Natural Resources Biometrics (Kiernan)

Natural Resources Biometrics begins with a review of descriptive statistics, estimation, and hypothesis testing. The following chapters cover one- and two-way analysis of variance (ANOVA), including multiple comparison methods and interaction assessment, with a strong emphasis on application and interpretation. Simple and multiple linear regressions in a natural resource setting are covered in the next chapters, focusing on correlation, model fitting, residual analysis, and confidence and prediction intervals. The final chapters cover growth and yield models, volume and biomass equations, site index curves, competition indices, importance values, and measures of species diversity, association, and community similarity.

Descriptive Statistics

A population is the group to be studied, and population data is a collection of all elements in the population. For example:

• All the fish in Long Lake.
• All the lakes in the Adirondack Park.
• All the grizzly bears in Yellowstone National Park.

A sample is a subset of data drawn from the population of interest. For example:

• 100 fish randomly sampled from Long Lake.
• 25 lakes randomly selected from the Adirondack Park.
• 60 grizzly bears with a home range in Yellowstone National Park.

Variables are divided into two major groups: qualitative and quantitative. Qualitative variables have values that are attributes or categories. Mathematical operations cannot be applied to qualitative variables. Examples of qualitative variables are gender, race, and petal color. Quantitative variables have values that are typically numeric, such as measurements. Mathematical operations can be applied to these data. Examples of quantitative variables are age, height, and length. Quantitative variables can be broken down further into two more categories: discrete and continuous variables. Discrete variables have a finite or countable number of possible values. Think of discrete variables as “hens”. Hens can lay 1 egg, or 2 eggs, or 13 eggs… There are a limited, definable number of values that the variable could take on. 958.png

Continuous variables have an infinite number of possible values. Think of continuous variables as “cows”. Cows can give 4.6713245 gallons of milk, or 7.0918754 gallons of milk, or 13.272698 gallons of milk … There are an almost infinite number of values that a continuous variable could take on.

Measures of Center

Mean

The arithmetic mean of a variable, often called the average, is computed by adding up all the values and dividing by the total number of values. The population mean is represented by the Greek letter (mu). The sample mean is represented by (x-bar). The sample mean is usually the best, unbiased estimate of the population mean. However, the mean is influenced by extreme values (outliers) and may not be the best measure of center with strongly skewed data. The following equations compute the population mean and sample mean.