Statistical Analysis

1
Statistical Analysis

• Programming in R

2
Vectors and assignment

• Simplest data structure is the numeric vector
• Type at the command line
• gt xlt-c(10.4, 5.6, 3.1, 6.4, 21.7)
• Type x at the command line to see the result
• gt x
• 1 10.4 5.6 3.1 6.4 21.7
• gt

3
c() is a function

• Function c() takes an arbitrary number of vector
  arguments and concatenates them.
• gt ylt-c(x, 0, x)
• gt y
• 1 10.4 5.6 3.1 6.4 21.7 0.0 10.4 5.6 3.1
  6.4 21.7

4
Vector arithmetic

• ,x,,/,
• log, exp, sin, cos, tan, sqrt,
• max, min, range
• length, sum, prod

5
Calculate mean in R mean and variation

• gt mean(x)
• 1 9.44
• gt
• gt var(x)
• 1 53.853
• gt

6
Calculate mean in R mean and variation

• mean(x) can be written as
• gt sum(x)/length(x)
• 1 9.44
• var(x) can be written as
• gt sum((x-mean(x))2)/(length(x)-1)
• 1 53.853

7
Two sample t-statistic

• twosam function(y1,y2)
• n1length(y1) n2 length(y2)
• yb1mean(y1) yb2mean(y2)
• s1var(y1) s2var(y2)
• s((n1-1)s1 (n2-1)s2)/(n1n2-2)
• tst(yb1-yb2)/sqrt(s2(1/n11/n2))
• tst

Copy and paste the above statements onto the
command line in R
8
Should look like this
gt twosam lt- function(y1,y2) n1lt-length(y1)
n2 lt-length(y2) yb1mean(y1) yb2mean(y2)
s1var(y1) s2var(y2) s((n1-1)s1
(n2-1)s2)/(n1n2-2) tst(yb1-yb2)/sqrt(s2(1/n1
1/n2)) tst
9
Test your function by calling it

• gt tstattwosam(x,x1)
• gt tstat
• 1 -0.2154592
• gt

10
Generating regular sequences

• 130 is the same with c(1,2,3,,29,30)
• operator has the highest priority within an
  expression. For example
• gt 215
• 1 2 4 6 8 10

11
factors

• gt codonsc("GCA","GCC","GCG","GCU","UGC","UGU")
• gt codons
• 1 "GCA" "GCC" "GCG" "GCU" "UGC" "UGU"
• gt aminoacidsc("Ala","Ala","Ala","Ala","Cys","Cys"
  )
• gt aminoacids
• 1 "Ala" "Ala" "Ala" "Ala" "Cys" "Cys"
• gt aaffactor(aminoacids)
• gt aaf
• 1 Ala Ala Ala Ala Cys Cys
• Levels Ala Cys
• gt iitapply(codons,aaf,print)
• 1 "GCA" "GCC" "GCG" "GCU"
• 1 "UGC" "UGU"
• gt

12
arrays

• gt xarray(120,dimc(4,5))
• gt x
• ,1 ,2 ,3 ,4 ,5
• 1, 1 5 9 13 17
• 2, 2 6 10 14 18
• 3, 3 7 11 15 19
• 4, 4 8 12 16 20

13
arrays

• gt xarray(0,dimc(4,5))
• gt x
• ,1 ,2 ,3 ,4 ,5
• 1, 0 0 0 0 0
• 2, 0 0 0 0 0
• 3, 0 0 0 0 0
• 4, 0 0 0 0 0
• gt

14
Indexing arrays

• gt iarray(c(13,31),dimc(3,2))
• gt i
• ,1 ,2
• 1, 1 3
• 2, 2 2
• 3, 3 1
• gt xarray(120,dimc(4,5))
• gt x
• ,1 ,2 ,3 ,4 ,5
• 1, 1 5 9 13 17
• 2, 2 6 10 14 18
• 3, 3 7 11 15 19
• 4, 4 8 12 16 20
• gt xi
• 1 9 6 3
• gt xi0
• gt x
• ,1 ,2 ,3 ,4 ,5
• 1, 1 5 0 13 17