STAT1201 Analysis of Scientific Data Semester Two Final Examinations, 2018 Formulas and Statistical Tables BASICS Exj n S =\ n-1 2(x-x)2 STANDARDISING If X ~ Normal(?,o) then Z = '-u _~ Normal(0, 1) BINOMIAL RANDOM VARIABLES P(X =x)=(n) px(1-p)"-x (but is usually available in tables) X E(X)=np sd(X)=\np(1-p) ? =- E(P)=p sd(?)=\ n n p(1-p) P-VALUES AND ERRORS Strong ¥Moderate Weak Inconclusive 00.01 0.05 0.1 1 Decision Reject Type I Error (a) Correct (1-B) Retain H0 is true H0 is false Correct (1-a) Type II Error (B) TESTS AND CONFIDENCE INTERVALS BASED ON STANDARD ERRORS se(estimate) estimate - hypothesised t = estimate + t*se(estimate) s se(x)= p n s2 n1 n2 s + 2 2 se(x1-X2)= 1 1-r2 se(r)= \ n-2 se(p)=1 n p(1-p) se(p1-p2)= 1 - ?(1-?1) + p2(1-p2) n1 n2 Use t for means, correlation and regression. Use z for proportions. Page 15 of 19
Semester Two Final Examinations, 2018 REGRESSION y = b0 + b1 x STAT1201 Analysis of Scientific Data ® 1, O,if Gf Cuyo Ep A X1 = y = bo + b1x + b2X1 POOLED VARIANCE s,2= (n1-1)s21 +(n2-1)s22 n1 + n2 - 2 ANOVA TABLES DFT = n - 1 DFG = k - 1 MS = DF SS R2 = SSG Sp = MSR p SST BONFERRONI CORRECTION FOR k COMPARISONS 0.05 k ODDS AND ODDS RATIOS p Odds = 1-p OR = Odds for group B Odds for group A CHI-SQUARED TESTS expected = (row total) x (column total) F = MI?SR 1 1 1 se(ln(OR))= v -+ -+ -+ - tla bcd x2 = X (observed -expected) overall total df =(# rows - 1) × (# columns - 1) SIGN TEST Count of positive values is X I Binomial(n, 0.5) SIGNED-RANK TEST S = sum of ranks corresponding to positive differences E(S)= n(n +1) Vtn(n+1)(2x4+1) sd(S)= 4 Page 16 of 19