summary.ProbBin.FCS {rflowcyt}R Documentation

Chi-Squared/Standard Normal Approximation Summary Statistics for a ProbBin.FCS object

Description

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.

Usage

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

Arguments

object ProbBin.FCS object
verbose Boolean whether to output all the counts in each bin
... not used

Details

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.

Value

A list consisting of:

PBinType Type of Probability Binning:
"by.control"
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
"combined"
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

Author(s)

A.J. Rossini and J.Y. Wan

References

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.

See Also

ProbBin.FCS, ProbBin.flowcytest, chisq.test

Examples


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)

}

[Package rflowcyt version 1.10.1 Index]