Lab 3

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library(ggplot2)
data("chickwts")
chickwts

##    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    casein

## a
ggplot (chickwts, aes(x = feed, y = weight, fill = feed )) + geom_boxplot() + labs(
  title = "chicken weight based on feed",
  x = "feed",
  y = "weight"
)+
  scale_fill_brewer(palette = "Pastel2")+
  theme_minimal()

## the preliminary observations about the feeds is that feeds sunflower and casian have a higher weight because there medians are higher but to prove it it would require further investigation. 

##b
##shaperio test 
stest <- by(chickwts$weight, chickwts$feed, shapiro.test)
stest

## chickwts$feed: casein
## 
##  Shapiro-Wilk normality test
## 
## data:  dd[x, ]
## W = 0.91663, p-value = 0.2592
## 
## ------------------------------------------------------------ 
## chickwts$feed: horsebean
## 
##  Shapiro-Wilk normality test
## 
## data:  dd[x, ]
## W = 0.93758, p-value = 0.5264
## 
## ------------------------------------------------------------ 
## chickwts$feed: linseed
## 
##  Shapiro-Wilk normality test
## 
## data:  dd[x, ]
## W = 0.96931, p-value = 0.9035
## 
## ------------------------------------------------------------ 
## chickwts$feed: meatmeal
## 
##  Shapiro-Wilk normality test
## 
## data:  dd[x, ]
## W = 0.97914, p-value = 0.9612
## 
## ------------------------------------------------------------ 
## chickwts$feed: soybean
## 
##  Shapiro-Wilk normality test
## 
## data:  dd[x, ]
## W = 0.9464, p-value = 0.5064
## 
## ------------------------------------------------------------ 
## chickwts$feed: sunflower
## 
##  Shapiro-Wilk normality test
## 
## data:  dd[x, ]
## W = 0.92809, p-value = 0.3603

##q-q plot
par(mfrow = c(2, 3)) 
for (feed_type in unique(chickwts$feed)) {
  qqnorm(chickwts$weight[chickwts$feed == feed_type], main = paste("q-q plot:", feed_type))
  qqline(chickwts$weight[chickwts$feed == feed_type])}

##c
anova <- aov(weight ~ feed, data = chickwts)
summary(anova)

##             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 ' ' 1

## the p value in this case is far lower then the significance value of 0.05. This means we reject the null hypothesis because the p value indicates there is a high significance of difference between the feeds. 

##d 
tukey <- TukeyHSD(anova)
tukey

##   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 0.0038845

## The results of the tukey tesy show that there is a large difference in each of the feeds. the type of feed that causes the greatest gtoeth is casein.

Lab 3

Mikayla Bishop

2024-11-15

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