statstests.R

# taken from http://sciencecases.lib.buffalo.edu/cs/files/mini_eco_stats.pdf
#
# NATIONAL CENTER FOR CASE STUDY TEACHING IN SCIENCE
# Mini Cases on Choosing Appropriate
# Statistical Tests for Ecological Data
# by
# Alyssa M. Gleichsner, Department of Biological Sciences
# Elizabeth A. Flaherty, Department of Forestry and Natural Resources
# Purdue University, West Lafayette, IN
# Instructions
# As scientists, we use statistics to quantify the significance of our results—to determine whether the patterns we observe
# are the result of a certain stimulus or are merely an artifact of chance. There are a variety of different experimental
# designs and types of data that we use to study the world around us, and different data require different statistical
# tests. This activity is designed to provide you with an opportunity to select and apply the appropriate statistical test
# to a given data set. We will focus on the application and use of four statistical tests: t-test, one-way ANOVA, linear
# regression, and Chi-square test.
# You will work in groups of 3–4 students. Your group will receive a data set related to a habitat use study for eastern
# cottontail rabbits and a description of why the data were collected. After reviewing these, you and your group will:# 1. Write a hypothesis set, both a null and alternative hypothesis, based on the research question provided in the
# scenario.
# 2. Determine the appropriate statistical test to evaluate the significance of the results and test your hypotheses.
# a. Ask yourself: What kind of data do I have? Am I comparing groups or evaluating a relationship?
# 3. Explain why this test is appropriate by describing the evaluation accomplished by using this test.
# 4. Use the statistical test your group selected to analyze the data set and test your hypothesis.
# 5. Discuss how to interpret the test results. Are additional tests needed to test your hypothesis? If so, what test
# would you use?
# 6. Evaluate the variance calculated in the test and interpret this number.
# 7. Create a four-slide PowerPoint presentation that includes: a brief description of the data set and research
# question; your hypotheses; the statistical test you selected to test your hypotheses; your test results and
# interpretation; a figure depicting your data; and whether you reject or fail to reject the null hypothesis.

# Data Set #1
# You have noticed that the field site for your cottontail rabbit research is experiencing declines in understory plant
# species richness. You suspect that the declines are caused by the spread of an invasive plant, Asian honeysuckle, and
# consider promoting a more rigorous honeysuckle removal program. To evaluate whether honeysuckle density is
# affecting understory richness, you set up an experiment where you record plant species richness as a function of
# honeysuckle density (stems per meter2) throughout the property. Using a random sampling design and geographical
# information system (GIS) to identify sampling points, you measure understory species richness and honeysuckle
# density resulting in the following data set: 
  
ds1 <- data.frame(c(23, 2, 27, 31, 5, 8, 36, 21, 5, 12), c(5, 15, 2, 1, 10, 8, 1, 3, 11, 5))
colnames(ds1) <- c("Honeysuckle density", "Species Richness")

# Data Set #2
# To investigate habitat use by cottontail rabbits at your field site, you estimate understory plant species richness.
# You decide to evaluate canopy cover as a variable that could possibly influence understory richness. You measure
# and record canopy cover and understory plant species richness at 10 randomly chosen survey sites resulting in the
# following data set: 

ds2 <- data.frame(c(21,33,92,65,31,43,94,76,69,58), c(5,15,2,1,10,8,1,3,11,5))
colnames(ds2) <- c("Canopy Cover (%)", "Species Richness")

# Data Set #3
# While investigating habitat use by cottontail rabbits, you decide to evaluate the impact of rabbit browsing on tree
# sapling growth. To accomplish this, you set up seven exclusion areas (“no predator”) using rabbit-proof fencing and
# seven non-exclusion areas of equal size with no fencing (“predator”). After two years you compare the mean tree
# sapling height (cm) from the “no predator” and “predator” treatments.

ds3 <- data.frame(c(218.3,224.8,244.09,230.1,211.33,250.2,234.95), c(52.07,25.91,39.88,48.8,35.7,64.2,59.4))
colnames(ds3) <- c("No Predator", "Predator")

# Data Set #4
# A portion of your field site for the study of habitat use by cottontail rabbits in Indiana is also part of a prairie
# restoration project. In prairies there are a variety of disturbance regimes and management practices used to promote
# diversity of grasses and prevent the growth of trees and shrubs. Some areas of this field site are managed using
# controlled burns, grazing by livestock, or both burning regimes and grazing. To evaluate rabbit habitat and grass
# diversity, you determine the total number of grass species present within areas of prairie experiencing no management,
# burns, grazing, and both controlled burn and grazing, using seven randomly selected survey sites per area.

ds4 <- data.frame(c(2,3,1,2,4,1,5), c(9,10,6,8,8,11,7), c(6,7,11,9,10,8,5), c(10,14,12,15,8,13,11))
colnames(ds4) <- c("No Management", "Burn", "Grazing", "Burn and Grazing")

# Data Set #5
# Habitat use of wildlife is often related directly, at least in part, to diet choice. You are interested in winter food
# preferences of cottontail rabbits at your field site in Indiana. You calculate the frequency of occurrence of five major
# food types in diet based on microhistological fecal analysis to determine if rabbits show a preference for a specific food
# that could be managed to either increase or control cottontail populations.

ds5 <- data.frame(c("Woody plants", "Grasses", "Other herbaceous plants (not grasses)", "Agricultural plant materials (corn, etc.)", "Arthropods"), c(45, 38, 10, 5, 2))
colnames(ds5) <- c("Diet Item", "Frequency of Occurrence")