HypTest6Step

# HypTest6Step - Hypothesis Testing Overview Model and...

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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.

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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 .
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HypTest6Step - Hypothesis Testing Overview Model and...

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