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 1.8.0 Index]