## Lab Worksheet 1 Solution

This worksheet uses the iris data set available in R. This data set gives the measurements in centimeters of the variables sepal length and width and petal length and width, respectively, for 50 flowers from each of 3 species of iris. The species are Iris setosa, versicolor, and virginica:

head(iris)
##   Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 1          5.1         3.5          1.4         0.2  setosa
## 2          4.9         3.0          1.4         0.2  setosa
## 3          4.7         3.2          1.3         0.2  setosa
## 4          4.6         3.1          1.5         0.2  setosa
## 5          5.0         3.6          1.4         0.2  setosa
## 6          5.4         3.9          1.7         0.4  setosa

Problem 1: Is there a difference in sepal length between species setosa and species virginica? Perform a t test and discuss your results (1-2 sentences).

t.test(iris$Sepal.Length[iris$Species == "setosa"], iris$Sepal.Length[iris$Species == "virginica"])
##
##  Welch Two Sample t-test
##
## data:  iris$Sepal.Length[iris$Species == "setosa"] and iris$Sepal.Length[iris$Species == "virginica"]
## t = -15.386, df = 76.516, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -1.78676 -1.37724
## sample estimates:
## mean of x mean of y
##     5.006     6.588

There is a significant difference in sepal length. Sepals of species virginica are on average 1.6 cm longer than sepals of species setosa.

Problem 2: Make side-by-side box plots of sepal length for the three species. Discuss what patterns you observe (1-2 sentences).

boxplot(iris$Sepal.Length ~ iris$Species, ylab = "Sepal Length (cm)")

Sepal length seems to increase from setosa to versicolor to virginica.

Problem 3: Make a scatter plot of sepal length vs. petal length for the three species. Make a single plot that shows the data for all three species at once, in different colors. Hint: To see all data in one plot, you will have to manually set the plot limits, using the xlim and ylim parameters of the plot function. Discuss your results (1-2 sentences).

setosa <- iris[iris$Species == "setosa", ] versicolor <- iris[iris$Species == "versicolor", ]
virginica <- iris[iris$Species == "virginica", ] plot(setosa$Sepal.Length, setosa$Petal.Length, pch = 19, col = "blue", xlim = c(3, 8), ylim = c(1, 8), xlab = "Sepal Length (cm)", ylab = "Petal Length (cm)") points(versicolor$Sepal.Length, versicolor$Petal.Length, pch = 19, col = "red") points(virginica$Sepal.Length, virginica\$Petal.Length, pch = 19, col = "green")

Setosa is plotted in blue, versicolor in red, and virginica in green. Both versicolor and virginica have much longer petals than setosa, but only somewhat longer sepals.