STAT 1201 : Summary Binomial Distribution: E(x)= up Var(x)= np(1-p), sd()=[np(ip) dbinom ( G, size, prob) , pbinom ( xc, size , proff, qbinom ( P , size, prob) Sample e.g. p=4 (9-4) dans TE (P)= P sd (p)= PCI-PJ C.I. = p+ =* * se (P) Proportion: random; sutton prop. test ( 1, n) z?= 2 norm(0.475) be the remranged forma for sensitive question proportion Normal Distribution: z=x2 E(x)=M, su(x)= jz se(x)= ===== C.I. = x± 1.96 ?/ (1.96=quorm(0.975)) qworm (P, mean, sd) , prorm (2, mem, cd) dnorm (x, menl, ad) T- Distribution : T = X-M E for use in T-ted e.g. paul=(- PACT), C.S. = & t EMa1x Jn (=qHours,uk) choosing sample size: n= ( SAN 1.465)? Moe, 1 qt (Pdt), dt (x, dE), pt(2, df) t. test (duta $x) Compusing 2 Population mams: T= (x), -ITx )- (M, -MC) se(xi -52) se( JE .- X) = JS2 + 5,20 2- sided +test: p-value = 2x (1-pt (Tout, df) C.J .= (x1-xz)????+ t+=2+ (0.475,dt) 1 df = min (1 , - 1, H2 - 1 ) E.test ( / mx, data) Pooled T-test: That = JS2(? +?) Sp=(1 -1) si2 +(N=1)S22 1 se (x - x= )= Jsp (+) 11+12 -2 C.J. = (v1-X2) = JSp (thi +2) 6. test CY ~x, data), power . t. test ) Comparing 2 Proportions: 2 stat = (P .- F)- (P,-Pv), se (p. - P=)= [CI-fi)_P2 (1-P) se(pi -Pi) C.J. = (P .- P2)= 2+ (p .- p.) where =quorum (0.425) Prop. test (table (duta$x, data $ Y) nz P-value = 1-prorm (Zstat) Correlation: se (1) = 1-8? n-2 T stolt = r-P se (r ) , moe = Mc - l Ho : P = 0 or cor(x, y) Simple Linear Regression: summary ( Im (5 ~ x, data) four = 01-01 Y=Bo +B,X C.J. = estimate = 6 * selon) where t* = g+(0.975, dt) se" Multiple Linear Regression: sums (hum( Y ~ X1+X2, data), Y=Bo + Bx1+Prixz Adjusted R= 1- [CH-R2 ) (+) ]
One Way Anova: Calcule sample means : aggregate (Y ~x, data , mean ) summus (cov( Yeux, dutu) R= 350 multiple comparisons: - pairwise. + test ( Y, x, p. adjust. method="name") use asfactor (variables when not categorical - Talking HSD(aov ( y ~x, data) TWO Wity AWOUH: aggregate CY ~ Group & X2, data, mean) summary Caou (Y ~ X1 #X2, data) ( observal - expected) ? expected Chi-Square Test: X start = { expected= Row Total × Column Total Total Tefal p- value = 1- pchisy (x2, df ) use: addmurgius (table ( Y, x) chisq : chisq . test (table ( Y , x , data) , chisy & exp gives expected values Logistic Regression: Odds= to model: In (Fr )= 60 + b1 x tio = e bike-bix , summary (slm ( Y~ x, data, family = "binomial") Sign Test: No: M=0.5 M. de> 0.5 p-value = sum (dbinom (D- 2) : 1, prob=0.5 size ) where q=