Question

IN R CODE, consider the following data in the table:

Consider the following data: Site Il 85 45 Site III 100 75 Site 93 120 65 105 115 82 Site IV 96 58 95 90 80 65 28 40 75 13 73 65 70 65 80 99 65 50 85 30 50 45 50 45 55 110

These figures provide the depths (in centimeters) at which
important archaeological finds were made at four sites in New Mexico
(see Woosley and Mcintyre, 1996). Store these data in your R
workspace, with one vector containing depth and the other vector
containing the site of each observation.

a. Produce side-by-side boxplots of the depths split by group, and
use additional points to mark the locations of the sample means.

b. Assuming independence, execute diagnostic checks for normality
and equality of variances.

c. Perform and conclude a one-way ANOVA test for evidence of a
difference between the means.

In Section 14.4, you looked at the data set providing measurements
on petal and sepal sizes for three species of iris flowers. This is available
in R as iris.

d. Based on diagnostic checks for normality and equality of variances,
decide which of the four outcome measurements (sepal
length/width and petal length/width) would be suitable for
ANOVA (using the species as the group variable).

e. Carry out one-way ANOVA for any suitable measurement
variables.

Please provide all relevant work: commands, the output and any interpretations/conclusions that are necessary.  

Answer 1

solu @ a=c(93, 120, 65, 105, 115, 82, 99,87,100 190.78, 95, 97 88,10) b = c(85, 45, 80,28,75,70,65,55,50,40) C = c(100, 75165,40 +73,65,50,30,45,50,45,55) d=C(96,08195,90165,80,85,95,82) N =CC"site 2", "side2", "rofe3" "ufen") sopplot (aid, Cd, hames=N,xlab = " depth in centimeter" Main = Boxplot of depths by group", horizontal - TRUE M = ( (mean Casi mean (b), meau (c), mean(d)) ruhe points (M. Col="red", Pch=18) ## sample means on Box plot. Box plot of depths by group. 40 60 80 100 120 seten cated in Sater sites depth in centimeter

6) Dec (abicid) RITA - qq hory (DJ qq line (DrCol=2) Normal 0 -Q plot to r ead. best THE 2 Tour ou Quantiles VOC oor os ag on Pin von HOP VODA Sample oź - O von 2 Theontical quantiles Bestlet's set & Compare the varioule of t Samples, where 'k' cause more than two Samples. The data nust be informally distributed. The Levene test is an alternat Live to Barfled test that is less sensetive to departores from Normality. group group = ((rep Clai, lenghth (a)), dep (46", leught (8)), rep ("c", light rep ", leught())) - C), ses <- bartlet. test (Dro group) > Xe Bartlett test of Homogeneity of variances. dato.D by group.

- Part left's k- savared = 1.7355, df =3, P-value = 0.6291 from the output, it can be seen that the p-value of 0.629) Ps not less than the coqueficance level of oos. that Mis means that there is no evidence to suggest The variance en four group is significantly diffesent form each other. c) res.gov C-aov CD wgroup) # Sommary of the Analysses. Summary (res.aov) s Summary (ses.aov), of fansa meanse Evalue prof group 3 12397 4132 15014 7oqge 07 *xx peseduals 42 11465 273 PW Imate BAT - - IT s orodos Setupf.coder: 0 ***" 0.002 *** 0.07 * Over ! Inferpret the result of one -way ANOVA Tests. As the p-value is less. rain The cognificance level 005, we can conclude that there are sogruficant differances between the groups means.

> dira s dould) - 320 SN R [1] 150 s Zlacbia for alormality we use shopino test. >Shapiro test Cd & sepalo lenghth) o pro shapiro - will normality testa) Pronun data? d f Scpal.coed me to W = 0.98492, p-value = 0.1022. > Shapiro.test (d& petalo lenghth) ENDO shapiso - wilk normality test daha :d& petal lenghthi W = 0.87627, P-value = 7.42e-10 > shapiro.test (& & pefale width) claPPю - unit ofоlеу ере pefalowidth W = 0.90 183, P-value=1.68 e-og #here only pualue for sepal, width 98>0.05 #only sepal width follows the normality. #zawalety of variance by using Box plot > par Confrow = C(1,4)) voxplot (d&sepal.lenghthondda > Coxplor (d & sepal. width ad & Species , hont = FALSE) > Loxplot (d & petal. Lenght was species) > boxplot (då pefalowidth nd& Species)

4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 тттттттт setosa ----- ------ D ----- -----O D F---------O 2.0 2.5 3.0 3.5 4.0 setosa - ------ ---- D -----+ -OD------ E- 1 2 3 4 5 6 7 setosa - + F 1-4 --- F--I --- E----- 0.5 1.0 1.5 2.0 2.5 setosa F .. --+ H ----- D H- U

**** Am happy to help you.Thank you. Please LIKE.

e) Here only sepal-width follows alormality and cavality of variance Hence we use sepalo widre. for Anova test. > Anova = aov (d & Sepal-width, wd & specie 2. Po s Summary Canoval of somsa d & Species zo 11035 meansa 5.672 fvalue Pr (>f) 49.16 [26-16*** Residuals 147 16.95 0.115 Doo gignif. codes : 0 *** 0.001 * * 0.01 + 0.05 0. s'a. As the p-value is less than the significance level 0.05, we can conclude that there are sognificant differances setween the species. .