# [R] Query : Chi Square goodness of fit test

priti desai priti.desai at kalyptorisk.com
Fri Jun 30 15:22:52 CEST 2006

```I want to calculate chi square test of goodness of fit to test,
Sample coming from Poisson distribution.

please copy this script in R & run the script
The R script is as follows

########################## start
#########################################

No_of_Frouds<-
c(4,1,6,9,9,10,2,4,8,2,3,0,1,2,3,1,3,4,5,4,4,4,9,5,4,3,11,8,12,3,10,0,7)

N <- length(No_of_Frouds)

# Estimation of Parameter

lambda<- sum(No_of_Frouds)/N
lambda

pmf  <- dpois(i, lambda, log = FALSE)

step_function  <- ppois(i, lambda, lower.tail = TRUE, log.p = FALSE)

# Chi-Squared Goodness of Fit Test

# Ho: The data follow a Poisson distribution Vs H1: Not Ho

Frauds <- c(1:13)

counts<-  c(2,3,3,5,7,2,1,1,2,3,2,1,1,0)  # Observed frequency

Expected
<-c(0.251005528,1.224602726,2.987288468,4.85811559,5.925428863,5.7817821
03,4.701348074,3.276697142,1.998288788,1.083247457,0.528493456,0.2344006
79,0.095299266,0.035764993)

chisq.test(counts, Expected, simulate.p.value =FALSE, correct = FALSE)

######################### end ########################################

The result of R is as follows

Pearson's Chi-squared test

data:  counts and poisson_fit
X-squared = 70, df = 65, p-value = 0.3135

Warning message:
Chi-squared approximation may be incorrect in: chisq.test(counts,
poisson_fit, simulate.p.value = FALSE, correct = FALSE)

But I have done calculations in Excel. I am getting different answer.

Observed  = 2,3,3,5,7,2,1,1,2,3,2,1,1,0
Expected=0.251005528,1.224602726,2.987288468,4.85811559,5.925428863,5.78
1782103,4.701348074,3.276697142,1.998288788,1.083247457,0.528493456,0.23
4400679,0.095299266,0.035764993

Estimated Parameter  =4.878788

Chi square stat =  0.000113

My excel answer tally with the book which I have refer for excel.
Please tell me the correct calculations in R.
########################################################################
######################