## Tuesday, January 24, 2017

### Using R to work through Sokal and Rohlf's Biometry: Chapter 6 (The Normal Probability Distribution), section 6.6

Previously in this series:

### Section 6.6 Skewness and Kurtosis

#Box 6.1 shows how to compute g1 (skewness) and g2 (kurtosis) from a frequency distribution.
#This is unlike to be how one would do it with your own table of data,
#but it is a helpful exercise in understanding how these moment statistics work and coding.
#This section assumes you have loaded the birthweights data from the last post.

mean.bw<-sum(birthweights[-16, "frequencies"]*(birthweights[-16, "classmark"]))/samplesize
yfreq<-(
birthweights[-16, "classmark"]-mean.bw #This is deviation from the mean (see pg 51, section 4.7)
)

(g1<-(
samplesize*
sum(birthweights[-16, "frequencies"]*yfreq^3)
)/
(
(samplesize-1)*(samplesize-2)*birthweights.sd^3
)
)

(g2<-(
(
(samplesize+1)*samplesize*sum(birthweights[-16, "frequencies"]*yfreq^4)
)/
(
(samplesize-1)*(samplesize-2)*(samplesize-3)*(birthweights.sd^4)
)
)-
(
(
3*(samplesize-1)^2
)/
(
(samplesize-2)*(samplesize-3)
)
)
)

#As an interesting side note, if you use the value of the mean given in the book,
birthweights.mean
#which is rounded to four decimal places, the calculation for cubing

#(and raising to the power of 4) both were off.  The power of three one was off by 118!