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> ## some examples of the KS test
> 
> ## unrealistic one of PR#14561
> ds1 <- c(1.7,2,3,3,4,4,5,5,6,6)
> ks.test(ds1, "pnorm", mean = 3.3, sd = 1.55216)

	One-sample Kolmogorov-Smirnov test

data:  ds1 
D = 0.274, p-value = 0.4407
alternative hypothesis: two-sided 

Warning message:
In ks.test(ds1, "pnorm", mean = 3.3, sd = 1.55216) :
  ties should not be present for the Kolmogorov-Smirnov test
> # how on earth can sigma = 1.55216 be known?
> 
> # R >= 2.14.0 allows the equally invalid
> ks.test(ds1, "pnorm", mean = 3.3, sd = 1.55216, exact = TRUE)

	One-sample Kolmogorov-Smirnov test

data:  ds1 
D = 0.274, p-value = 0.3715
alternative hypothesis: two-sided 

Warning message:
In ks.test(ds1, "pnorm", mean = 3.3, sd = 1.55216, exact = TRUE) :
  ties should not be present for the Kolmogorov-Smirnov test
> 
> ## Try out the effects of rounding
> set.seed(123)
> ds2 <- rnorm(1000)
> ks.test(ds2, "pnorm") # exact = FALSE is default for n = 1000

	One-sample Kolmogorov-Smirnov test

data:  ds2 
D = 0.0194, p-value = 0.8452
alternative hypothesis: two-sided 

> ks.test(ds2, "pnorm", exact = TRUE)

	One-sample Kolmogorov-Smirnov test

data:  ds2 
D = 0.0194, p-value = 0.8379
alternative hypothesis: two-sided 

> ## next two are still close
> ks.test(round(ds2, 2), "pnorm")

	One-sample Kolmogorov-Smirnov test

data:  round(ds2, 2) 
D = 0.0192, p-value = 0.856
alternative hypothesis: two-sided 

Warning message:
In ks.test(round(ds2, 2), "pnorm") :
  ties should not be present for the Kolmogorov-Smirnov test
> ks.test(round(ds2, 2), "pnorm", exact = TRUE)

	One-sample Kolmogorov-Smirnov test

data:  round(ds2, 2) 
D = 0.0192, p-value = 0.8489
alternative hypothesis: two-sided 

Warning message:
In ks.test(round(ds2, 2), "pnorm", exact = TRUE) :
  ties should not be present for the Kolmogorov-Smirnov test
> # now D has doubled, but p-values remain similar (if very different from ds2)
> ks.test(round(ds2, 1), "pnorm")

	One-sample Kolmogorov-Smirnov test

data:  round(ds2, 1) 
D = 0.0367, p-value = 0.1344
alternative hypothesis: two-sided 

Warning message:
In ks.test(round(ds2, 1), "pnorm") :
  ties should not be present for the Kolmogorov-Smirnov test
> ks.test(round(ds2, 1), "pnorm", exact = TRUE)

	One-sample Kolmogorov-Smirnov test

data:  round(ds2, 1) 
D = 0.0367, p-value = 0.1311
alternative hypothesis: two-sided 

Warning message:
In ks.test(round(ds2, 1), "pnorm", exact = TRUE) :
  ties should not be present for the Kolmogorov-Smirnov test
> 
> 
