l7_anova4

# l7_anova4 - Analysis of Variance ANOVA 16.881 Robust System...

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Analysis of Variance ANOVA Robust System Design 16.881 Session #7 MIT

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Proposed Schedule Changes • Switch lecture No quiz – Informal (ungraded) presentation of term project ideas Read Phadke ch. 7 -- Construction Orthogonal Arrays – Quiz on ANOVA – Noise experiment due Robust System Design 16.881 Session #7 MIT
Learning Objectives • Introduce hypothesis testing • Introduce ANOVA in statistic practice • Introduce ANOVA as practiced in RD • Compare to ANOM • Get some practice applying ANOVA in RD • Discuss / compare / contrast Robust System Design 16.881 Session #7 MIT

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Hypothesis Testing A technique that uses sample data from a population to come to reasonable conclusions with a certain degree of confidence Robust System Design 16.881 Session #7 MIT
Hypothesis Testing Terms Null Hypothesis (H o ) -- The hypothesis to be tested (accept/reject) Test statistic -- A function of the parameters of the experiment on which you base the test Critical region -- The set of values of the test statistic that lead to rejection of H o Robust System Design 16.881 Session #7 MIT

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Hypothesis Testing Terms (cont.) Level of significance ( α ) -- A measure of confidence that can be placed in a result not merely being a matter of chance p value -- The smallest level of significance at which you would reject H o Robust System Design 16.881 Session #7 MIT
Robust System Design Session #7 MIT 16.881 Comparing the Variance of Two Samples • Null Hypothesis -- H o : • Test Statistic -- • Acceptance criteria -- • Assumes independence & normal dist. r = 2 1 σ σ F 1 r 2 Var X1 ( Var X2 ( . 2 1 5 . 0 ) 2 , 1 , ( α < d d F pF ) )

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F Distribution • Three arguments – d1 (numerator DOF) – d2 (denominator DOF) – x (cutoff) F(x,d1,d2) Γ d1 d2 2 d1 d1 2 .
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