R Homework 6
Ana Milian
Ecology Lab - Summer 2017
# Chicken Weights by Feed Type ####
# An experiment was conducted to measure and compare the effectiveness
# of various feed supplements on the growth rate of chickens.
data("chickwts")
summary(chickwts)## weight feed
## Min. :108.0 casein :12
## 1st Qu.:204.5 horsebean:10
## Median :258.0 linseed :12
## Mean :261.3 meatmeal :11
## 3rd Qu.:323.5 soybean :14
## Max. :423.0 sunflower:12Plot your data first (as always). Be sure to include an informative figure caption.
data("chickwts") #chicken Weights by Feed Type
summary (chickwts) ## weight feed
## Min. :108.0 casein :12
## 1st Qu.:204.5 horsebean:10
## Median :258.0 linseed :12
## Mean :261.3 meatmeal :11
## 3rd Qu.:323.5 soybean :14
## Max. :423.0 sunflower:12chickwts## weight feed
## 1 179 horsebean
## 2 160 horsebean
## 3 136 horsebean
## 4 227 horsebean
## 5 217 horsebean
## 6 168 horsebean
## 7 108 horsebean
## 8 124 horsebean
## 9 143 horsebean
## 10 140 horsebean
## 11 309 linseed
## 12 229 linseed
## 13 181 linseed
## 14 141 linseed
## 15 260 linseed
## 16 203 linseed
## 17 148 linseed
## 18 169 linseed
## 19 213 linseed
## 20 257 linseed
## 21 244 linseed
## 22 271 linseed
## 23 243 soybean
## 24 230 soybean
## 25 248 soybean
## 26 327 soybean
## 27 329 soybean
## 28 250 soybean
## 29 193 soybean
## 30 271 soybean
## 31 316 soybean
## 32 267 soybean
## 33 199 soybean
## 34 171 soybean
## 35 158 soybean
## 36 248 soybean
## 37 423 sunflower
## 38 340 sunflower
## 39 392 sunflower
## 40 339 sunflower
## 41 341 sunflower
## 42 226 sunflower
## 43 320 sunflower
## 44 295 sunflower
## 45 334 sunflower
## 46 322 sunflower
## 47 297 sunflower
## 48 318 sunflower
## 49 325 meatmeal
## 50 257 meatmeal
## 51 303 meatmeal
## 52 315 meatmeal
## 53 380 meatmeal
## 54 153 meatmeal
## 55 263 meatmeal
## 56 242 meatmeal
## 57 206 meatmeal
## 58 344 meatmeal
## 59 258 meatmeal
## 60 368 casein
## 61 390 casein
## 62 379 casein
## 63 260 casein
## 64 404 casein
## 65 318 casein
## 66 352 casein
## 67 359 casein
## 68 216 casein
## 69 222 casein
## 70 283 casein
## 71 332 caseinplot(chickwts$weight ~ chickwts$feed)
Are your data normal and have homogeneity of variance? Provide three pieces of graphical evidence that argues your case. Be sure to include informative figure captions. Explain your answer.
hist (chickwts$weight) #Histogram shows an structure like poisson distribution, so data is not normal.
qqnorm(chickwts$weight)
qqline(chickwts$weight)# In the Q-Q plots the data does not fall along the 1:1 line. so data is not normal
boxplot(chickwts$weight ~ chickwts$feed) #the spread of the box plots are not equal, so data is not normal 
Did you transform your data? If so, state which transformation you used. Provide three pieces of evidence that your data more closely approximates a normal distribution and homogeneity of variance. If not, state why you did not transform the data.
#I run the three transformations
logNormalSQRT <- sqrt(chickwts$weight) #Square Root Transformation
qqnorm (logNormalSQRT)
qqline (logNormalSQRT)
logNolmalX2<- (chickwts$weight) ^2 #squared transformation
qqnorm (logNolmalX2)
qqline (logNolmalX2)
lognormalLog <- log10 (chickwts$weight + 0.0001)#Log transformation
qqnorm (lognormalLog)
qqline (lognormalLog) 
Create an ANOVA object with the appropriate data (raw or transformed). Present your results in the R Markdown file. Did you accept or reject the null hypothesis? Are the results statistically significant? Provide and interpret two evidence graphs that the residuals meet the assumption of the ANOVA.
weight.aov <- aov(weight ~ feed, data = chickwts)
plot (weight.aov)
summary(weight.aov) # this show that the Pr(>F) or p-value is significant, because is less then 0.05 so we reject the null hypothesis## Df Sum Sq Mean Sq F value Pr(>F)
## feed 5 231129 46226 15.37 5.94e-10 ***
## Residuals 65 195556 3009
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Did you perform a multiple comparison test? Why or why not? Explain. Present your code if appropriate.
#yes, I did run a multiple comparison test because the p-value is singnificant, it is less then 0.05
TukeyHSD(weight.aov)## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = weight ~ feed, data = chickwts)
##
## $feed
## diff lwr upr p adj
## horsebean-casein -163.383333 -232.346876 -94.41979 0.0000000
## linseed-casein -104.833333 -170.587491 -39.07918 0.0002100
## meatmeal-casein -46.674242 -113.906207 20.55772 0.3324584
## soybean-casein -77.154762 -140.517054 -13.79247 0.0083653
## sunflower-casein 5.333333 -60.420825 71.08749 0.9998902
## linseed-horsebean 58.550000 -10.413543 127.51354 0.1413329
## meatmeal-horsebean 116.709091 46.335105 187.08308 0.0001062
## soybean-horsebean 86.228571 19.541684 152.91546 0.0042167
## sunflower-horsebean 168.716667 99.753124 237.68021 0.0000000
## meatmeal-linseed 58.159091 -9.072873 125.39106 0.1276965
## soybean-linseed 27.678571 -35.683721 91.04086 0.7932853
## sunflower-linseed 110.166667 44.412509 175.92082 0.0000884
## soybean-meatmeal -30.480519 -95.375109 34.41407 0.7391356
## sunflower-meatmeal 52.007576 -15.224388 119.23954 0.2206962
## sunflower-soybean 82.488095 19.125803 145.85039 0.0038845Summarize your results in a paragraph similar to the example in the ``Reporting Your Results’’ section.
#The weight and the feed of the chickens were significantly different (ANOVA p-value = 0.0000). The data was transformed to approximate normality. We run a Tukey HSD multiple comparison test to find out which groups are different. The feeds with a significan p-value (p-value < or = to 0.05) are: Chickens that eat horsebean-casein, linseed-casein, soybean-casein, meatmeal-horsebean, soybean-horsebean, sunflower-horsebean, sunflower-linseed and sunflower-soybean. The feeds with not significan p-value ( equal or > than 0.05) are: meatmeal-casein, sunflower-casein, linseed-horsebean, meatmeal-linseed, soybean-linseed, soybean-meatmeal, sunflower-meatmeal.Please turn–in your homework via Sakai by saving and submitting an R Markdown PDF or HTML file from R Pubs!