# STAT 503 Quiz V

 Sample proportion p-hat = y/ny = success n = number of trials Wilson-adjusted proportion p-tilda = (y+2)/(n+4)to keep p-tilda from 0 or 1 SE for p-hat √(p-hat (1-p-hat)/n) CI for p-hat (95%) p-hat +/- z.025√(p-hat(1-p-hat)/n) =p-hat +/- 1.96√(p-hat(1-p-hat)/n)set upper limit to 1 and lower limit to 0 if surpassunstable, sometimes over coverage, sometimes less (not always 95%) Wilson adjusted 95% CI p-tilda +/- 1.96√(p-tilda(1-p-tilda)/(n+4))set upper limit to 1 and lower limit to 0Gives better coverage (closer to 95%) One sided confidence interval (-∞,p-tilda + 1.65 * SEp-tilda)(p-tilda - 1.65 * SEp-tilda, ∞)Still between 0 or 1 Wilson SE √(p-tilda(1 - p-tilda)/ (n + 4)) Χ2 for more than 2 (Observed - Expected)2 / Expected + all valuesUse dfAll expected have to be greater than 5Can just say if they are different than expectedObserved-expect2 will always be the same so X2 for 2 directional could use binomial H0: p = .75HA: p ≠ .75check with tableFor one sided, ts has to be >/< than 2*alpha ts AND on the right side of expected Test for independence w/ contingency tables p1 = (A|B)p2 = (A|C)H0: p1 = p2 HA: p1 = p2 (p1 >< p2) Expected values in 2x2 tables row total * column total / Grand totalMake sure each is at least 5 df in 2x2 tables (# rows - 1) * (# columns - 1) Directional test with X2 and 2x2 X2 > Xtablefor 2alphaandAlternate hypothesis was satisfiedNon-directional don't double Interpretation for X2 association not causalmaybe causal in controlled studyif one H0 is rejected, differently defined p will be also be rejected from same table What is significance level the likely-hood of making a type I error CI for p-tilda p-tilda1 - p-tilda2 +/- ZApha/2 * SEp1-p2If it contains 0 no differences SE for p-tilda To keep it away from 0 Assumptions for ANOVA each population is normally distributed samples are independentsamples are random For several categories why not pair-wise t-test? Because chance of committing type I error is large for whole testalpha for each pair1- (1-alpha)# columsProblem of multiple comparisonsif lower alpha get higher type II AuthorMRK ID270224 Card SetSTAT 503 Quiz V DescriptionChapter 9 and 10 Updated2014-04-18T01:03:21Z Show Answers