um df = 9, denom df = 9, p-value = 0.559
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
0.3712079 6.0167710
sample estimates:
ratio of variances
1.494481
二项分布的总体检验
- 有一批蔬菜种子的平均发芽率为P=0.85,现在随机抽取500粒,用种衣剂进行浸种处理,结果有445粒发芽,问种衣剂有无效果。
binom.test(445,500,p=0.85)
Exact binomial test
data: 445 and 500
number of successes = 445, number of trials = 500, p-value = 0.01207
alternative hypothesis: true probability of success is not equal to 0.85
95 percent confidence interval:
0.8592342 0.9160509
sample estimates:
probability of success
0.89
- 按照以往经验,新生儿染色体异常率一般为1%,某医院观察了当地400名新生儿,有一例染色体异常,问该地区新生儿染色体是否低于一般水平?
binom.test(1,400,p=0.01,alternative="less")
Exact binomial test
data: 1 and 400
number of successes = 1, number of trials = 400, p-value = 0.09048
alternative hypothesis: true probability of success is less than 0.01
95 percent confidence interval:
0.0000000 0.0118043
sample estimates:
probability of success
0.0025
非参数检验
数据是否正态分布的Neyman-Pearson 拟合优度检验-chisq
- 5种品牌啤酒爱好者的人数如下
A 210
B 312
C 170
D 85
E 223
问不同品牌啤酒爱好者人数之间有没有差异?
X<-c(210, 312, 170, 85, 223)
chisq.test(X)
Chi-squared test for given probabilities
data: X
X-squared = 136.49, df = 4, p-value < 2.2e-16
X<-scan()
25 45 50 54 55 61 64 68 72 75 75
78 79 81 83 84 84 84 85 86 86 86
87 89 89 89 90 91 91 92 100
A<-table(cut(X, br=c(0,69,79,89,100)))
#cut 将变量区域划分为若干区间
#table 计算因子合并后的个数
p<-pnorm(c(70,80,90,100), mean(X), sd(X))
p<-c(p[1], p[2]-p[1], p[3]-p[2], 1-p[3])
chisq.test(A,p=p)
Chi-squared test for given probabilities
data: A
X-squared = 8.334, df = 3, p-value = 0.03959
#均值之间有无显著区别
大麦的杂交后代芒性状的比例 无芒:长芒: 短芒=9:3:4,而实际观测值为335:125:160 ,检验观测值是否符合理论假设?
chisq.test(c(335, 125, 160), p=c(9,3,4)/16)
Chi-squared test for given probabilities
data: c(335, 125, 160)
X-squared = 1.362, df = 2, p-value = 0.5061
- 现有42个数据,分别表示某一时间段内电话总机借到呼叫的次数,
接到呼叫的次数 0 1 2 3 4 5 6
出现的频率 7 10 12 8 3 2 0
问:某个时间段内接到的呼叫次数是否符合Possion分布?
x<-0:6
y<-c(7,10,12,8,3,2,0)
mean<-mean(rep(x,y))
q<-ppois(x,mean)
n<-length(y)
p[1]<-q[1]
p[n]<-1-q[n-1]
for(i in 2:(n-1))
p[i]<-1-q[i-1]
chisq.test(y, p= rep(1/length(y), length(y)) )
Chi-squared test for given probabilities
data: y
X-squared = 19.667, df = 6, p-value = 0.003174
Z<-c(7, 10, 12, 8)
n<-length(Z); p<-p[1:n-1]; p[n]<-1-q[n-1]
chisq.test(Z, p= rep(1/length(Z), length(Z)))
Chi-squared test for given probabilities
data: Z
X-squared = 1.5946, df = 3, p-value = 0.6606
P值越小越有理由拒绝无效假设,认为总体之间有差别的统计学证据越充分。需要注意:不拒绝H0不等于支持H0成立,仅表示现有样本信息不足以拒绝H0。
传统上,通常将P>0.05称为“不显著”,0.0l<P≤0.05称为“显著”,P≤0.0l称为“非常显著”。
注:本文参考来自张金龙科学网博客。
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