Explain the difference between Type I and Type II errors.

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Type I and Type II errors are two kinds of mistakes that can occur in statistical hypothesis testing.

✅ Type I Error (False Positive):

Occurs when the null hypothesis is true, but we incorrectly reject it.

• You're saying there's an effect or difference when there isn't.

• Think of it as a false alarm.

Example:

A medical test wrongly indicates a person has a disease when they actually don’t.

• Probability of Type I error = α (alpha), usually set at 0.05 (5%)

❌ Type II Error (False Negative):

Occurs when the null hypothesis is false, but we fail to reject it.

• You're saying there's no effect or difference when there is one.

• Think of it as missing the signal.

Example:

A medical test fails to detect a disease that a person actually has.

• Probability of Type II error = β (beta)

• Power of the test = 1 − β (the chance of correctly detecting an effect)

Why It Matters:

• In critical fields (like medicine or engineering), minimizing Type I errors may be more important to avoid false positives.

• In other cases, avoiding Type II errors may be the priority, especially if missing a true effect is riskier.

Balancing both errors is key to sound statistical analysis.

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