Quality of Tests (Edexcel A-Level Further Mathematics): Flashcards

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Type I & Type II Errors
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Type I Error

Rejecting H0H_0 when it is true

Type II Error

Failing to reject H0H_0 when it is false

Probability of Type I error

Denoted by α\alpha (significance level)

Probability of Type II error

Denoted by β\beta

Power of a test formula

1β1 - \beta

Power of a test meaning

Probability of correctly rejecting H0H_0 when H1H_1 is true

Effect of larger critical region on α\alpha and β\beta

Increases α\alpha, decreases β\beta

Effect of smaller critical region on α\alpha and β\beta

Decreases α\alpha, increases β\beta

Power function π(θ)\pi(\theta)

P(Reject H0θ)P(\text{Reject } H_0 | \theta)

Critical region purpose

Determines when H0H_0 is rejected

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