# L4_Stat - ECEN 689 Statistical Computation in GSP...

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ECEN 689 Statistical Computation in GSP http://www.ece.tamu.edu/~ulisses/ECEN689/ Lecture 4: Review of Statistics Ulisses Braga Neto Genomic Signal Processing Laboratory Department of Electrical and Computer Engineering Texas A&M University

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Variability/Reproducibility • Results can be expected to have reproducibility only if variability in taken into account in experimental design . • Even if the subject and assay are clearly specified, there are two sources of variability – Techical Variability : it comprises random changes from an experiment (e.g., microarray) to the next. – Biological Variability : it comprises random changes from a biological sample to the next.
Replicates • In order to address variability (and thus ensure reproducibility), one needs replicates "technical replicates"

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Replicates - II • As long as the assay is reliable, biological replicates are more critical for reproducibility "biological replicates"
Differential Expression • Suppose there are two conditions A and B (e.g., normal and diseased, wild-type and mutant, good and bad prognosis, etc.) under study, and one measurement Y (e.g. gene expression). • Suppose further that there are n replicate specimens, n/2 under condition A and n/2 under condition B (since A and B are represented by the same number of samples, this is called a balanced design ).

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Differential Expression - II • The question of interest is: "Based on the set of n replicates, can we conclude that Y is differentially expressed between A and B?" • To examine this question, let us assume that there is indeed a difference between A and B. Suppose for example that in truth we have Y = 100, under A Y = 200, under B If A is the baseline, then we would say that Y is over-expressed in B.
Differential Expression - III • The fold-change is 200/100 = 2. • If there were no variability, then with n=2 (1 replicate for each condition) we would be able to conlude there was a difference. • But clearly there will be some variability, both technical and biological. Let us model this by using Gaussian distributions Y ~ N(100, σ 2 ) under A Y = N(200, σ 2 ) under B where σ 2 is the variance (assumed equal, for the moment) in A and B.

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Differential Expression - IV • The following code simulates these data, with n = 20 and σ = 25. > n = 20 > cond = factor(c(rep("A",n/2),rep("B",n/2))) > Y_25 = c(rnorm(n/2,100,25), rnorm(n/ 2,200,25)) > data.frame(Y=Y_25,cond=cond)
Differential Expression -V • Stripchart plot of data: > stripchart(Y_25~cond,vert=TRUE, method="jitter",jitter=0.1,pch=c(16,17)) > mu = c(100,200) > arrows(1:2-0.12,mu,1:2+0.12, mu,angle=90,code=3,length=0,lwd=1.5) > arrows(1:2,mu-25,1:2,mu+25, angle=90,code=3, length=0.1,lwd=1.5)

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Differential Expression - VI • It seems clear here that there is indeed differential expression in Y between A and B.
• But what if variability were larger, e.g. σ = 200? There does not seem to be a difference now.

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L4_Stat - ECEN 689 Statistical Computation in GSP...

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