ONTNU Single hypothesis testing ●Hypothesis test: pH=0:0∈曰o versus 。H=1:0∈Θ1（Θ0∩Θ1=0） Test statistics:T(X),observed t. ●Rejection region:T oIft∈T reject H=O. .IftT accept H=0. Multiple hypothesis testing-recent developments and future challenges-p.4/28
NTNU Single hypothesis testing Hypothesis test: H = 0 : θ ∈ Θ0 versus H = 1 : θ ∈ Θ1 (Θ0 ∩ Θ1 = ∅). Test statistics: T(X), observed t. Rejection region: Γ If t ∈ Γ reject H = 0. If t ∈/ Γ accept H = 0. Multiple hypothesis testing - recent developments and future challenges – p.4/28
ONTNU Single hypothesis testing 0 Rejection region:D pIft∈T reject H=O. .Ift T accept H=0. Multiple hypothesis testing-recent developments and future challenges-p.4/28
NTNU Single hypothesis testing Γ α f T|H=0 t Rejection region: Γ If t ∈ Γ reject H = 0. If t ∈/ Γ accept H = 0. Multiple hypothesis testing - recent developments and future challenges – p.4/28
ONTNU Single hypothesis testing Two types of errors: accept Ho reject Ho Ho type-I error Hu type-II error .Type I error(false positive),θ∈yet t∈T. TypeⅡerror(false negative),O∈Θ1 yett Multiple hypothesis testing-recent developments and future challenges-p.4/28
NTNU Single hypothesis testing Γ α f T|H=0 t Two types of errors: accept H0 reject H0 H0 type-I error H1 type-II error Type I error (false positive), θ ∈ Θ0 yet t ∈ Γ. Type II error (false negative), θ ∈ Θ1 yet t ∈/ Γ Multiple hypothesis testing - recent developments and future challenges – p.4/28
ONTNU Single hypothesis testing Want to control type I error rate; Pr(t∈TH=0), and minimise type II error rate; Pr(tH=1). ·Power=1-Pr(tTH=1) Multiple hypothesis testing-recent developments and future challenges-p.4/28
NTNU Single hypothesis testing Γ α f T|H=0 t Want to control type I error rate; Pr(t ∈ Γ|H = 0), and minimise type II error rate; Pr(t ∈/ Γ|H = 1). Power = 1 − Pr(t ∈/ Γ|H = 1). Multiple hypothesis testing - recent developments and future challenges – p.4/28
ONTNU Single hypothesis testing 。Significant level a=Pr(t∈TlH=O) Multiple hypothesis testing-recent developments and future challenges-p.4/28
NTNU Single hypothesis testing Γ α f T|H=0 t Significant level α = Pr(t ∈ Γ|H = 0). Multiple hypothesis testing - recent developments and future challenges – p.4/28