Project_P2

Part 2: Basic Inferential Data Analysis Instructions

Now in the second portion of the project, we’re going to analyze the ToothGrowth data in the R datasets package.

Load the ToothGrowth data and perform some basic exploratory data analyses Provide a basic summary of the data. Use confidence intervals and/or hypothesis tests to compare tooth growth by supp and dose. (Only use the techniques from class, even if there’s other approaches worth considering) State your conclusions and the assumptions needed for your conclusions. Required packages:

library(ggplot2)

1. Load the ToothGrowth data and perform some basic exploratory data analyses

data(ToothGrowth)
str(ToothGrowth)

## 'data.frame':    60 obs. of  3 variables:
##  $ len : num  4.2 11.5 7.3 5.8 6.4 10 11.2 11.2 5.2 7 ...
##  $ supp: Factor w/ 2 levels "OJ","VC": 2 2 2 2 2 2 2 2 2 2 ...
##  $ dose: num  0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 ...

head(ToothGrowth, 5)

##    len supp dose
## 1  4.2   VC  0.5
## 2 11.5   VC  0.5
## 3  7.3   VC  0.5
## 4  5.8   VC  0.5
## 5  6.4   VC  0.5

2. Provide a basic summary of the data.

Look at the summary of the data

summary(ToothGrowth)

##       len        supp         dose      
##  Min.   : 4.20   OJ:30   Min.   :0.500  
##  1st Qu.:13.07   VC:30   1st Qu.:0.500  
##  Median :19.25           Median :1.000  
##  Mean   :18.81           Mean   :1.167  
##  3rd Qu.:25.27           3rd Qu.:2.000  
##  Max.   :33.90           Max.   :2.000

Compare means of the different delivery methods

tapply(ToothGrowth$len,ToothGrowth$supp, mean)

##       OJ       VC 
## 20.66333 16.96333

Make a plot to look at data graphically

ggplot(ToothGrowth, aes(factor(dose), len, fill = factor(dose))) +
      geom_boxplot() +
      # facet_grid(.~supp)+
      facet_grid(.~supp, labeller = as_labeller(
            c("OJ" = "Orange juice", 
              "VC" = "Ascorbic Acid"))) +
      labs(title = "Tooth growth of 60 guinea pigs 
           by dosage and\nby delivery method of vitamin C",
           x = "Dose in milligrams/day", 
           y = "Tooth Lengh") +
      scale_fill_discrete(name = "Dosage of\nvitamin C\nin mg/day")

3. Use confidence intervals and/or hypothesis tests to compare tooth growth by supp and dose.

Comparison by delivery method for the same dosage

t05 <- t.test(len ~ supp, 
       data = rbind(ToothGrowth[(ToothGrowth$dose == 0.5) & 
                                      (ToothGrowth$supp == "OJ"),],
                    ToothGrowth[(ToothGrowth$dose == 0.5) & 
                                      (ToothGrowth$supp == "VC"),]), 
       var.equal = FALSE)

t1 <- t.test(len ~ supp, 
       data = rbind(ToothGrowth[(ToothGrowth$dose == 1) & 
                                      (ToothGrowth$supp == "OJ"),],
                    ToothGrowth[(ToothGrowth$dose == 1) & 
                                      (ToothGrowth$supp == "VC"),]), 
       var.equal = FALSE)

t2 <- t.test(len ~ supp, 
       data = rbind(ToothGrowth[(ToothGrowth$dose == 2) & 
                                      (ToothGrowth$supp == "OJ"),],
                    ToothGrowth[(ToothGrowth$dose == 2) & 
                                      (ToothGrowth$supp == "VC"),]), 
       var.equal = FALSE)

# Make summary of the conducted t.tests, which compare the delivery methods by dosage
# take p-values and CI
summaryBYsupp <- data.frame(
      "p-value" = c(t05$p.value, t1$p.value, t2$p.value),
      "Conf.Low" = c(t05$conf.int[1],t1$conf.int[1], t2$conf.int[1]),
      "Conf.High" = c(t05$conf.int[2],t1$conf.int[2], t2$conf.int[2]),
      row.names = c("Dosage .05","Dosage 1","Dosage 2"))
# Show the data table 
summaryBYsupp

##                p.value  Conf.Low Conf.High
## Dosage .05 0.006358607  1.719057  8.780943
## Dosage 1   0.001038376  2.802148  9.057852
## Dosage 2   0.963851589 -3.798070  3.638070

4. State your conclusions and the assumptions needed for your conclusions.

We reject the null hypothesis at 95% confidence. So, there is no difference in the tooth growth by the delivery method for 0.5 and 1 milligrams/day. We observe p-values less than the treshold of 0.05 and the confidence levels don’t include 0. So, for dosage of .5 milligrams/day and 1 milligrams/day does matter the delivery method. With 95% confidence we fail to reject the null hypothesis, stating that there is no difference in the tooth growth by the delivery method for 2 milligrams/day. We observe p-values more than the treshold of .05 and the confidence levels include 0. So, for dosage of 2 milligrams/day the delivery method doesn’t matter.