codice_prob.R

#https://gist.github.com/cristiano74/d778e0347fea9ff00da6a24b7aae87e5
#gists_temp3

test_proportion=8/9                 #percentuale di successi osservata
total_tested=9                    #nr di deliverd 
passed = round(test_proportion*total_tested)  #nr successi
benchmark_value=0.70                       #valore di riferimento
conf_level=0.95
scope="UniqueOpenRate"

if ( passed<15 )
{ 

            #######################################
            # SAMPLE SELECTION - exact 
            #######################################
            pvalue=binom.test(passed,total_tested,test_proportion,alternative="greater")$p.value
            
            #pvalue= 0,699
            #pvalue
            
            wald.binom.ci <- function(m,n,alpha) {
              theta.hat <- m/n
              theta.se <- sqrt(theta.hat*(1 - theta.hat)/n)
              z.val <- qnorm(1-(1 - alpha/100)/2)
              return(c(theta.hat-theta.se*z.val,theta.hat+theta.se*z.val)) }
            
            
            ac.binom.ci <- function(m,n,alpha) {
              adjust <- qnorm(1-(1 - alpha/100)/2)^2
              return(wald.binom.ci(m+adjust/2,n+adjust,alpha)) }
            
            ac.binom.ci(passed,total_tested,conf_level*100)
            
            library(exactci) 
              #https://cran.r-project.org/web/packages/exactci/exactci.pdf
              
            g=binom.exact(passed,total_tested,p=benchmark_value,
                  alternative = c("greater"),
                  tsmethod = c("central"),
                  conf.level = conf_level,plot=FALSE, midp=TRUE)$p.value
              
              #The probability the observed proportion 0.09 comes from a population greater than 0.11 is 41.34%
              
              prob_pop= 1-g
              prob_pop
              
              if (ac.binom.ci(passed,total_tested,conf_level*100)[2]>1) 
              {upper=1} 
              else 
              {
                upper=ac.binom.ci(passed,total_tested,conf_level*100)[2]
              }
              
              print (paste(c("numero total_tested:"),total_tested), collapse=(" "))
              print (paste(c("benchmark:"),benchmark_value*100,"%"), collapse=(""))
              print (paste("Intervallo di confidenza del",scope,":",c(round(ac.binom.ci(passed,total_tested,conf_level*100)[1]*100,2)),"-",
                           round(upper*100,2),"%"
              )
              )
              
              print(paste(c("Possiamo essere confidenti al", round(prob_pop*100,2),"% di ottenere un",scope,"superiore al benchmark del" ,(benchmark_value*100),"%"),collapse=" "))            
              print(paste(c("Possiamo essere confidenti al", round((1-prob_pop)*100,2),"% di ottenere un",scope,"inferiore al benchmark del" ,(benchmark_value*100),"%"),collapse=" ")) 
                check=0
                  for(i in 1:total_tested)
                  { if (ac.binom.ci(i,total_tested,conf_level*100)[1] >= benchmark_value)
                  { check=check+1}
                  if (check==1)
                    {
                   
                                
                      
                      print (paste(c("numero di successi per ottenere un Lower(ci) >= benchmark:(base",total_tested,"delivered)",i,"successi"), collapse=(" ")))
                      
                      #print(total_tested)
                    
                      print(paste(c("percentuale di successi richiesta per validare il campione in confronto al benchmark (nr delivered prestabilito):", round(i/total_tested*100,2),"%"), collapse = ""))
                      print(paste(c("Nuovo CI (",conf_level*100,"%)", "sulla base dei",i,"successi",
                                    round(ac.binom.ci(i,total_tested,conf_level*100)[1]*100,2),
                                    "-",
                                    round(ac.binom.ci(i,total_tested,conf_level*100)[2]*100,2),
                                    "%",
                                    "(benchmark:", benchmark_value*100, "%)"
                                    ), collapse = " "))
                      
                      
                      }
                
                  }

}
if ( passed>=15)
{ 
##################
# SAMPLE SELECTION - exact 
# NORMAL distribution, large SAMPLE.
##################


  # total_tested=922
  # test_proportion=0.46
  # passed=round(test_proportion*total_tested)
  # benchmark_value=0.31
  # scope="UniqueOpenRate"
  
  res <- prop.test(x = passed, n = total_tested, p = test_proportion, 
                   correct = FALSE)
  # Printing the results
  res 

z=(test_proportion-benchmark_value)/sqrt(benchmark_value*(1-benchmark_value)/total_tested)
pvalue_norm=1-pnorm(z)
#if (pvalue_norm < 1-conf_level)
# { print("risultato sign")
#   print(pvalue_norm)
#   print (paste(c("numero total_tested:"),total_tested), collapse=(" "))
#   print (paste(c("benchmark:"),benchmark_value*100,"%"), collapse=(""))
#   print (paste(c("numero di successi per ottenere un Lower(ci) >= benchmark:(base",total_tested,"delivered)",i,"successi"), collapse=(" ")))
#   
#   print(paste(c("Possiamo essere confidenti al", round(pnorm(z)*100,2),"% di ottenere un",scope,"superiore al benchmark del" ,(benchmark_value*100),"%"),collapse=" "))
#   print(res$conf.int[1])
#   
# }

check=0
for(i in 1:total_tested)
{   prop_value=prop.test(x = i, n = total_tested, p = test_proportion,correct = FALSE)
 if  (prop_value[["conf.int"]][1] >= benchmark_value)  
{check=check+1}
  if (check==1)
  {
    print("Normal")
    print (paste(c("numero total_tested:"),total_tested), collapse=(" "))
    print (paste(c("benchmark:"),benchmark_value*100,"%"), collapse=(""))
    print (paste("Intervallo di confidenza del",scope,":",c(round(res[["conf.int"]][1]*100,2)),"-",
                 round(res[["conf.int"]][2]*100,2),"%"    )    )
    print(paste(c("Possiamo essere confidenti al", round(pnorm(z)*100,2),"% di ottenere un",scope,"superiore al benchmark del" ,(benchmark_value*100),"%"),collapse=" "))            
    print(paste(c("Possiamo essere confidenti al", round((1-pnorm(z))*100,2),"% di ottenere un",scope,"inferiore al benchmark del" ,(benchmark_value*100),"%"),collapse=" "))            
    
    print (paste(c("Validazione: numero di successi minimo per ottenere un Lower(ci) >= benchmark:(base",total_tested,"delivered)",i,"successi"), collapse=(" ")))
   
    #print(total_tested)
    
    print(paste(c("percentuale di successi richiesta per validare il campione in confronto al benchmark (nr delivered prestabilito):", round(i/total_tested*100,2),"%"), collapse = ""))
    print(paste(c("Nuovo CI (",conf_level*100,"%)", "sulla base dei",i,"successi",
                  round(prop_value[["conf.int"]][1]*100),
                  "-",
                  round(prop_value[["conf.int"]][2]*100),
                  "%",
                  "(benchmark:", benchmark_value*100, "%)"), collapse = " "))
      
                  
    
  }
    
  
}

}

stuff.Rmd

Stuff and things
------------------

## head of mtcars

```{r}
head(mtcars)
```

## head of iris

```{r}
head(iris)
```

test.R

test1
test2
ghsdghasgdh