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by: Kiara Lynch

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# Biostatistics Week 8 Notes BIO 472

Marketplace > La Salle University > Biology > BIO 472 > Biostatistics Week 8 Notes
Kiara Lynch
La Salle
Biostatistics

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Week 8 class notes and R code
COURSE
Biostatistics
PROF.
TYPE
Class Notes
PAGES
0
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KARMA
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This 0 page Class Notes was uploaded by Kiara Lynch on Tuesday March 22, 2016. The Class Notes belongs to BIO 472 at La Salle University taught by in Summer 2015. Since its upload, it has received 23 views. For similar materials see Biostatistics in Biology at La Salle University.

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Date Created: 03/22/16
Biostatistics Week 8 Notes ANOVA Compare two or more means analysis of variance 0 standard deviation variance and sums of squares compare two means ttests 0 have to account for standard error assess differences bw 2 or more means 0 assess variation among means 0 1 factor ANOVA factor explanatory variable gender treatment levels categories win a factor factor gender levels male female factor treatment levels control treatment 1 treatment 2 etc o for designs with 1 factor and 2 levels the twosample t test may be appropriate for comparison of means 0 ANOVA allows for multifactorial designs o F mean square groupmean square error sher ratio of the variation among groups measure of variation among group means measure of variation within groups assesses the among group variation relative to within group variation partitioning the variation 0 Rquot2 coef cient of determination proportion of the variation in the overall response variable that is explained by the explanatory variable sums of squares group measure of variation among group means sums of squares total measure of variation of the response variable want a value of 100 numerator in R equation sample sizesample meangroup meanquot2 One Factor ANOVA each object is measured once and values are independent homogeneity of variance leveneTest residuals are normally distributed t a linear model calculate residuals histogram and shapiro test don39t need a subset residual an error in prediction line drawn from observed value through linear model 0 if sample sizes are equal or large sometimes you can violate these assumptions sample size depends on how great of a deviation you have from normality bigger sample size for a bigger deviation from normality predicted value is the group mean 0 pool residuals and look at normality of all of the residuals null hypothesis 0 O 0 all means are equal at least one mean differs if comparing 2 means equivalent of a 2sample ttest degrees of freedom 0 O O groups 1 N groups N1 overall sample size 1 bnegatibV statistics 0 O 0 large F statistics gt samll p values p value gt 05 not signi catnt lt 05 at least one mean is different can39t do pairwise t tests for every combination 0 multiple comparison procedures 0 O planned unplanned conduct pairwise comparison Bonferroni on the same exact data set bonferroni will get larger p values if afraid of making a type 2 error easiest to calculate tukey will give moderate p values 0 student newman keuls many differences R codenotes pimaltreadcsvquotpimacsvquotheaderT attachpima namespima boxplotgutype summaryaovgutype ttestgutype varequaT histlmglutyperesiduals makes histogram of the residuals shapirotestlmglutyperesiduals normality test gt 05 then normal dataltreadcsvquotDDTDrosophilacsvquotheaderT attachdata data namesdata Fecundity is the mean number of eggsfemaleday strain is the 39factor39 evesStrain Iists the 39eves39 in the 39factor39 Control not selected Resistant DDT Resistant Susceptible Susceptible to DDT tapplyFecundity Strain mean what is the mean for each group residualsltlmFecundityStrainresiduals calculate residuals make linear model response variableexplanatory variableattribute of model residuals are errors of the linear model histresiduals normal distribution shapirotestresiduals pvalue gt 05 so normal tapplyFecundity Strain var tapplyYXvar are the variances equal librarycar leveneTest in car package leveneTestFecundityStrain big pvalue gt homogeneity of variance create an ANOVA object If this is signi cant we will need this object for multiple comparisons procedure anovastrainltaovFecundityStrain resp var exp var summaryanovastrain gives summary of the object we created degrees of freedom sums of squares means of squares F value very small p value reject null hypothesis there is a difference bw one of the means add strain and residuals to get totals 136213625659 R2SSGSST 19 so it is signi cant Tukey is the most common multiple comparisons approach in Biology TukeyHSDanovastrain TukeyHSDobject honest signi cant difference difference con dence interval lower and upper adjusted p values plotTukeyHSDanovastrain can see if conf intervals overlap with 0 if they do then there is not a difference between those menas if they don39t overlap there is a signi cant difference boxplotFecundityStrain mainquotFecundity vs Strainquot colcquotightseagreenquot quotcoralquot quotmaroonquot ylabquotFecundityquot barplot needs the sample means and standard errors meanslttappyFecundity Strain mean sdlttapplyFecundity Strain sd nilttappyFecundity Strain length number of individuals seltsdsqrtni bpltbarplotmeans ylimcO40 axislty1 ylabquotMean Daily Fecundityquot colquotlightseagreenquot layer the error bars onto the existing object segments x1y1x2y2 segmentsbp meansse bp meansse create error bars change thickness lwd2 segmentsbp01 meansse bp01 meansse upper cap segmentsbp01 meansse bp01 meansse lower cap

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