1. Lecture 4: Statistical inference
Statistical Genomics
Lecture 4: Statistical inference
Zhiwu Zhang
Washington State University

2. Observed and expected frequency
Transgenetic
Non transgenetic
SUM
Herbicide 35 5 40
No herbicide 25 60 70 30
100
Transgenetic
Non transgenetic
SUM
Herbicide 28 12 40
No herbicide 42 18 60 70 30
100

3. Approximate Distributions
Poisson distribution: Mean=Var=Expected
(Observed-Expected)/Sqrt(Expected) ~ N(0,1)
SUM(Observed-Expected)2/ Expected ~ X2(df)
df=number of independent cells

4. Observed and expected frequency
Transgenetic
Non transgenetic
SUM
Herbicide 35 5 40
No herbicide 25 60 70 30
100
Transgenetic
Non transgenetic
SUM
Herbicide 28 12 40
No herbicide 42 18 60 70 30
100
49/28+49/12+49/42+49/18=9.72

5. Distribution of x2(1) 99% percentile 6.97 Observed 9.72 P<1%
par(mfrow=c(2,2),mar = c(3,4,1,1))
x=rchisq(k,1)
d=density(x)
plot(x)
plot(d)
hist(x)
plot(ecdf(x))
quantile(x,.99)
Observed
9.72
P<1%