summary.ProbBin.FCS         package:rflowcyt         R Documentation

_C_h_i-_S_q_u_a_r_e_d/_S_t_a_n_d_a_r_d _N_o_r_m_a_l _A_p_p_r_o_x_i_m_a_t_i_o_n _S_u_m_m_a_r_y _S_t_a_t_i_s_t_i_c_s _f_o_r
_a _P_r_o_b_B_i_n._F_C_S _o_b_j_e_c_t

_D_e_s_c_r_i_p_t_i_o_n:

     This function provides summary statistics for the test of
     distribution difference of two samples that have been
     probability-binned or in histogram form.

     Given two probability-binned samples, of which one will be called
     the stimulated sample and the other the unstimulated/control
     sample, the null hypothesis is that both the unstimulated/Control
     Data Histogram/Bins are the statistically the same as the
     Stimulated Data Histogram/Bins.  Thus, the two samples have the
     same distribution in the null hypothesis.

     The alternative hypothesis is that the Unstimulated/Control Data
     Histogram/Bins are significantly different from the Stimulated
     Data Histogram/Bins.  Thus, the two distributions have a different
     distribution.

_U_s_a_g_e:

       summary.ProbBin.FCS(object, verbose=FALSE,...)

_A_r_g_u_m_e_n_t_s:

  object: ProbBin.FCS object

 verbose: Boolean whether to output all the counts in each bin

     ...: not used

_D_e_t_a_i_l_s:

     There are four main test statistics involved which are the
     following:

     1.  Test1: T.chi.unadj=max(0,(PBmetric-mean(PBmetric)) /
     SD(PBmetric)) is approximately standard normal (by the Central
     Limit Theorem (CLT)).  Thus, the test of significance used the
     standard normal test as proposed by Mario Roederer.

     2.  Test2: Adjusted PB metric statistic is distributed as a
     chi-squared statistics.  Thus, the test of significance uses the
     chi-squared test as proposed by Keith A. Baggerly.

     3.  Test3: Adjusted T.chi.unadj statistic is approximately  the
     standard normal (by CLT).  Thus the test of significance uses the
     standard normal test as proposed by Keith A. Baggerly.

     4.  Test4: Pearson's statistic using the Chi-Squared Test. There
     has been a suggestion of using a different number of degrees of
     freedom

     Please note that all four tests use different statistics to test
     the same null hypothesis against the same alternative hypothesis. 

     Test 2 and 3 are ajusted forms of the statistics mentioned in Test
     1.

     Different p-values both one and two-sided are given for those
     applicable statistics.

_V_a_l_u_e:

     A list consisting of: 

PBinType: Type of Probability Binning:

     "_b_y._c_o_n_t_r_o_l" uses the control dataset to obtain the breaks/cutoffs
          to bin the stimulated dataset given a certain number of
          observations in each bin of the control dataset

     "_c_o_m_b_i_n_e_d" uses the combined dataset (both control and stimulated
          datasets) to obtain the breaks/cutoffs for the bins given a
          certain number in each bin 

control.bins: single column matrix of the counts in each bin of the
          control dataset

stim.bins: single column matrix of the counts in each bin of the
          stimulated dataset

total.control: numeric; total number in the control dataset

total.stim: numeric; total number in the stimulated dataset

T.chi.unadj: Roederer's unadjusted normalized PB metric statistic which
          is normalized by subtracting off the mean and then dividing
          by the standard deviation.  This statistic is approximately
          standard normal.

p.val.2tail.z.unadj: Two-tailed standard normal p-value corresponding
          to the Roederer's unadjusted normalized PB metric statistic
          which is approximated as a standard normal

p.val.1tail.z.unadj: Upper standard normal one-tailed p-value
          corresponding to the Roederer's unadjusted PB metric
          statistic which is approximated as a standard normal

PBmetric.unadj: Roederer's unadjusted PB metric which is ((n.c +
          n.s)/(2*nc.*n.s))*Chi-squared or an unadjusted chi-squared
          statistic, where n.c is the number of control observations
          (unbinned) and n.s is the number of stimulated observations
          (unbinned)

PBmetric.adj: Baggerly's adjusted PB metric statistic which is a
          Chi-squared statistic

   PB.df: The degrees of freedom of the PB metric (adjusted and
          unadjusted) which is B-1, where B is the number of bins in
          the eitherthe control or the stimulated binned data

p.val.1tail.chi.adj: Upper one-tailed chi-squared p-value corresponding
          to Baggerly's adjusted PB metric

T.chi.adj: Baggerly's PB metric which is normalized by subtracting off
          the mean and dividing by the standard deviation; This
          normalized statistic is approximately standard normal.

p.val.1tail.z.adj: Upper one-tailed standard normal p-value
          corresponding to the Baggerly's adjusted normalized PB metric
          statistic which is approximated as a standard normal

p.val.2tail.z.adj: Standard normal two-tailed p-value corresponding to
          the Baggerly's adjusted PB metric statistic which is
          approximated as a standard normal

pearson.stat: Pearson's Chi-Squared Statistic with degrees of freedom
          2B-1, where B is the number of bins in either the control or
          the stimulated binned data

pearson.df: the degrees of freedom for the chi-squared statistic

pearson.p.value: The p-value corresponding to the chi-squared
          distribution

pearson.method: string of the indicating the type of test and options
          performed

pearson.dataname: string of the name(s) of the data

pearson.observed: a vector of the observed counts

pearson.expected: a vector of the expected counts under the null
          hypothesis

pearson.p.val.PB.df: Fisher's Chi-squared statistic with degrees of
          freedom B-1, where B is the number of bins in either the
          control or the stimulated binned data

_A_u_t_h_o_r(_s):

     A.J. Rossini and J.Y. Wan

_R_e_f_e_r_e_n_c_e_s:

     Keith A. Baggerly "Probability Binning and Test Agreement between
     Multivariate Immunofluorescence Histograms: Extending the
     Chi-Squared test" Cytometry 45: 141:150 (2001).

     Mario Roederer, et al. "Probability Binning Comparison: A Metric
     for Quantitating Univariate Distribution Differences" Cytometry
     45:37-46 (2001).

     Documentation for 'chisq.test'.

_S_e_e _A_l_s_o:

     'ProbBin.FCS', 'ProbBin.flowcytest', 'chisq.test'

_E_x_a_m_p_l_e_s:

     if (require(rfcdmin)){
       ## obtaining the FCS objects from VRC data
     if ( !(is.element("unst.1829", objects()) & is.element("st.1829", objects())) ){
     data(VRCmin)
     }
     IFN.gamma.1<-unst.1829@data[1:2000,4]
     IFN.gamma.2<-st.1829@data[1:2000,4]

     #Probability binning using the control dataset to determine the breaks
     PB1<-ProbBin.FCS(IFN.gamma.1, IFN.gamma.2, 200,
     varname=colnames(unst.1829@data)[4], PBspec="by.control",MY.DEBUG=FALSE)

     sum.PB1.1<-summary(PB1)
     sum.PB1.2<-summary.ProbBin.FCS(PB1)

     }

