Math 338Lab Assignment

In this lab, we will be working with subsets of a much larger data set commonly known as Fisher's or Anderson's Iris data set, see Fisher, R.A. (1936), The use of multiple measurements in taxonomic problems. The data set describes the petal length, petal width, sepal length, and sepal width of 50 setosa, 50 versicolor, and 50 virginica iris flowers.It can be found in the Rguroo Data Repository (Data Data Import Repository) by selecting the R Datasets Repository and then scrolling down to find the iris dataset. Import the dataset into Rguroo and View it. We are interested in figuring out whether there is a difference in the mean sepal length among the three species.

Let's start by creating side-by-side Boxplots of the sepal length for each of the three species by selecting Sepal.Length as the Numerical variable and Species as the Factor variable. Add an appropriate title and axis labels. As usual, you can mess around in the Factor Level Editor to change colors and other things.

Question #1 Insert the set of boxplots below.

Question #2 Based on your set of boxplots, does there appear to be an effect of species type on the mean sepal length? If so, describe the effect.

Now, create a Histogram of sepal length for each of the three species by selecting Sepal.Length as the Variable and selecting Species as the Factor variable in the Plot by Group section of the dialog. It may be useful to check the Uniform x-y Limit box as well. Add appropriate axis labels.

Question #3 Insert the set of histograms below.

Question #4 Based on your boxplots and histograms, do any assumptions (normally distributed populations, no outliers, reasonably constant standard deviation across groups) seem to be violated?

Regardless of your answer to Question #4, we will proceed to do a one-way ANOVA by "hacking" the Linear Regression module. Just like in Labs 10 and 11, we will select our Response variable and put a single variable in the Formula box. Unlike in Labs 10 and 11, our Formula variable will be a categorical explanatory variable, Species. The screenshot below shows the dialog before previewing.

Question #5 Write the null and alternative hypothesis for this particular one-way ANOVA F test.

Question #6 Copy and paste the ANOVA table from the output below.

Question #7 What is the value of the pooled sample variance? (Hint: think about how this sample variance is computed, and which cell in the ANOVA table is computed using an equivalent formula)

Question #8 What is the value of the observed test statistic? What sampling distribution does it come from (include the degrees of freedom)?

Question #9 What is the p-value? At the = 0.05 significance level, do you reject or fail to reject the null hypothesis?

Question #10 What can you conclude about the sepal lengths of the three species?