howmany               package:howmany               R Documentation

_N_u_m_b_e_r _o_f _c_o_r_r_e_c_t _r_e_j_e_c_t_i_o_n_s, _f_o_r _i_n_d_e_p_e_n_d_e_n_t _t_e_s_t _s_t_a_t_i_s_t_i_c_s

_D_e_s_c_r_i_p_t_i_o_n:

     Lower bounds for the number of correct rejections, for independent
     test statistics.

_U_s_a_g_e:

     howmany(pvalues, alpha = 0.05, cutoff = 0.05/length(pvalues))

_A_r_g_u_m_e_n_t_s:

 pvalues: a numeric vector of p-values  

   alpha: the level, a scalar in [0,1]

  cutoff: a scalar in [0,1] 

_D_e_t_a_i_l_s:

     When testing multiple hypotheses simultaneously (test statistics
     are supposed to be independent), a quantity of interest is the
     number of correctly rejected hypotheses.  Given a list of
     p-values, the function provides a  lower bound for the number of
     correct rejections, which is simultaneously valid for all possible
     number of rejections. The bound is monotonically increasing with
     the number of made rejections.

     The level is asymptotically valid (for a large number of tested
     hypotheses). To ensure better small sample behaviour, it is
     recommended to truncate p-values by setting a non-zero value of
     'cutoff'. For a value c of 'cutoff', p-values below c are set to
     c.

_V_a_l_u_e:

     An object of class 'howmany', for which summary, plot, and print
     methods are available. 

     The lower bound for the number of correct rejections (as a
     function of the number of rejections) can be accessed with the
     function 'lowerbound'.

_A_u_t_h_o_r(_s):

     Nicolai Meinshausen, nicolai@stat.math.ethz.ch

_R_e_f_e_r_e_n_c_e_s:

     N. Meinshausen and J. Rice (2006) "Estimating the proportion of
     false discoveries among a large number of independently tested
     hypotheses", Annals of Statistics 34(1)

_S_e_e _A_l_s_o:

     'lowerbound' for extracting the number of correct rejections (as a
     function of the number of made rejections).

     'howmany_dependent' for similar functionality for multiple tests
     of associations, where test statistics can be dependent.

_E_x_a_m_p_l_e_s:

     ##  create a list of pvalues,
     ##  of which 1000 are uniform on [0,1]
     ##  (1000 true null hypotheses),
     ##  and 200 follow a (truncated) chi-squared distribution
     ##  (200 false null hypotheses).
     pvalues <- c(   runif(1000),   pmin(1,0.05*rchisq(200,df=1))  )

     ## compute object of class 'howmany' and print the result
     (object <- howmany(pvalues))

     ## extract the lower bound
     (lower <- lowerbound(object))

     ## plot the result
     plot(object)

     ## for comparison: number of rejections with Bonferroni's correction
     (bonf <- sum( pvalues < (0.05/1200) ))

