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1、Hypothesis Testing,Pan HaitaoSchool of Statistics, pbinom(12,20,.8)1 0.03214266, 1-pbinom(12,20,.6)1 0.4158929, pbinom(11,20,.8)1 0.009981786 pbinom(10,20,.8)1 0.002594827 pbinom(12,20,.8)1 0.03214266 pbinom(13,20,.8)1 0.08669251,R command,Power calculations for one and two sample t testsDescription
2、Compute power of test, or determine parameters to obtain target power. Usagepower.t.test(n = NULL, delta = NULL, sd = 1, sig.level = 0.05, power = NULL, type = c(two.sample, one.sample, paired), alternative = c(two.sided, one.sided), strict = FALSE) ArgumentsnNumber of observations (per group)deltaT
3、rue difference in meanssdStandard deviationsig.levelSignificance level (Type I error probability)powerPower of test (1 minus Type II error probability)typeType of t testalternativeOne- or two-sided teststrictUse strict interpretation in two-sided case, power.t.test(n = 20, delta = 1) Two-sample t te
4、st power calculation n = 20 delta = 1 sd = 1 sig.level = 0.05 power = 0.8689528 alternative = two.sided NOTE: n is number in *each* group, power.t.test(power = .90, delta = 1) Two-sample t test power calculation n = 22.02110 delta = 1 sd = 1 sig.level = 0.05 power = 0.9 alternative = two.sided NOTE:
5、 n is number in *each* group,Power Calculations for Two-Sample Test for Proportions,DescriptionCompute power of test, or determine parameters to obtain target power. Usagepower.prop.test(n = NULL, p1 = NULL, p2 = NULL, sig.level = 0.05, power = NULL, alternative = c(two.sided, one.sided), strict = F
6、ALSE) ArgumentsnNumber of observations (per group)p1probability in one groupp2probability in other groupsig.levelSignificance level (Type I error probability)powerPower of test (1 minus Type II error probability)alternativeOne- or two-sided teststrictUse strict interpretation in two-sided case, powe
7、r.prop.test(n = 50, p1 = .50, p2 = .75) Two-sample comparison of proportions power calculation n = 50 p1 = 0.5 p2 = 0.75 sig.level = 0.05 power = 0.7401659 alternative = two.sided NOTE: n is number in *each* group, power.prop.test(p1 = .50, p2 = .75, power = .90) Two-sample comparison of proportions
8、 power calculation n = 76.70693 p1 = 0.5 p2 = 0.75 sig.level = 0.05 power = 0.9 alternative = two.sided NOTE: n is number in *each* group, power.prop.test(n = 50, p1 = .5, power = .90) Two-sample comparison of proportions power calculation n = 50 p1 = 0.5 p2 = 0.8026141 sig.level = 0.05 power = 0.9
9、alternative = two.sided NOTE: n is number in *each* group,power.t.test(power = .90, delta = 1, alternative = one.sided) Two-sample t test power calculation n = 17.84713 delta = 1 sd = 1 sig.level = 0.05 power = 0.9 alternative = one.sided NOTE: n is number in *each* group, 2*(1-pnorm(1.58)1 0.114106
10、9 1-pnorm(1.58)1 0.05705343,R solution, d=c(66,74,79,80,69,77,78,65,79,81) t.test(d,mu=75,alternative=greater) One Sample t-testdata: d t = -0.1055, df = 9, p-value = 0.5408alternative hypothesis: true mean is greater than 75 95 percent confidence interval: 71.32406 Inf sample estimates:mean of x 74
11、.8, par(mfrow=c(2,1) boxplot(d) qqnorm(d) qqline(d) par(mfrow=c(1,1), binom.test(14,120,p=0.08,alternative=greater) Exact binomial testdata: 14 and 120 number of successes = 14, number of trials = 120, p-value = 0.09905alternative hypothesis: true probability of success is greater than 0.08 95 percent confidence interval: 0.0719279 1.0000000 sample estimates:probability of success 0.1166667,Page 373,
