################## 1. example ################################
# Create a user-defined function to convert temperature from degrees Fahrenheit to degrees Celsius # (the result will be presented as “….degrees Fahrenheit  =  ….. degrees Celsius”. )
# T(°C) = (T(°F) - 32)× 5/9


FtoC <- function(f)
{
  c <- (f - 32 ) * 5 / 9
  c=round(c,1)
  cat(f,"Fahrenheit degrees =", c ,"Celsius degrees")
}

FtoC(120)

####################### 2. example ###########################
# Create a user-defined function to convert temperature from degrees Fahrenheit to degrees Celsius # and vice versa. Function allows you to decide what type of conversion (F to C or C to F) will be # used and  the result will be presented automatically as "… .degrees Fahrenheit =… .. degrees # Celsius " or"… .degrees (Celsius) =… .. degrees (Fahrenheit) " according to the selected # conversion type.

TempConv <- function(t,FtoC=T)
{
  if(FtoC)
  {
    c <- (t - 32 ) * 5 / 9
    c=round(c,1)
    cat(t,"Fahrenheit degrees =", c ,"Celsius    degrees")
  }
  
  else
  {
    f <- (9*t/5)+32
    cat(t,"Celsius degrees =", f ,"Fahrenheit degrees")
  }
  
}

TempConv(120)
TempConv(25,FtoC=F)



####################### 3. example #################################
# Create a user defined function to calculate the statistical measure of central tendency (mean or # median) and variability (standard deviation or interquartile range - IQR) according to the result # of the test of normality. The function allows you to specify α value for the test. The result will # present the p-value of the normality test and conclusion that data are sampled from normal or # non-normal population, respectively, and automatically presents the mean and standard deviation # for data from a population with a normal distribution, while for data from a population with a # non-normal distribution the median and IQR.


mysummary = function(x,alpha=0.05) 
{
  x=x[!is.na(x)]
  SW=shapiro.test(x)
  if (SW$p.value>alpha) 
  {
    center = mean(x); 
    spread = sd(x)
    cat("p-value = ",SW$p.value, "data are sampled from normal distribution","\n","Mean = ", center, "\n","SD = ",spread, "\n")
  } 
  else 
  {
    center = median(x); 
    spread = IQR(x)
    cat("p-value = ",SW$p.value, "data are not sampled from normal distribution","\n","Median = ", center, "\n","IQR = ", spread, "\n")
  }
}


a=c(2,5,8,2,4,6,4,7,8,9,5,4,2,5,7,5,6)
b=c(2,5,8,2,4,6,4,7,8,9,5,4,2,5,7,55,68)
mysummary(a)

mysummary(b)
sd(b)
mean(b)

############################ 4. example  ####################################
# Create a user defined function to calculate the confidence interval of standard deviation for # small sample. Function allows you to choose one sided or two sided test and specify α value. The # result will present the lower and upper limits of the interval (in the same way as in the example # of the confidence interval of mean)
 


ci_sd<-function(sample, alpha=0.05, one_sided=FALSE)
{
  sample<-sample[!is.na(sample)]
  
  sample_var<-var(sample)
  
  n<-length(sample)
  
  low<- ifelse(one_sided, sqrt((n-1)*sample_var/qchisq(1-alpha, n-1)), sqrt((n-1)*sample_var/qchisq(1-alpha/2, n-1)) ) 
  
  upp<-ifelse(one_sided, sqrt((n-1)*sample_var/qchisq(alpha, n-1)), sqrt((n-1)*sample_var/qchisq(alpha/2, n-1) )) 
  
  c(low,upp)
  
  
}




sd_a2= ci_sd(a)
sd_a2
sd_a1= ci_sd(a,one_sided=T)
sd_a1


sd_a2= ci_sd(a)
sd_a2
sd_a1= ci_sd(a,one_sided=T)
sd_a1

#function "confint.sd" - library "Ecfun"

sd1=confint.sd(sd(a),length(a)-1)
sd1

sd2=confint.sd(sd(a),length(a)-1, level=0.90)
sd2