power.n <- function(sigma,e,ci) {
  ci=qnorm((1-z)/2+ci)
  n=(ci^2*sigma^2)/e^2
  if(is.integer(n)){
    paste('所需统计量为',n)
  }else{
    n=ceiling(n)
    paste('所需统计量为小数,整理后为',n)
  }
}#算均值所需的n

power.p=function(pi=0.5,e,ci) {
  ci=qnorm((1-ci)/2+ci)
  s=pi*(1-pi)
  n=(ci^2*s)/e^2
  if(is.integer(n)){
    paste('所需统计量为',n)
  }else{
    n=ceiling(n)
    paste('所需统计量为小数,整理后为',n)
  }
}#算比例所需的n

twom.s=function(sigma.x,sigma.y,n.x,n.y){
  sigmat=sqrt((sigma.x)^2/n.x+(sigma.y)^2/n.y)
  return(sigmat)
}#双均值标准误差

onem.s <- function(s,n) {
  onem.s=s/sqrt(n)
  return(onem.s)
}#单均值标准误差

onep.s<- function(p,n) {
  onep.s=sqrt(p*(1 - p)/n)
  return(onep.s)
}#单个比例标准误差

twop.s <- function(p1,p2,pai1,pai2,n1,n2) {
  twop.s=(p1-p2)-(pai1-pai2)/
    sqrt((pai1*(1-pai1))/n1+
           (pai2*(1-pai2))/n2)
  return(twop.s)
}#双比例标准误差

one.zt.mean <- function(mean.x,mu,s,n) {
  one.z=(mean.x-mu)/(s/sqrt(n))
  return(one.z)
}#求均值的单个z或t统计值

two.zt.mean <- function(mean.x1,mean.x2,mu.x1,mu.x2,sigma.x1,sigma.x2,
                        n1,n2) {
  h=sqrt((sigma.x1^2)/n1+(sigma.x2^2)/n2)
  two.zt.mean=((mean.x1-mean.x2)-(mu.x1-mu.x2))/h
  return(two.zt.mean)
}#没有区别时mu1-mu2=0。双均值的统计量

one.z.prop <- function(p,pai=0.5,n) {
  one.z.prop=(p-pai)/sqrt((pai*(1-pai))/n)
  return(one.z.prop)
}#求比例的单个z或t统计值

two.z.prop.zero=function(x1,x2,n1,n2){
  p=(x1+x2)/(n1+n2)
  p1=x1/n1
  p2=x2/n2
  two.z.prop.zero=
    (p1-p2)/
    sqrt(
      p*(1-p)*(1/n1+1/n2)
    )
  return(two.z.prop.zero)
}#求双比例的统计量等于0

two.z.prop.nonzero <- function(p1,p2,pi1,pi2,n1,n2) {
  h=sqrt((p1*(1-p1))/n1+(p2*(1-p2))/n2)
  two.z.prop.nonzero=
    (p1-p2-(pi1-pi2))/h
  return(two.z.prop.nonzero)
  
}#求双比例的统计量不等于0

one.chisp.var <- function(s,sigma,n) {
  one.chisp.var=(n-1)*(s^2/sigma^2)
  return(one.chisp.var)
}#求方差的单个统计量



normalplot <- function(lengths=3,times=5000) {
  x=pretty(c(-lengths,lengths),times)
  y=dnorm(x)
  plot(x,y,
       type = "l",
       xlab = "Normal Deviate",
       ylab = "Density",
       yaxs = "i")
}

chisqplot <- function(lengths=40,times=5000) {
  x=pretty(c(-lengths,lengths),times)
  y=dchisq(x,10)
  plot(x,y,
       type = "l",
       xlab = "chisp Deviate(n=10)",
       ylab = "Density",
       yaxs = "i")
}
#求分位数
#qchisq(lower.tail = FALSE)
#qt(lower.tail = FALSE)
#qnorm(lower.tail = FALSE)
#求离散变量的累计如P(X<2)
pbinom(2,8,0.5)-dbinom(2,8,0.5)
xSmallerNumber=function(X,n,prob){
  result=pbinom(X,n,prob)-dbinom(X,n,prob)
  return(result)
}
xSmallerNumber(2,8,0.5)

#标准正态分布
pnorm(0.56)-pnorm(-0.38)

#不标准正态分布比例
xunnormal=function(mu,sigma,nbig,nsmall){
  normal1=(nbig-mu)/sigma
  normal2=(nsmall-mu)/sigma
  result=pnorm(normal1)-pnorm(normal2)
  return(result)
}
#普通标准差
#std=sigma/sqrt(n)

#双样本样本标准误
two.std=function(sigma.x1,sigma.x2,n1,n2){
  h=sqrt((sigma.x1^2)/n1+(sigma.x2^2)/n2)
  return(h)
}
#SSA为组间,df=k-1,MSA=SSA/df
#SSR为回归平方和，df=1.MSE=SSE/df
#SSE为组内,df=n-k.MSE=SSE/df
#SSE为残差，df=n-2.MSE=SSE/df
#SST为总平方和,df=n-1.SST=SSA+SSE=SSR+SSE
#R^2=SSA/SST=SSR/SST=1-SSE/SST,R^2为判定系数，r为相关系数
#s_E=sqrt(SSE/(n-2))=sqrt(MSE)
#观测值为总df+1=n
#F=MSR/MSE=SSR/(SSE/n-2)