Overview

This data set contains information on the types and sizes of trees in an old-growth beech-maple forest in northeastern Ohio.

Details

The study described here was carried out at the James H. Barrow Field Station (owned and maintained by Hiram College in northeastern Ohio) during the summer of 1993. In this study, an extensive survey of the forest was performed to assess the diversity and distribution of tree species that occupy the forest. The forest was subdivided into a collection of 50m × 50m plots, and within each of these 67 plots, four 10m x 10m sub-plots were randomly selected to be surveyed. For each surveyed sub-plot, all tree species occurring within the sub-plot were counted and recorded. The diameter at breast height (dbh) was measured for any tree that was larger than 3cm dbh.

In this project, your goal will be to understand how tree species distribution varies throughout the forest. Four main areas of the forest can be identified. These are (1) a portion of the forest which had been mostly cleared within the last hundred years and used as pasture; (2) a portion of the forest which historically consisted primarily of chestnut trees; these trees died in the early 1900s as a result of chestnut blight (a fungal infection of chestnut trees); (3) areas in which the land slopes fairly steeply in a west-facing direction; and (4) all other areas of the forest. In the data set we’ll examine, these areas are labeled (1) Pasture, (2) Chestnut, (3) West, and (4) Central (since this area is primarily in the middle of the forest).

Your goal in this project is to compare these areas of the forest with respect to basal area for the two dominant trees species, maple and beech. To do this, we will carry out a series of two-sample t-tests to compare the mean basal area in pairs of areas using data on each of the plots for each species. We will also examine graphical displays, and compare the results of our t-tests with these displays.

Data Description

Variable Description
Column 1: Quadrat label
Column 2: Area of the forest
Column 3: Total basal area of maple trees in that quadrat
Column 4: Total basal area of beech trees in that quadrat 
forest_data = read.table("data/forest_ba2D.txt", header = TRUE)
head(forest_data)

Data Files

Objectives

As stated above the overall objective is to compare the various areas of the forest with respect to the basal area of beech and maple trees. Specifically, address the following:

  1. Considering maple and beech trees separately, construct an appropriate graphical display to examine the distribution of basal area across the four areas of the forest. Do the areas seem to differ with respect to basal area for these two species?
  2. Carry out all pairwise t-tests, and summarize your findings using an \(\alpha\) of 0.05. Do your results agree with the graphical summaries you produced? Are these divisions into areas of the forest meaningful?
  3. Note that we have now performed 12 distinct hypothesis tests. Assuming that there is no difference in the mean basal area for any of the forest areas for either species, how many of these tests would be expected to show a significant result (e.g., to reject \(H_0\))? What is the probability that at least one of the tests is significant? What is the probability that more than one of the tests is significant? Compare your calculations here to the actual number of observed significant results.
  4. What assumptions did we make in carrying out the t-tests? Do you think these assumptions are reasonable in this setting? If you can identify a better test or set of tests for the main question considered here, carry out that test (or describe it, if it is too complicated to carry out).