R help - Aug 2008 - Problem with Poisson - Chi Square Goodness of Fit Test - New Mail

Dear R-help,

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Chi Square Test for Goodness of Fit

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I have got a discrete data
as given below (R script)

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No_of_Frauds<-c(1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,2,1,2,2,2,1,1,2,1,1,1,1,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,5,1,2,1,1,1,1,1,1,1,3,2,1,1,1,2,1,1,2,1,1,1,1,1,2,1,3,1,2,1,2,14,2,1,1,38,3,3,2,44,1,4,1,4,1,2,2,1,3)

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I am trying to fit Poisson
distribution to this data using R.

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My R script is as under :

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________________________________________________________

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# R SCRIPT for Fitting
Poisson Distribution

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No_of_Frauds<-c(1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,2,1,2,2,2,1,1,2,1,1,1,1,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,5,1,2,1,1,1,1,1,1,1,3,2,1,1,1,2,1,1,2,1,1,1,1,1,2,1,3,1,2,1,2,14,2,1,1,38,3,3,2,44,1,4,1,4,1,2,2,1,3)

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N ???? ??????? <-???????????? length(No_of_Frauds)

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Average???? <-???????????? mean(No_of_Frauds)

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Lambda???? <-???????????? Average

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i?????????????? <-???????????? c(0:(N-1))

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pmf??? ?????? <-???????????? dpois(i, Lambda, log = FALSE)

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#
----------------------------------------------------------------------------

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# Ho: The data follow Poisson
Distribution Vs H1: Not Ho

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# observed frequencies (Oi)

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variable.cnts
????? <- ??? table(No_of_Frauds)

variable.cnts.prs
 <-???? dpois(as.numeric(names(variable.cnts)),
lambda)

variable.cnts
????? <-???? c(variable.cnts, 0)

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variable.cnts.prs <-???? c(variable.cnts.prs,
1-sum(variable.cnts.prs))

tst
?????????????????? <-???? chisq.test(variable.cnts,
p=variable.cnts.prs)

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chi_squared
?????? <-???? as.numeric(unclass(tst)$statistic)

p_value? ?????????? <-???? as.numeric(unclass(tst)$p.value)

df
??????????????????? <-???? tst[2]$parameter

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cv1??????????????????? <-???? qchisq(p=.01, df=tst[2]$parameter, lower.tail =
FALSE, log.p FALSE)

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cv2??????????????????? <-???? qchisq(p=.05, df=tst[2]$parameter, lower.tail =
FALSE, log.p FALSE)

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cv3??????????????????? <-???? qchisq(p=.1, df=tst[2]$parameter, lower.tail =
FALSE, log.p FALSE)

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#-----------------------------------------------------------------------------

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# Expected value

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# variable.cnts.prs *
sum(variable.cnts) 

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#
if tst > cv reject Ho at alpha confidence level

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#-----------------------------------------------------------------------------

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if(chi_squared > cv1)

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Conclusion1 <- 'Sample
does not come from the postulated probability distribution at 1% los' else

Conclusion1 <- 'Sample
comes from postulated prob. distribution at 1% los'

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if(chi_squared > cv2)

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Conclusion2 <- 'Sample
does not come from the postulated probability distribution at 5% los' else

Conclusion2 <- 'Sample
comes from postulated prob. distribution at 1% los'

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if(chi_squared > cv3)

Conclusion3 <- 'Sample
does not come from the postulated probability distribution at 10% los' else

Conclusion3 <- 'Sample
come from postulated prob distribution at 1% los'

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#-----------------------------------------------------------------------------

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# Printing RESULTS 

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print(chi_squared)

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print(p_value)

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print(df)

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print(cv1)

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print(cv2)

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print(cv3)

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print(Conclusion1)

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print(Conclusion2)

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print(Conclusion3)

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##### End of R Script
########

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________________________________________________________

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Problem Faced :

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When I run this script using
R ? console,

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I am getting value of Chi ? Square Statistics as
high as ?6.95753e+37?

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When I did the same calculations in Excel, I got
the Chi Square Statistics value = 138.34.


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Although it is clear that the sample data doesn?t
follow Poisson distribution, and I will have to look for other discrete
distribution, my problem is the HIGH Value of Chi Square test statistics. When
I analyzed further, I understood the problem. 

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(A) By convention, if your Expected
frequency is less than 5, then by we put together such classes and form a new
class such that Expected frequency is greater than 5 and also accordingly
adjust the observed frequencies.

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  X
  
  
  Oi
  
  
  Ei
  
  
  ((Oi - Ei)^2)/Ei
  


  
  0
  
  
  0
  
  
  10
  
  
  9.96
  


  
  1
  
  
  72
  
  
  23
  
  
  103.79
  


  
  2
  
  
  17
  
  
  27
  
  
  3.54
  


  
  3
  
  
  5
  
  
  21
  
  
  11.85
  


  
  4
  
  
  3
  
  
  12
  
  
  6.71
  


  
  5
  
  
  4
  
  
  9
  
  
  2.51
  


  
  Total
  
  
  101
  
  
  101
  
  
  138.34
  





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When I apply this logic in Excel, I am getting the
reasonable result (i.e. 138.34), however in Excel also, if I don?t apply this
logic, my Chi square test statistic value is as high as 4.70043E+37.

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My
question is how do I modify my R ? script, so that the logic mentioned in (A)
i.e. adjusting the Expected frequencies (and accordingly Observed frequencies)
is
applied so that the expected frequency becomes greater than 5 for a given
class, thereby resulting in reasonable value of Chi Square test Statistics.

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I am also attaching the xls file for ready
reference.

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I sincerely apologize for taking liberty of writing
such a long mail and since I am very new to this ?R language? can someone help
me out.

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Thanking in advance for your kind co-operation.

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Ashok (Mumbai,
 India)

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