Kids Calories

kidscalories <- read.csv("~/Downloads/kidscalories.csv")
summary(kidscalories)
##   helpedinprep   calorieintake  
##  Min.   :1.000   Min.   :139.7  
##  1st Qu.:1.000   1st Qu.:300.7  
##  Median :1.000   Median :404.0  
##  Mean   :1.468   Mean   :391.8  
##  3rd Qu.:2.000   3rd Qu.:447.5  
##  Max.   :2.000   Max.   :635.2
var(kidscalories$calorieintake)
## [1] 12169.81
sd(kidscalories$calorieintake)
## [1] 110.3168
plot(density(kidscalories$calorieintake))

library(moments)
agostino.test(kidscalories$calorieintake)
## 
##  D'Agostino skewness test
## 
## data:  kidscalories$calorieintake
## skew = -0.011821, z = -0.037082, p-value = 0.9704
## alternative hypothesis: data have a skewness
anscombe.test(kidscalories$calorieintake)
## 
##  Anscombe-Glynn kurtosis test
## 
## data:  kidscalories$calorieintake
## kurt = 2.89410, z = 0.25439, p-value = 0.7992
## alternative hypothesis: kurtosis is not equal to 3
shapiro.test(kidscalories$calorieintake)
## 
##  Shapiro-Wilk normality test
## 
## data:  kidscalories$calorieintake
## W = 0.97936, p-value = 0.5663
helpedinprep <- factor(kidscalories$helpedinprep)
bartlett.test(kidscalories$calorieintake,helpedinprep)
## 
##  Bartlett test of homogeneity of variances
## 
## data:  kidscalories$calorieintake and helpedinprep
## Bartlett's K-squared = 0.079795, df = 1, p-value = 0.7776
summary(aov(kidscalories$calorieintake ~ helpedinprep, data = kidscalories))
##              Df Sum Sq Mean Sq F value  Pr(>F)   
## helpedinprep  1  83755   83755   7.917 0.00724 **
## Residuals    45 476056   10579                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
model1<- aov(calorieintake ~ helpedinprep, data = kidscalories)

qqnorm(model1$residuals)

TukeyHSD(aov(kidscalories$calorieintake~factor(kidscalories$helpedinprep)))
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = kidscalories$calorieintake ~ factor(kidscalories$helpedinprep))
## 
## $`factor(kidscalories$helpedinprep)`
##          diff       lwr       upr     p adj
## 2-1 -84.60051 -145.1586 -24.04243 0.0072362
tapply(kidscalories$calorieintake, kidscalories$helpedinprep, mean)
##        1        2 
## 431.3996 346.7991
tapply(kidscalories$calorieintake, kidscalories$helpedinprep, sd)
##         1         2 
## 105.70124  99.50114

This dataset is normally distributed. The mean and the standard diviation shows that group 1 has higher caolories than group 2.

Cholesterol data

library(readxl)
library(readr)
library(readxl)
CholestoralData <- read_excel("~/Downloads/CholestoralData.xlsx")
summary(CholestoralData)
##        ID            Before           After         Margarine        
##  Min.   : 1.00   Min.   : 3.910   Min.   : 3.660   Length:40         
##  1st Qu.:10.75   1st Qu.: 6.530   1st Qu.: 5.290   Class :character  
##  Median :20.50   Median : 7.860   Median : 6.415   Mode  :character  
##  Mean   :20.50   Mean   : 8.932   Mean   : 6.886                     
##  3rd Qu.:30.25   3rd Qu.:10.380   3rd Qu.: 7.690                     
##  Max.   :40.00   Max.   :17.730   Max.   :12.100
plot(density(CholestoralData$Before))

plot(density(CholestoralData$After))

library(moments)
agostino.test(CholestoralData$Before)
## 
##  D'Agostino skewness test
## 
## data:  CholestoralData$Before
## skew = 0.89653, z = 2.38360, p-value = 0.01714
## alternative hypothesis: data have a skewness
agostino.test(CholestoralData$After)
## 
##  D'Agostino skewness test
## 
## data:  CholestoralData$After
## skew = 0.73814, z = 2.01770, p-value = 0.04362
## alternative hypothesis: data have a skewness
anscombe.test(CholestoralData$Before)
## 
##  Anscombe-Glynn kurtosis test
## 
## data:  CholestoralData$Before
## kurt = 3.05270, z = 0.53771, p-value = 0.5908
## alternative hypothesis: kurtosis is not equal to 3
anscombe.test(CholestoralData$After)
## 
##  Anscombe-Glynn kurtosis test
## 
## data:  CholestoralData$After
## kurt = 2.58600, z = -0.27481, p-value = 0.7835
## alternative hypothesis: kurtosis is not equal to 3
shapiro.test(CholestoralData$Before)
## 
##  Shapiro-Wilk normality test
## 
## data:  CholestoralData$Before
## W = 0.91834, p-value = 0.00683
shapiro.test(CholestoralData$After)
## 
##  Shapiro-Wilk normality test
## 
## data:  CholestoralData$After
## W = 0.91706, p-value = 0.006231
Before <- log(CholestoralData$Before)
plot(density(Before))

After<- log(CholestoralData$After)
plot(density(After))

t.test(Before, After, paired=TRUE, alternative='two.sided')
## 
##  Paired t-test
## 
## data:  Before and After
## t = 4.7191, df = 39, p-value = 3.026e-05
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  0.1379106 0.3448133
## sample estimates:
## mean of the differences 
##                0.241362
margarine <- factor(CholestoralData$Margarine)
bartlett.test(After,margarine)
## 
##  Bartlett test of homogeneity of variances
## 
## data:  After and margarine
## Bartlett's K-squared = 0.93119, df = 1, p-value = 0.3346
difference = Before-After 
summary(aov(difference ~ margarine, data = CholestoralData))
##             Df Sum Sq Mean Sq F value   Pr(>F)    
## margarine    1  1.506  1.5059   22.22 3.23e-05 ***
## Residuals   38  2.575  0.0678                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
model3<- aov(difference ~ margarine, data = CholestoralData)

qqnorm(model3$residuals)

Based on result above, group A has higher cholestrol level than group B.

Espresso Data

espressodata <- read.csv("~/Downloads/EspressoData.csv")
plot(density(espressodata$cereme))

library(moments)
agostino.test(espressodata$cereme)
## 
##  D'Agostino skewness test
## 
## data:  espressodata$cereme
## skew = 0.54679, z = 1.32790, p-value = 0.1842
## alternative hypothesis: data have a skewness
anscombe.test(espressodata$cereme)
## 
##  Anscombe-Glynn kurtosis test
## 
## data:  espressodata$cereme
## kurt = 2.33130, z = -0.58842, p-value = 0.5563
## alternative hypothesis: kurtosis is not equal to 3
shapiro.test(espressodata$cereme)
## 
##  Shapiro-Wilk normality test
## 
## data:  espressodata$cereme
## W = 0.92201, p-value = 0.04414
cereme <- log(espressodata$cereme)
plot(density(cereme))

brewmethod <- factor(espressodata$brewmethod)
bartlett.test(cereme, brewmethod)
## 
##  Bartlett test of homogeneity of variances
## 
## data:  cereme and brewmethod
## Bartlett's K-squared = 1.3633, df = 2, p-value = 0.5058
summary(aov(cereme ~ brewmethod))
##             Df Sum Sq Mean Sq F value   Pr(>F)    
## brewmethod   2 1.9797  0.9898   24.41 1.64e-06 ***
## Residuals   24 0.9732  0.0405                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
model<- aov(cereme ~ brewmethod)

qqnorm(model$residuals)

tukeytest<- TukeyHSD(aov(cereme ~ brewmethod))
tukeytest
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = cereme ~ brewmethod)
## 
## $brewmethod
##           diff         lwr        upr     p adj
## 2-1  0.6506828  0.41362616  0.8877395 0.0000013
## 3-1  0.2139631 -0.02309354  0.4510198 0.0823041
## 3-2 -0.4367197 -0.67377635 -0.1996630 0.0003265
plot(tukeytest)

tapply(cereme, brewmethod, mean)
##        1        2        3 
## 3.452541 4.103223 3.666504
tapply(cereme, brewmethod, sd)
##         1         2         3 
## 0.2475991 0.1698051 0.1775045

Based on result aboeve, I understand that method 2 has the highest creme. In comparison, method 1 has the lowest creme.