Hypothesis Testing
ELI5: Imagine you want to prove that a toy is safe for children under 3. To prove this, you play with the toy with various kids and then see if they're harmed or not.
Trading Context: Hypothesis testing in trading could be used to prove or disprove a theory, like "Buying stocks on Monday and selling on Friday is more profitable than any other combination of days."
Null and Alternate Hypothesis
ELI5: Using the toy example, the starting belief (or the null hypothesis) is "The toy is not safe for kids under 3." The alternate hypothesis, which you want to prove, is "The toy is safe for kids under 3."
Trading Context: Using the above trading theory: Null Hypothesis (H_0): "Buying on Monday and selling on Friday is not more profitable." Alternate Hypothesis (H_a): "Buying on Monday and selling on Friday is more profitable."
Significance Level (α)
ELI5: When testing the toy, let's say we decide that if even 1 in 100 kids get hurt, that's too many. So, we set a limit of 1% (or 0.01) as our level where we decide the toy is not safe. This limit is called the significance level.
Trading Context: If we decide we need to be 99% sure our trading strategy works, our significance level (α) is 0.01.
P-value
ELI5: After testing, let's say only 1 in 500 kids get hurt. The chance of this happening is 0.002 (or 0.2%). This number is the p-value.
Trading Context: After testing our Monday-Friday theory, let's say there's only a 0.5% chance (p-value = 0.005) that the results happened by random chance.
Rejection Region
ELI5: Remember our 1% limit? If our test results (p-value) fall within this 1%, we reject our starting belief.
Trading Context: If our p-value is less than 0.01, we're in the rejection region, and we reject our null hypothesis. Meaning, our Monday-Friday theory might be valid.
Non-Rejection Region
ELI5: If our test results show that more than 1% of kids could get hurt, we're in the safe zone, and our toy might be safe.
Trading Context: If our p-value is greater than 0.01, we're in the non-rejection region, meaning we don't have enough evidence to believe our trading theory.
Critical Value
ELI5: It's like a cutoff score in a test. If you score above it, you pass; if below, you fail.
Trading Context: This is a value from the distribution (like a z or t distribution) that corresponds to our significance level. If our test statistic exceeds this value, we reject the null hypothesis.
Z-Score
ELI5: It's like measuring how far a student's score is from the average score in a class.
Trading Context: It's how many standard deviations our result is from the mean. If it's very high or very low, it's likely our result didn't happen by chance.
Right-Tailed, Left-Tailed, Two-Tailed
ELI5: If we're only looking at very high scores, it's right-tailed. Very low scores, it's left-tailed. Both ends, it's two-tailed.
Trading Context:
- Right-Tailed: We're only interested if our trading strategy performs significantly better than average.
- Left-Tailed: We're only interested if it performs significantly worse.
- Two-Tailed: We're interested in any significant deviation from the average, whether it's better or worse.
Trading Example:
Let's assume you have a theory that a particular stock rises after a certain news report comes out.
- Null Hypothesis: The news report has no effect on the stock price.
- Alternate Hypothesis: The news report causes the stock price to rise.
- You set a Significance Level (α) of 0.05 (5%).
- After observing the stock for a number of such news reports, you find a p-value of 0.02.
- Since 0.02 is less than 0.05, you're in the Rejection Region.
- This suggests that the news report does indeed affect the stock price, and the likelihood that your observation was due to random chance is only 2%.
- If the stock price consistently goes up significantly more than the average, you have a high Z-score, indicating the result is not just random.
By connecting these dots, you can validate or invalidate trading theories, helping you make more informed trading decisions.