Lab 02 Fall 2007 Statistics

# Lab 02 Fall 2007 Statistics - STATISTICAL ANALYSIS Lab 2...

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STATISTICAL ANALYSIS Lab 2 2-1 Reminders! Bring a Calculator Bring memory stick or floppy disk Key Concepts Frequency distribution (histogram) Descriptive Statistics Mean, Median Variance, Standard Deviation, Standard Error Inferential Statistics Student’s t-Test Regression & Correlation The purpose of this laboratory is to introduce you to the basics of statistical analysis. Why do you have to do math in an ecology class? Statistics are used in every science. They are critical to understanding whether any patterns we see in experimental results are due to real effects or just normal random variation. Let’s say we are interested in the size of rock wallabies that were introduced to Hawaii and those found in their native Australia. We then catch a bunch of wallabies in Hawaii and Australia and compare the average sizes. It might be a little odd if the averages were exactly the same. The important question, though, is whether or not the difference in the average size is due to normal variation in wallaby size or is it because the two populations grow to different sizes. How different are the averages? When do we say that the difference in size is outside the range of normal variability? How does the mean compare to the variance? These are the questions that statistics will help us answer, and answering these questions is a critical aspect of doing any science. In this lab, you will work with real data acquired by field ecologists during their studies. You will also carefully consider the hypotheses and perform statistical analyses on the data. I. FREQUENCY DISTRIBUTIONS The frequency distribution of a group of numbers (measurements) is most easily visualized by plotting the measurements on the x-axis versus the frequency of occurrence on the y-axis. This type of graph is called a histogram . As an example, a histogram from a past year's final exam scores is shown in Figure 1. Most frequency distributions are mound-shaped. One specific type of mound- shaped frequency distribution is called the normal distribution . The normal distribution is often referred to as a 'bell-shaped curve'. A perfect example is shown in Figure 2B. Because some statistical tests that we will be using assume a normal frequency distribution, it is important to understand how to visualize a frequency distribution (using a histogram), so that Figure 1 . Histogram of final exam scores. # Individuals Median Median Mean Mean Median Figure 2. Frequency distributions of three different sets of data. In A, the distribution is negatively skewed. In B, the distribution is normal. In C, the distribution is positively skewed. Notice that the median is a better indicator of the mid point of the data when the data do not have a normal distribution.

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## This note was uploaded on 04/10/2008 for the course BIO 265L taught by Professor Fukami during the Fall '07 term at Hawaii.

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Lab 02 Fall 2007 Statistics - STATISTICAL ANALYSIS Lab 2...

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