在R软件中检验“种族不影响工资”联合假设的方法咨询

Hey there! Let's break down how to test your joint hypothesis clearly. Your goal is to verify whether race has no impact on wages, which means we're testing the null hypothesis that both the black and hispanic coefficients are simultaneously zero (H₀: β_BLACK = 0 and β_HISP = 0; H₁: at least one of these coefficients is non-zero). Here are two reliable methods to do this in R:

Method 1: Using linearHypothesis() from the car Package #

This is the most direct way to test joint hypotheses for linear models:

1. First, make sure you've fitted your full regression model (replace wage with your actual dependent variable name):

   # Fit the full model including all your variables
   full_model <- lm(wage ~ BLACK + EXPER + HISP + MAR + school + union, data = P1)
   

2. If you haven't already, install and load the car package (you only need to install it once):

   install.packages("car")
   library(car)
   

3. Run the joint hypothesis test:

   # Test that both BLACK and HISP coefficients equal 0
   linearHypothesis(full_model, c("BLACK = 0", "HISP = 0"))
   

   • How to interpret the result: Look at the F-statistic and its corresponding Pr(>F) (p-value). If the p-value is smaller than your chosen significance level (e.g., 0.05), you reject the null hypothesis—meaning race does affect wages. If the p-value is larger, you can't reject the null.

Method 2: Comparing Restricted vs. Full Models with anova() #

This method works by comparing a model that excludes the race variables (restricted model) to your full model:

1. Fit the restricted model (omit BLACK and HISP):

   restricted_model <- lm(wage ~ EXPER + MAR + school + union, data = P1)
   

2. Use the anova() function to compare the two models:

   anova(restricted_model, full_model)
   

   • Interpretation: The output will show an F-test for the difference between the models. The p-value here tells you the same thing as above—if it's below your significance threshold, reject the null hypothesis that race doesn't affect wages.

A quick note: Double-check that your dependent variable name (I used wage as a stand-in) matches what's in your dataset, and that variable names in the model match exactly what's in P1 (e.g., BLACK vs. black—case matters in R!).

内容的提问来源于stack exchange，提问作者Ken Okech