Econometrics
Explainer
Is Your Coefficient Significant? The t-Test
A big slope can still be statistically meaningless. Here's why.
Quick check · tap an answer to continue
Lesson notes
Key points
- Because estimates come from a sample, every coefficient has a standard error measuring how much it would vary across samples.
- To test whether X matters, we set the null hypothesis that the true slope equals zero.
- The t-statistic divides the estimated slope by its standard error, measuring how many standard errors it sits from zero.
- In large samples, if the absolute t exceeds about 1.96, we reject the null at the five percent significance level.
Definitions
- Standard error
- The estimated standard deviation of a coefficient's sampling distribution
Takeaway: Significance depends on the estimate relative to its standard error.
Quick check: β̂₁ = 0.4, se = 0.5. At 5%, what do you conclude?
- Fail to reject H₀
- Reject H₀
- X definitely causes Y
Standard errorNull hypothesist-statisticReject H₀
Lessons like this, for your syllabus.
Short narrated study videos written for your course, level and exam. Free to start.
Get lessons for your own syllabus