Hypothesis Testing: Is it Real or Random?

Scientific discovery doesn’t happen with a simple “Look.” It happens through Hypothesis Testing. We need a way to determine if a change we observe is a true effect or just a result of random chance.

1. The Power of “No” (The Null Hypothesis)

In statistics, we stay humble. We start by assuming that “there is no effect” (the Null Hypothesis, $H_0$ ). We only accept our new idea (Alternative Hypothesis, $H_1$ ) if the evidence against $H_0$ is overwhelming.

2. The 5-Step Logic Flow

Set Hypotheses

Define H0 (no effect) and H1 (new claim).

Choose Threshold

Select a significance level (α), usually 0.05.

Calculate Statistic

Convert your sample data into a standardized score (z or t).

Find P-value

Calculate the probability $( ext{P})$ of seeing your data if H0 were true.

Make a Decision

If $P < alpha$, we reject H0 and accept H1.

3. Understanding the P-value

The P-value is the most misunderstood number in science. A P-value of 0.03 doesn’t mean your theory is 97% likely to be true; it means there’s only a 3% chance that your data occurred by pure luck if there was absolutely no real effect.

💡 Professor’s Tip

Statistics never “proves” anything for certain. It simply gives us a way to say, “The evidence is strong enough that it’s highly unlikely this was an accident.” Always stay skeptical of a small sample size!

🔗 Next Step

Ch4: Correlation and Regression