to a correlation. It’s not a modeling technique so there is no dependent variable. So the question is do you want to describe the strength of a relationship or do you want to model the determinants of and predict the likelihood of an outcome." Rebekah Mize

In a simple bivariate model, if you want to explicitly define a dependent variable and make predictions, logistic regression is the appropriate choice, as it allows for the modeling of the determinants and prediction of the likelihood of the outcome.

Therefore, the decision to use a chi-square test should be made based on the need to describe the relationship between variables rather than to predict the outcome. Once you have identified relevant predictors through a chi-square test, you can proceed to build a logistic regression model to predict the outcome variable.

Conclusion

To summarize, the p-value from the chi-square test is a useful tool to determine the significance of categorical predictors in logistic regression. A p-value

Remember, the choice between descriptive and predictive models is not a continuum. Use descriptive tests like the chi-square test to explore the relationship between variables and then use predictive models like logistic regression to make meaningful predictions and draw conclusions from the data.