Testing Errors (Mistakes)

Type 𝐈 & Type 𝐈𝐈 Errors

Type I & Type II Errors are conditional probabilities given the hypothesis is true or false.

Refer to Khan academy: Introduction to Type I and Type II errors

What will happen when we’re to reject a hypothesis?

• Reject the truth: Type I Error
• Not reject the truth
• Reject the false: Power
• Not reject the false: Type II Error

The good thing to do is to Reject the false and Not reject the truth.
The bad thing (error) to do is to Reject the truth and Not reject the false, which are called the Type I Error and Type II Error.

Truth World & Lies World

Although both of them are mistakes for doing the right thing, but they’re under totally opposite conditions:
One is existing in the Truth World, the other in the Lies World

• Type I Error is in a "world" that the null hypothesis is actually true.
• Type II Error is in a "world" that the null hypothesis is actually a lie.

Since they’re “living in a different world”, and they’re Conditional Probabilities, so the calculation is different too:

Example

Solve:

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