R中统计假设检验总结(一)-白红宇

先PS一个：

考虑到这次的题目本身的特点尝试下把说明性内容都直接作为备注写在语句中另外用于说明的部分例子参考了我的教授Guy Yollin在Financial Data Analysis and Modeling with R这门课课件上的例子部分参考了相关package的帮助文档中的例子下面正题

- 戌

> # Assume the predetermined significance level is 0.05.

假设预定的显着性水平是0.05。

> # 1 Shapiro-Wilk Test

> # Null hypothesis:

零假设:

> # The sample came from a normally distributed population.

样本来自正态分布总体

> install.packages("stats")

> library(stats)

> # args() function displays the argument names and corresponding default values of a function or primitive.

args()函数显示一个函数的参数名称和相应的默认值。

> args(shapiro.test)

function (x)

NULL

> # Example 1:

> # Test random sample from a normal distribution.

测试来自正态分布的随机抽样。

> set.seed(1)

> x <- rnorm(150)

> res <- shapiro.test(x)

> res$p.value # > 0.05

[1] 0.7885523

> # Conclusion: We are unable to reject the null hypothesis.

结论：我们无法拒绝零假设。

> # Example 2:

> # Test daily observations of S&P 500 from 1981-01 to 1991-04.

测试S＆P500指数从1981-01到1991-04的日观察值。

> install.packages("Ecdat")

> library(Ecdat)

> data(SP500)

> class(SP500)

[1] "data.frame"

> SPreturn = SP500$r500 # use the $ to index a column of the data.frame

用$符号取出数据框中的一列

> (res <- shapiro.test(SPreturn))

Shapiro-Wilk normality test

data: SPreturn

W = 0.8413, p-value < 2.2e-16

> names(res)

[1] "statistic" "p.value" "method" "data.name"

> res$p.value # < 0.05

[1] 2.156881e-46

> # Conclusion: We should reject the null hypothesis.

结论：我们应该拒绝零假设。

> # 2 Jarque-Bera Test

> # Null hypothesis:

> # The skewness and the excess kurtosis of samples are zero.

样本的偏度和多余峰度均为零

> install.packages("tseries")

> library(tseries)

> args(jarque.bera.test)

function (x)

NULL

> # Example 1:

> # Test random sample from a normal distribution

> set.seed(1)

> x <- rnorm(150)

> res <- jarque.bera.test(x)

> names(res)

[1] "statistic" "parameter" "p.value" "method" "data.name"

> res$p.value # > 0.05

X-squared

0.8601533

> # Conclusion: We should not reject the null hypothesis.

> # Example 2:

> # Test daily observations of S&P 500 from 1981–01 to 1991–04

> install.packages("Ecdat")

> library(Ecdat)

> data(SP500)

> class(SP500)

[1] "data.frame"

> SPreturn = SP500$r500 # use the $ to index a column of the data.frame

> (res <- jarque.bera.test(SPreturn))

Jarque Bera Test

data: SPreturn

X-squared = 648508.6, df = 2, p-value < 2.2e-16

> names(res)

[1] "statistic" "parameter" "p.value" "method" "data.name"

> res$p.value # < 0.05

X-squared

> # Conclusion: We should reject the null hypothesis.

> # 3 Correlation Test

> # Null hypothesis:

> # The correlation is zero.

样本相关性为0

> install.packages("stats")

> library(stats)

> args(getS3method("cor.test","default"))

function (x, y, alternative = c("two.sided", "less", "greater"),

method = c("pearson", "kendall", "spearman"), exact = NULL,

conf.level = 0.95, continuity = FALSE, ...)

NULL

> # x, y: numeric vectors of the data to be tested

x, y: 进行测试的数据的数值向量

> # alternative: controls two-sided test or one-sided test

alternative: 控制进行双侧检验或单侧检验

> # method: "pearson", "kendall", or "spearman"

> # conf.level: confidence level for confidence interval

conf.level: 置信区间的置信水平

> # Example:

> # Test the correlation between the food industry and the market portfolio.

测试在食品行业的收益和市场投资组合之间的相关性。

> data(Capm,package="Ecdat")

> (res <- cor.test(Capm$rfood,Capm$rmrf))

Pearson's product-moment correlation

皮尔逊积矩相关

data: Capm$rfood and Capm$rmrf

t = 27.6313, df = 514, p-value < 2.2e-16

alternative hypothesis: true correlation is not equal to 0

备择假设：真正的相关性不等于0

95 percent confidence interval:

95%置信区间

0.7358626 0.8056348

sample estimates:

样本估计

cor

0.7730767

> names(res)

[1] "statistic" "parameter" "p.value" "estimate"

[5] "null.value" "alternative" "method" "data.name"

[9] "conf.int"

> res$p.value # < 0.05

[1] 0

> # Conclusion: We should reject the null hypothesis.

本文转自einyboy博客园博客，原文链接：http://www.cnblogs.com/einyboy/p/3197584.html，如需转载请自行联系原作者。