2700 days ago by macieksk

%r faircoin <- function(nf_vec){ #Lamiemy wektor "na pol" twocol<-matrix(nf_vec,ncol=2) if (length(nf_vec)%%2 != 0) twocol <- twocol[-nrow(twocol),] #zabieramy ostatni wiersz #twocol # [...] - tutaj wpisz brakujacy kod porownujacy twocol[,1] i twocol[,2] - 1sza i druga kolumne macierzy #Mozna tak jak ponizej #res<-c() #for (i in 1:nrow(twocol)){ # if (twocol[i,1]!=twocol[i,2]) # res<-c(res,twocol[i,1]) #} #res #Ale mozna tez tak, i tak jest duzo szybciej - nie ma przyrostowej alokacji i petli goodpairs <- twocol[,1]!=twocol[,2] res<-twocol[goodpairs,1] res } 
%r res<-faircoin(rnorm(2500)>1.0) summary(res) 
   Mode   FALSE    TRUE    NA's 
logical     157     177       0 
%r #sum(res) - przy sumowaniu True zamieniane są na 1 a False na 0. binom.test(sum(res),length(res)) 
	Exact binomial test

data:  sum(res) and length(res) 
number of successes = 177, number of trials = 334, p-value = 0.2985
alternative hypothesis: true probability of success is not equal to
95 percent confidence interval:
 0.4748554 0.5844893 
sample estimates:
probability of success 
%r ?binom.test 
binom.test                package:stats                R

_E_x_a_c_t _B_i_n_o_m_i_a_l _T_e_s_t


     Performs an exact test of a simple null hypothesis about the
     probability of success in a Bernoulli experiment.


     binom.test(x, n, p = 0.5,
                alternative = c("two.sided", "less", "greater"),
                conf.level = 0.95)

       x: number of successes, or a vector of length 2 giving the
          numbers of successes and failures, respectively.

       n: number of trials; ignored if 'x' has length 2.

       p: hypothesized probability of success.

alternative: indicates the alternative hypothesis and must be one of
          '"two.sided"', '"greater"' or '"less"'.  You can specify
          the initial letter.

conf.level: confidence level for the returned confidence interval.


     Confidence intervals are obtained by a procedure first given in
     Clopper and Pearson (1934).  This guarantees that the
     level is at least 'conf.level', but in general does not give
     shortest-length confidence intervals.


     A list with class '"htest"' containing the following

statistic: the number of successes.

parameter: the number of trials.

 p.value: the p-value of the test.

conf.int: a confidence interval for the probability of success.

estimate: the estimated probability of success.

null.value: the probability of success under the null, 'p'.

alternative: a character string describing the alternative

  method: the character string '"Exact binomial test"'.

data.name: a character string giving the names of the data.


     Clopper, C. J. & Pearson, E. S. (1934).  The use of
confidence or
     fiducial limits illustrated in the case of the binomial.
     _Biometrika_, *26*, 404-413.

     William J. Conover (1971), _Practical nonparametric
     New York: John Wiley & Sons.  Pages 97-104.

     Myles Hollander & Douglas A. Wolfe (1973), _Nonparametric
     Statistical Methods._ New York: John Wiley & Sons.  Pages

_S_e_e _A_l_s_o:

     'prop.test' for a general (approximate) test for equal or given


     ## Conover (1971), p. 97f.
     ## Under (the assumption of) simple Mendelian inheritance, a
     ##  between plants of two particular genotypes produces progeny
1/4 of
     ##  which are "dwarf" and 3/4 of which are "giant",
     ##  In an experiment to determine if this assumption is
reasonable, a
     ##  cross results in progeny having 243 dwarf and 682 giant
     ##  If "giant" is taken as success, the null hypothesis is that
p =
     ##  3/4 and the alternative that p != 3/4.
     binom.test(c(682, 243), p = 3/4)
     binom.test(682, 682 + 243, p = 3/4)   # The same.
     ## => Data are in agreement with the null hypothesis.