ss.maxT               package:multtest               R Documentation

_P_r_o_c_e_d_u_r_e_s _t_o _p_e_r_f_o_r_m _m_u_l_t_i_p_l_e _t_e_s_t_i_n_g

_D_e_s_c_r_i_p_t_i_o_n:

     Given observed test statistics, a test statistics null
     distribution, and alternetive hyptheses, these multiple testing
     procedures provide family-wise error rate (FWER) adjusted
     p-values, cutoffs for test statistics, and possibly confidence
     regions for estimates. Four methods are implemented, based on
     minima of p-values and maxima of test statistics.

_U_s_a_g_e:

     ss.maxT(null, obs, alternative, get.cutoff, get.cr, 
     get.adjp, alpha = 0.05)

     ss.minP(null, obs, rawp, alternative, get.cutoff, get.cr, 
     get.adjp, alpha=0.05)

     sd.maxT(null, obs, alternative, get.cutoff, get.cr, 
     get.adjp, alpha = 0.05)

     sd.minP(null, obs, rawp, alternative, get.cutoff, get.cr, 
     get.adjp, alpha=0.05)

_A_r_g_u_m_e_n_t_s:

    null: A matrix containing the test statistics null distribution,
          e.g. the output of 'boot.resample'.

     obs: A vector of observed test statistics, e.g. the output of a
          test statistics closure such as 'meanX'. These are stored as
          a matrix with numerator (possibly absolute value or negative,
          depending on the value of alternative) in the first row,
          denominator in the second row, and a 1 or -1 in the third row
          (depending on the value of alternative). The observed test
          statistics are obs[1,]*obs[3,]/obs[2,].

    rawp: Numeric vector of unadjusted ("raw") marginal p-values.

alternative: Character string indicating the alternative hypotheses, by
          default 'two.sided'. For one-sided tests, use 'less' or
          'greater' for null hypotheses of 'greater than or equal'
          (i.e. alternative is 'less') and 'less than or equal',
          respectively.

get.cutoff: Logical indicating whether to compute thresholds for the
          test statistics. Default is 'FALSE'.

  get.cr: Logical indicating whether to compute confidence intervals
          for the estimates. Not available for f-tests. Default is
          'FALSE'.

get.adjp: Logical indicating whether to compute adjusted p-values.
          Default is 'TRUE'.

   alpha: The target nominal type I error rate, which may be a vector
          of error rates. Default is 0.05.

_D_e_t_a_i_l_s:

     Having selected a suitable test statistics null distribution,
     there remains the main task of specifying rejection regions for
     each null hypothesis, i.e., cut-offs for each test statistic. One
     usually distinguishes between two main classes of multiple testing
     procedures, single-step and stepwise procedures. In single-step
     procedures, each null hypothesis is evaluated using a rejection
     region that is  independent of the results of the tests of other
     hypotheses. Improvement in power, while preserving Type I error
     rate control, may be achieved by stepwise (step-down or step-up)
     procedures, in which rejection of a particular null hypothesis
     depends on the outcome of the tests of other hypotheses. That is,
     the (single-step) test procedure is applied to a sequence of
     successively smaller nested random (i.e., data-dependent) subsets
     of null hypotheses, defined by the ordering of the test statistics
     (common cut-offs or maxT procedures) or unadjusted p-values
     (common-quantiles or minP procedures). 

     In step-down procedures, the hypotheses corresponding to the most
     significant test statistics (i.e., largest absolute test
     statistics or smallest unadjusted p-values) are considered
     successively, with further tests depending on the outcome of
     earlier ones. As soon as one fails to reject a null hypothesis, no
     further hypotheses are rejected. In contrast, for step-up
     procedures, the hypotheses corresponding to the least significant
     test statistics are considered successively, again with further
     tests depending on the outcome of earlier ones. As soon as one
     hypothesis is rejected, all remaining more significant hypotheses
     are rejected.

     These functions perform the following procedures: 
      ss.maxT: single-step, common cut-off (maxima of test statistics) 
      ss.minP: single-step, common quantile (minima of p-values) 
      sd.maxT: step-down, common cut-off (maxima of test statistics) 
      sd.minP: step-down, common quantile (minima of p-values) 

_V_a_l_u_e:

     A list with the following components: 

       c: Object of class '"matrix"', for each nominal (i.e. target)
          level for the test, a vector of threshold values for the
          vector of test statistics.

      cr: Object of class '"array"', for each nominal (i.e. target)
          level for the test, a matrix of lower and upper confidence
          bounds for the parameter of interest for each hypothesis. Not
          available for f-tests.

    adjp: Object of class '"numeric"', adjusted p-values for each
          hypothesis.

_A_u_t_h_o_r(_s):

     Katherine S. Pollard with design contributions from Sandrine
     Dudoit and Mark J. van der Laan.

_R_e_f_e_r_e_n_c_e_s:

     M.J. van der Laan, S. Dudoit, K.S. Pollard (2004), Augmentation
     Procedures for Control of the Generalized Family-Wise Error Rate
     and Tail Probabilities for the Proportion of False Positives,
     Statistical Applications in Genetics and Molecular Biology, 3(1). 
     <URL: http://www.bepress.com/sagmb/vol3/iss1/art15/>

     M.J. van der Laan, S. Dudoit, K.S. Pollard (2004), Multiple
     Testing. Part II. Step-Down Procedures for Control of the
     Family-Wise Error Rate, Statistical Applications in Genetics and
     Molecular Biology, 3(1). <URL:
     http://www.bepress.com/sagmb/vol3/iss1/art14/>

     S. Dudoit, M.J. van der Laan, K.S. Pollard (2004), Multiple
     Testing. Part I. Single-Step Procedures for Control of General
     Type I Error Rates, Statistical Applications in Genetics and
     Molecular Biology, 3(1). <URL:
     http://www.bepress.com/sagmb/vol3/iss1/art13/>

     Katherine S. Pollard and Mark J. van der Laan, "Resampling-based
     Multiple Testing: Asymptotic Control of Type I Error and
     Applications to Gene Expression Data" (June 24, 2003). U.C.
     Berkeley Division of Biostatistics Working Paper Series. Working
     Paper 121. <URL: http://www.bepress.com/ucbbiostat/paper121>

_S_e_e _A_l_s_o:

     'MTP'

_E_x_a_m_p_l_e_s:

     ## These functions are used internally by the MTP function
     ## See MTP function: ? MTP

