# Thread: p-value and hypothesis testing

1. ## p-value and hypothesis testing

Hi, I've one question concerning the p-value. I've run a regression in STATA with one independent variable (x1) with a small positive coefficient and a p-value smaller than 5%. Then, I added another independent variable (x2) that affects my dependent variable and is correlated with my x1. In my new output, my p-value for x1 is still slightly below 5%, the p-value for x2 is below 1%. Can I reject the null hypothesis that x2 has no effect on the dependent variable on a 1%-significance level?

I don't know whether the aggregated p-value for x1 or the single p-value for x2 has to be used.

Thanks!

2. ## Re: p-value and hypothesis testing

So your second model has two independent variables. What was your hypothesis and a priori alpha level of significance?

3. ## Re: p-value and hypothesis testing

First null hypothesis: x1 has no effect on y, significance level <5%
Now I don't know if the combined p-value for x1 and x2 counts, which is still <5% or if I have to take the p-value for x2, which is below 1%, when I want to reject the null hypothesis that x2 has no effect on y, knowing that x2 is correlated with x1.

4. ## Re: p-value and hypothesis testing

Why don't you just drop the first model, since it gets addressed in the second model, so just use the saturated model to test them both. Because if X2 is correlated with X1 that means X1 is correlated with X2.

Ho: X1 not predictive of Y
Ho: X2 not predictive of Y

Model with both terms is significant then you are fine, it will account for the colinearity within the estimates' standard errors. You can also run a Tolerance Test or Variance Inflation Factor to measure the degree of correlation.

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