Significance Level
Understanding ๐ผ (Significance Level)
The P-value is compared to a threshold called the significance level, denoted as ๐ผ (alpha).
What Is ๐ผ?
- ๐ผ represents the level of risk you're willing to accept for rejecting the null hypothesis when it's actually true (a Type I error).
- It is chosen before running the test and is typically set to:
- ๐ผ = 0.05 (5% risk level): Most common in practice.
- ๐ผ = 0.01 (1% risk level): For more stringent tests.
- ๐ผ = 0.10 (10% risk level): For less stringent tests.
How Does ๐ผ Work?
- If P-value < ๐ผ:
- Reject the null hypothesis.
- The result is considered statistically significant.
- Example: If P = 0.02 and ๐ผ = 0.05, you conclude the result is significant.
- If P-value โฅ ๐ผ:
- Fail to reject the null hypothesis.
- The result is not statistically significant.
- Example: If P = 0.07 and ๐ผ = 0.05, you conclude the result is not significant.
Example in Practice
Imagine testing two ads (A and B):
- Case 1: P = 0.03, and ๐ผ = 0.05:
- Since P < ๐ผ, you conclude that one ad performs significantly better than the other.
- Case 2: P = 0.08, and ๐ผ = 0.05:
- Since P โฅ ๐ผ, you conclude thereโs no significant difference between the ads.
What Happens if You Change ๐ผ?
- A smaller ๐ผ (e.g., 0.01) makes it harder to declare results significant, reducing the risk of false positives (Type I errors).
- A larger ๐ผ (e.g., 0.10) makes it easier to find significance but increases the risk of false positives.
Key Takeaway
The threshold for comparison is the significance level (๐ผ), and it determines whether your result is statistically significant:
- Typical values: ๐ผ = 0.05, ๐ผ = 0.01, or ๐ผ = 0.10.
- P-value < ๐ผ means the result is statistically significant.
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