| Title: | Exact Goodness-of-Fit Test for Multinomial Data with Fixed Probabilities |
|---|---|
| Description: | Tests whether a set of counts fit a given expected ratio. For example, a genetic cross might be expected to produce four types in the relative frequencies of 9:3:3:1. To see whether a set of observed counts fits this expectation, one can examine all possible outcomes with xmulti() or a random sample of them with xmonte() and find the probability of an observation deviating from the expectation by at least as much as the observed. As a measure of deviation from the expected, one can use the log-likelihood ratio, the multinomial probability, or the classic chi-square statistic. A histogram of the test statistic can also be plotted and compared with the asymptotic curve. |
| Authors: | Bill Engels [aut, cre] |
| Maintainer: | Bill Engels <[email protected]> |
| License: | GPL |
| Version: | 1.0.4.1 |
| Built: | 2024-11-06 09:24:30 UTC |
| Source: | CRAN |
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)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)#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)
Use xmulti to compute a P value to test whether a set of counts fits a specific multinomial distribution. It does this by examining all possible outcomes with the same total count and determining the total (multinomial) probability of those cases which deviate from the expectation by at least as much as the observed. Please see the vignette for more.
xmulti(obs, expr, statName = "LLR", histobins = F, histobounds = c(0, 0), showCurve = T, detail = 1, safety = 1e+09)xmulti(obs, expr, statName = "LLR", histobins = F, histobounds = c(0, 0), showCurve = T, detail = 1, safety = 1e+09)
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 |
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. |
xmulti returns a list with the following components:
$ obs |
the observed numbers used as imput |
$ expr |
expected ratios |
$ statType |
which test statistic was used |
$ pLLR |
the P value with LLR as the test statistic |
$ pProb |
the P value with the multinomial probability as test statistic |
$ pChi |
the P value with the chisquare as test statistic |
$ 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 |
$ cases.examined |
the total number of possible tables |
# #One of Gregor Mendel's crosses produced four types of pea seeds in the numbers: # 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 Mendel's theory using # xmulti(peas, expected) # #In this example, the number of cases examined was 28956759, #and it probably took your computer less than half a second. #To see a histogram of the likelihood ratio statistic, use: # xmulti(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: # xmulti(peas, expected, statName="Chisq", histobins=TRUE)# #One of Gregor Mendel's crosses produced four types of pea seeds in the numbers: # 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 Mendel's theory using # xmulti(peas, expected) # #In this example, the number of cases examined was 28956759, #and it probably took your computer less than half a second. #To see a histogram of the likelihood ratio statistic, use: # xmulti(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: # xmulti(peas, expected, statName="Chisq", histobins=TRUE)