HypTest6Step - Hypothesis Testing Overview Model and...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Hypothesis Testing Overview Golde Holtzman HypTest6Step.doc 10/31/2006 Model and assumptions , e.g., Y ~N(?, σ ) H 0 : μ = μ 0 H A : μ < μ 0 , μ > μ 0 , μ μ 0 Design α = 0.01, 0.05, 0.10 n β , 1- β Power Perform Survey, Experiment, or Observational Study. Estimator, Standard error, C.I., Test Criterion P-value P < α P > α Decision Reject H 0 NOT Reject H 0 Characterize Statistically Sig, or NOT Stat Sig Conclusion Method. Assuming [ Y ~N(?, σ ), verbally], we tested [H 0 vs. H A , verbally], using the z-test ([cite reference]) with significance level [ α ] and sample size [ n ]. Results. There is significant statistical evidence that [H A , verbally] ([P-value]). There is NOT significant statistical evidence that [H A , verbally] ([P-value]). Truth Table True State of Nature Decision H 0 H A Reject H 0 Type 1 error, α Correct Decision, (1 β ) Power NOT Reject H 0 Correct Decision Type 2 error, β ≡ O.C. P P-value The probability that the distance between the estimator and the hypothetical value of the parameter, in the direction specified by H A , would be as great or greater as that observed, if H 0 were true. α significance level Type 1 error rate, is set by investigator in Design step. β operating characteristic Type 2 error rate = f ( δ ; α , n , σ ), δ = μ - μ 0 , i.e., is a function of (i) the effect , i.e., the difference between the true and the hypothetical (null) value of the parameter of interest, (ii) the significance level, (iii) the sample size, and (iv) the underlying variability. (1 β ) Power P{Reject H 0 | δ ; α , n , σ } = 1 f ( δ ; α , n , σ ). Effect δ = μ μ 0 . The hypotheses, in terms of the effect, are H 0 : δ = 0 H A : δ < 0, δ > 0, or δ 0 Estimated Effect 0 ˆ μδ = Y P-Value = the probability that the estimated effect would be as great as or greater than that observed, in the direction specified by H A , if H 0 were true.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Hypothesis Testing Overview Golde Holtzman HypTest6Step.doc 10/31/2006 Significance level, α Sample size, n Underlying variability, σ Type 1 error rate, α Type 2 error rate, β Controlled by investigator Guiding objectives of Hypothesis Testing Power, (1 −β ) + Effect, δ = ( θ − θ 0 ) + α = significance level = Type 1 error rate = probability of rejecting a true null hypothesis. β = operating characteristic = Type 2 error rate = probability of not rejecting a false null hypothesis. ( 1 β ) = power = sensitivity = probability of rejecting a false null hypothesis. δ = ( θ − θ 0 ) = effect = unknown true value of the parameter, θ , minus null hypothetical value, θ 0 .
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 5

HypTest6Step - Hypothesis Testing Overview Model and...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online