xmonte {XNomial} | R Documentation |
Use xmonte
to compute a P value to test whether a set of counts fits a specific multinomial distribution. It does this by examining a large number of random outcomes and finding the probability of those cases which deviate from the expectation by at least as much as the observed.
xmonte(obs, expr, ntrials = 1e+05, statName = "LLR", histobins = F, histobounds = c(0, 0), showCurve = T, detail = 1, safety = 1e+08)
obs |
vector containing the observed numbers. All are non-negative integers summing to |
expr |
vector containing expectation. The length should be the same as that of |
ntrials |
the number of random trials to look at, such as |
statName |
name of the test statistic to use as a measure of how deviant an observation is from the expectation. The choices are: “LLR” for the log-likelihood ratio, “Prob” for the probability, “Chisq” for the chisquare statistic. |
histobins |
specifies histogram plot. If set to 0, |
histobounds |
vector of length 2 indicating the bounds for the histogram, if any. If unspecified, bounds will be determined to include about 99.9 percent of the distribution. |
showCurve |
should an asymptotic curve be drawn over the histogram? |
detail |
how much detail should be reported concerning the P value. If 0, nothing is printed for cases where the function is used programmatically. Minimal information is printed if |
safety |
a large number, such as one billion, to set a limit on how many samples will be examined. This limit is there to avoid long computations. |
xmonte
returns a list with the following components:
$ obs |
the observed numbers used as imput |
$ expr |
expected ratios, arbitrary scale |
$ ntrials |
the number of random tables examined |
$ statType |
which test statistic was used |
$ pLLR/pProb/pChi |
the P value computed for the given test statistic |
$ standard.error |
the binomial standard error of the estimated P value |
$ observedLLR |
the value of LLR statistic for these data |
$ observedProb |
the multinomial probability of the observed data under the null hypothesis |
$ observedChi |
observed value of the chi square statistic |
$ histobins |
number of bins in the histogram (suppressed if zero) |
$ histobounds |
range in histogram (suppressed if not used) |
$ histoData |
data for histogram (suppressed if not used) Length is |
$ asymptotoc.p.value |
the P value obtained from the classical asymptotic test – use for comparison only |
#One of Gregor Mendel's crosses produced four types of pea seeds in the numbers as follows: peas <- c(315, 108, 101, 32) #and he expected them to appear in the ratio of 9:3:3:1 according to his genetic model. expected <- c(9, 3, 3, 1) #Test Mendels theory using xmonte(peas, expected) #To see a histogram of the likelihood ratio statistic, use: xmonte(peas, expected, histobins = TRUE) #The red areas of the histogram represent those outcomes deviating from the expected 9:3:3:1 ratio #at least as much as the observed numbers. (Much has been made of the tendency for Mendel's data #to fit the expectations better than expected!) #If you wish to use the standard chisquare statistic as a measure of goodness-of-fit instead #of the LLR, use: xmonte(peas, expected, statName="Chisq", histobins=TRUE)