So… what even is hypothesis testing?

Okay, let’s start with a simple question. Say you flip a coin 10 times and get 7 heads. Is the coin rigged? Or did you just get lucky?

That’s basically what hypothesis testing does — it helps you figure out whether something you observed in data is a real pattern, or whether it could’ve just happened by chance.

In economics, we deal with this all the time. Did raising the minimum wage actually reduce jobs? Did a new training programme actually raise people’s earnings? Did a new tax actually change consumer behaviour? We can’t just look at the numbers and say “looks about right.” We need a proper way to test it.

Hypothesis testing is that proper way.

Think of it like a court case

Here’s a useful way to think about it. In a court, the accused is presumed innocent until proven guilty. You need strong enough evidence to convict.

Hypothesis testing works the same way:

• The null hypothesis (H₀) is “innocent” — no effect exists.
• Your data is the evidence.
• The significance level is the standard of proof you need.
• If the evidence is strong enough (p-value < 0.05), you “convict” — you reject the null and conclude something real is happening.

And just like in a court — failing to convict doesn’t mean the person is definitely innocent. It just means you didn’t have enough evidence. Similarly, failing to reject H₀ doesn’t mean the effect doesn’t exist. It just means your data couldn’t prove it.

The 5 steps every economist follows

1. State your hypotheses. Write out H₀ and H₁ clearly. Example: H₀: the new drug has no effect on blood pressure. H₁: it does have an effect.
2. Pick your significance level. Usually α = 0.05 (5%).
3. Calculate your test statistic. This tells you how unusual your results are.
4. Find the p-value. How likely are these results under H₀?
5. Make your call. If p < 0.05 → reject H₀. If p ≥ 0.05 → don’t reject H₀.

The t-statistic — let’s do the maths (don’t panic!)

The most common test in economics is the t-test. The formula looks scarier than it is:

Think of it this way: the t-statistic just asks “how many standard errors away from zero is my estimate?” If it’s far away (say, 2 or more), that’s suspicious. It suggests your result probably isn’t just random noise.

For a regression coefficient β̂:

If |t| > 1.96, you reject H₀ at the 5% level. Simple as that.

Quick reference table — critical values

Type I and Type II errors — the two ways to be wrong

Here’s something students always find tricky. There are two ways to mess up a hypothesis test:

Confidence intervals — the range version of hypothesis testing

Instead of just saying “significant or not,” a confidence interval gives you a range where the true value probably sits.

So if your estimate is 0.08 and your SE is 0.03, your 95% CI is (0.08 − 0.059, 0.08 + 0.059) = (0.021, 0.139).

If zero is NOT inside that interval, your result is statistically significant at 5%. If zero IS inside — you can’t rule out “no effect.”

Wait — what does the p-value actually mean?

This is probably the most misunderstood thing in all of statistics. Let’s clear it up.

A p-value of 0.03 means: “If there was truly no effect, there’s only a 3% chance we’d see results this extreme by pure luck.”

It does NOT mean:

• “There’s a 97% chance the effect is real.” (Nope.)
• “The effect is large or important.” (Nope.)
• “We found truth.” (Definitely nope.)

A big sample can give you a tiny p-value even for a completely meaningless effect. Always ask: “Okay, but is this effect actually big enough to matter in real life?”

📋 Case Study: Did Raising Minimum Wage Kill Jobs?

✏️ Practice Questions

🎯 Summary — the key things to remember

• Hypothesis testing tells you whether a result is likely to be real or just a fluke.
• H₀ is your “nothing’s happening” baseline. H₁ is what you’re trying to show.
• The t-statistic measures how far your estimate is from zero, in standard error units.
• If p < 0.05, you reject H₀ and call the result statistically significant.
• Type I error = false alarm. Type II error = missed a real effect.
• Statistical significance ≠ economic importance. Always check the size of the effect too.
• The Card-Krueger minimum wage study is a brilliant example of data overturning theory.

📚 References & Further Reading

1. Card, D. & Krueger, A.B. (1994). Minimum wages and employment. American Economic Review, 84(4), 772–793. — The classic study that started the minimum wage debate.
2. Wooldridge, J.M. (2019). Introductory Econometrics (7th ed.). Cengage. — Best textbook for beginners going deeper.
3. Stock, J.H. & Watson, M.W. (2020). Introduction to Econometrics (4th ed.). Pearson.
4. Wasserstein et al. (2019). Moving beyond “p < 0.05.” The American Statistician, 73(S1). — A must-read on why p-values are often misused.
5. Ziliak, S.T. & McCloskey, D.N. (2008). The Cult of Statistical Significance. University of Michigan Press. — Great accessible read on economic significance vs statistical significance.