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# Biostatistics Week 15 Notes BIO 472

La Salle

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This 6 page Class Notes was uploaded by Kiara Lynch on Saturday May 7, 2016. The Class Notes belongs to BIO 472 at La Salle University taught by in Summer 2015. Since its upload, it has received 10 views. For similar materials see Biostatistics in Biology at La Salle University.

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Date Created: 05/07/16

Analyzing Proportions: Binomials What proportion? •“What proportion of people with disease X will live for 10 years?” •“What proportion of people in the population have disease X?” Proportion= # Successes / # trials or samples What is the probability of a result? •Binomial probability •Probability of the number of successes in a fixed number of independent trials •Assumptions: • Number of trials is fixed • Each trial is independent • Probability of success in each trial is independent Binomial Probability Probability of X number of successes= (n choose X) * (p^x) * (1-p)^(n-X) Probability of X number of successes= total number of possible combinations * probability of success raised to the number of successes * probability of failure raised to the number of failures Coins •Toss a coin 4 times, what is the probability of getting 3 heads? 4 3 (4-3) P(X=3) = ( )3* .5 * (1-.05) = .25 10% of the population is left handed, what isthe probability of a sample of 20 peoplehaving 5 left-handed individuals? P(X=5) = ( 25) * .1 * (1-.01)20-= .0319 p(X=x) dbinom(x,n,p) dbinom(5,20,.1) P= .0319 Addition rule P(X<5) or pbinom pbinom(4,20,.1) = .9568 Complement Rule P(X≥5) 1-pbinom(4,20,0.1) Or pbinom(4,20,0.1,lower.tail=F) P.X<-c(dbinom(0,8,0.8), dbinom(1,8,0.8), dbinom(2,8,0.8), dbinom(3,8,0.8), dbinom(4,8,0.8), dbinom(5,8,0.8), dbinom(6,8,0.8), dbinom(7,8,0.8), dbinom(8,8,0.8)) sum(P.X) #check to make sample space adds up to 1 max(P.X) #find the max value to better create the y axis barplot(P.X, ylim=c(0,0.35), names=0:8, #"names" the values on the x axis, don't forget to make 0 a possibility space=0, #no space b/w the bars col=c(rep("lavender",length=6),rep("lightseagreen",length=3))) Binomial Test •The relative frequency of successes in a population is p0•The relative frequency of successes in a population is not p0 The probability that a spermatogenesis genefalls on the X-chromosome = 0.061 A study samples 25 mice, 10 of them have the spermatogenesis geneon the X- chromosome H0: The probability that this gene falls on the X-chromosome is 0.061 p=0.061 Ha: The probability that this gene falls on the X-chromosome isdifferent from 0.061 p≠0.061 P-Value – look at tails of the distribution P-value=2*P(Successes ≥ 10) P-value=2*P(Successes ≥ 10) 2*pbinom(9,25,.061, lower.tail=F) #P=1.987976e-06 #low value- reject the null hypothesis #pbinom(x-1,n,p) Sex Ratios in GSD animals are usually 50:50 at birth Dr. Iglesias surveys adult ducks and is concerned that females may have lower survival than males. In his survey, he counted 54 females and 75 males. What is the probability of getting 54 females out of a total of 129 ducks? dbinom(54,129,.5) #looking at tails 0.01276294 pbinom(54,129,.5, #probability of getting the exact result lower.tail=F) 0.9610753 2*pbinom(54,129,.5) 0.07784941 There is no significant difference b/w the number of males and females BARPLOT CODE div<-read.csv("animaldiversity.csv",header=T) attach(div) names(div) par(mar=c(5,8,4,2)) #change the plot margins, default is c(5,4,4,2) barplot(Species, horiz=T, names.arg=Phylum, las=1, #rotates labels 90 degrees cex.axis=1.2, cex.names=1.2)

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