Unit 5 - Inference for categorical variables

independent proportions The test statistics analyzed by this procedure assume that the difference between the two proportions is zero or their r atio is one under the null hypothesis The non-null (offset) case is discussed in another procedure This procedure computes and compares the power achieved by each of several test statistics that have

Syntax - Stata

r(z) zstatistic r(P #) proportion for variable # r(N #) number of observations for variable # Methods and formulas SeeAcock(2014, 155–161) for additional examples of tests of proportions using Stata A large-sample 100(1 ) conﬁdence interval for a proportion pis bp z 1 =2 r bpqb n

Tests for Two Correlated Proportions (McNemar Test)

N R n R n PD D PD PD D n IR R r N N R n R n − − − + − = = − − ∑∑ 12 0 12 12 1 2 2 where PD = P10+P01 D = P10-P01 N is total of all four cells (N11+N12+N21+N22) r is the smallest integer for which 1 2 ≤ r α IR is the largest integer such that R j j IR R ≤ = ∑ 0 1 2 α Difference or Odds Ratio The formula given above

Introductory Statistics Lectures Testing a claim about two

Two sample proportion hypothesis test requirements (1) simple independent random samples, (2) normal approx to binomial applies to both samples (npand nq 5 for both groups) null hypothesis p 1 = p 2 (specify which is p 1 & p 2 ) alternative hypothesis (1) p 1 6= p 2, (2) p 1 p 2 test in R : prop test(x, n, alternative="two

Chapter 6: Inference for Proportions

r p^(1 ^p) n where the multiplier, z , depends on the desired con dence level For instance, for signi cance level = 0:05 and 95 con dence we would use z = 1:96, and for a more general (1 ) level of con dence we would calculate z with the R command qnorm(1 alpha=2) An hypothesis test for a proportion posits the null hypothesis H 0: p= p 0

Package ‘Exact’ - R

•Z-unpooled - Uses the test statistic from a Z-test without using the pooled proportion 6 exact test •Santner and Snell - Uses the difference in proportion

Package ‘mctest’ - R

R-squared from regression of all x’s on y, Farrar and Glauber chi-square test for detecting the strength of collinearity over the complete set of regressors, Condition Index, Sum of reciprocal of Eigenvalues, Theil’s and Red indicator

Grade 11 Mathematics Practice Test - Nebraska

d = distance, r = rate, t = time: Triangle Rectangle Trapezoid Parallelogram Circle Shape Area Circumference Perimeter C = πd = 2πr P = 2l + 2w 1 A = 2 bh A = lw h (b 1 + b 2) 1 A = 2 A = bh A = r2 Key b = base w = width B = area of base d = diameter h = height r = radius l = length ℓ = slant Use 3 14 for π Right-Triangle Relationships