Analysis of Variance anoVa Robust System Design 16881 mit 人 Session #7
Analysis of Variance ANOVA Robust System Design 16.881 Session #7 MIT
Proposed Schedule changes Switch lecture N o quiz Informal (ungraded) presentation of term project ideas Read Phadke ch. 7--Construction Orthogonal arrays Quiz on anova Noise experiment due Robust System Design 16881 mit 人 Session #7
Proposed Schedule Changes • Switch lecture • N o qu iz – 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 16881 mit 人 Session #7
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
ypothesis lesting a technique that uses sample data from a population to come to reasonable conclusions with a certain degree of confidence Robust System Design 16881 mit 人 Session #7
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(Ho)-- 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 ofh Robust System Design mit 人 16881 Session #7
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 Ho Robust System Design 16.881 Session #7 MIT
Hypothesis Testing Terms(cont Level of significance(a)-- 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 p-value in a right-tailed test p-value in a two-tailed test Robust System Design mit 人 16881 Session #7
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 Ho Robust System Design 16.881 Session #7 MIT
C omparing the Variance of two samples Null hy hypothesis 0 2 Test statistic --F lVar(Ⅹ1) 2 Var(X2) Acceptance criteria-PPF(F, d1, d 2)-05< 1-a Assumes independence normal dist Robust System Design mit 人 16881 Session #7
Robust System Design 16.881 Session #7 MIT Comparing the Variance of Two Samples • Null Hypothesis -- Ho: • Test Statistic -- • Acceptance criteria -- • Assumes independence & normal dist. = r 2 1 σ σ F 1 r 2 Var ( X1 Var ( X2 . 2 1 ( , 1, 2) 0.5 −α pF F d d − < ) )
F Distribution Three arguments di (numerator doF) d2(denominator DOF) x(cutoff) d1 +d2 d1.d2 2 or x 十 F(x, dl, d2) Robust System Design mit 人 16881 Session #7
F Distribution • Three arguments – d1 (numerator DOF) – d2 (denominator DOF) – x (cutoff) F(x,d1,d2) Γ d1 d2 2 d1 d1 2 . d2 d2 2 . Γ d1 2 Γ d2 2 . x d1 2 1 d1 x. ( d2 d1 d2 2 . for x > 0 x ) Robust System Design 16.881 Session #7 MIT
Rolling dice Population 1-- roll one die Population 2-- roll two die Go to excel sheet dice f test.xls Robust System Design mit 人 16881 Session #7
Rolling Dice • Population 1 -- Roll one die • Population 2 -- Roll two die • Go to excel sheet “dice_f_test.xls” Robust System Design 16.881 Session #7 MIT
One-way anova Null Hypothesis-- Ho: A=2=u3 SSB Test statistic F. dfB SW Acceptance criteria -- pF(F, dfB, dfW)<(1-a) A ssumes independence normal dist Robust System Design 人 16881 Session #7
One-way ANOVA • Null Hypothesis -- H o: µ1 = µ2 = µ3 = L • Test Statistic -- F SSB SSW dfB dfW • Acceptance criteria -- pF (F , dfB , dfW) < (1 α) • Assumes independence & normal dist. Robust System Design 16.881 Session #7 MIT