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 ##  Classic univariate statistics - R Tutorial  ##


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# Please read the tutorial's general instructions first, and prepare 


# for loading an external datafile, when you are going to use one.


# The content of this file can be pasted directly into the R console.


# It should blurp lost of errors only at the point where you 


# are supposed to have an external dataset available.


# However, it is much handier to use the "display file" command 


# within the R menu to look at this file, and paste command by command 


# to the console, using control-V.  Take your time to experiment a bit 


# with the listed commands.





library(gnlm)





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








# .Rclassics: Univariate Statistics in R.








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








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


# | I. Probability Distributions |


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








# Hypothesis testing in statistics makes use of probability distributions. 


# They are also an essential part of model checking


# You can simulate probability distributions in R, 


# calculate p-values from them, and fit them to data.


# Many distributions are available.


# Let's simulate a sample from a binomial distribution.


# We draw 100 samples of 20 individuals, and the 


# probability of success per individual is 0.34.





help(Binomial)





x<-rbinom(100,20,0.34)


hist(x)





# For model checking, quantile plots are often used.


# I guess that everybody is familiar with normal probability plots.





qqnorm(x)





# However, you can make the same type of plots for other distributions 


# as well. These always have 'quantiles' of a probability distribution 


# on one axis, and ordered datapoints on the vertical. 


# If the distribution fits, you should observe a more or less straight line. 





plot(qt(ppoints(x),9),sort(x)) # compare sample x to a poisson with mean 9.


plot(qbinom(ppoints(x),20,0.34),sort(x)) # compare to a binomial.


plot(qgamma(ppoints(x),9),sort(x)) ## compare to a gamma.





# Take a look at the ppoints() function.








# We can also fit a distribution to a sample using likelihood theory.


# Now follows an example using car accidents data discussed in


# Lindsey (1995).





f3 <- c(447,132,42,21,3,2) #Car Accidents


y3 <- seq(0,5)#categories


z3 <- fit.dist(y3,f3,"Poisson",plot=T,xlab="Number of accidents", main="",bty="L") # fit a Poisson





# watch out, the AIC here is deviance plus parameters!!!





z3a <- fit.dist(y3,f3,"negative binomial",exact=F,plot=T,add=T,lty=3)


z3b <- fit.dist(y3,f3,"negative binomial")





# fit.dist() allows us to fit a distribution either using exact 


# integration or an approximation to the probability distribution.








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


# | II. Hypothesis Testing |


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





# Hypothesis testing on samples is also available in R.


# Please type in two samples of data.





sample1<-scan()


sample2<-scan()





#We now run a test on them, to test whether they have equal variances





var.test(sample1, sample2)





# Many tests are available in R. Please type the following to take a 


# look at the available ones.





library(help=ctest)





# Try to run some on samples of data.





# Another example from the help files: 


# Under (the assumption of) simple Mendelian inheritance, a cross


# between plants of two particular genotypes produces progeny 1/4 of


# which are ``dwarf'' and 3/4 of which are ``giant'', respectively.


# In an experiment to determine if this assumption is reasonable, a


# cross results in progeny having 243 dwarf and 682 giant plants.


# If ``giant'' is taken as success, the null hypothesis is that p =


# 3/4 and the alternative that p != 3/4.





binom.test(c(682, 243), p = 3/4)


binom.test(682, 682 + 243, p = 3/4)   # Produces the same result.





# What is the conclusion?





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


# When finished running this file, please continue with 


# the more advanced tutorial files.


# There are more examples of specific graphics in those.


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








# Much of the material in this short tutorial comes from





# Modern Applied Statistics with S


# by W. N. Venables and B. D. Ripley (2002)








# Introductory Statistics. A Modelling Approach


# J. K. Lindsey. 1995.








# Tom Van Dooren, version 17/10/2002