Statistics is essentially the process of learning from data. The goal of statistics is to make correct statements or inferences about a population based on a sample.

Almost all natural resource professionals deal with data, for example a wildlife biologist may look at the number of owl packs on a given forest or a fuels specialist may look at the surface fuel loadings present in a prescribed burning block. In either case statistics is used to help us design how the data will be collected collected and to summarize the data after it is collected. Not only do we want to understand how to collect and summarize data we also want to be able to understand data that is published.

Understanding published data is just as important to us as natural resource professionals as collecting and summarizing our own data. Since we are not always able to collect the data we would like to have we often rely on published data to provide critical information. For example, it may not be possible to collect fire history data for completion of a restoration project, so we can use published data to provide that information. 

Random variables are any measurable characteristic or trait, in other words a measurement!

Example

We could measure the diameter of a tree or the spread rate of a forest fire. The object from which we collected the data is called an experimental unit. So for the last two examples the experimental unit would be a tree and the forest fire.

Population

A population is the set of all values of a single measurement (random variable) collected under certain conditions called the environmental conditions.

In both cases our environmental conditions limit our population to the Boise National Forest in 2006.

Sample

A sample is a subset of the population. For example, we may only measure the diameter of 20,000 trees or collect the spread rate for 10 of forest fires on the Boise National Forest in 2006.

Although we are usually interested in the population we can often not obtain measurements on the entire population. So a sample provides us with some information about the population.

Remember that both populations and samples are sets of numbers, they are never sets of physical units or experimental units.

Example

It is important to remember that we are often concerned about the population and the calculated parameters associated with that population. However, we usually do not know or can not obtain these values, so we rely on sampling and statistics to provide us with inferences about the population.

For any given population such as the fire rate of spread for all forest fires in Idaho during 2006 the parameters are fixed numbers, while statistics will vary depending upon the sample within the population.

Example

Let’s assume we collected fuel loading data from 50 stands on a National Forest. So we can now summarize this data in one of two ways. First we can summarize the data numerically by computing statistics such as the mean and standard deviation; to show the average amount of fuel loading and the degree to which fuel loading differs between stands. WE WILL GO OVER CALCULATING THESE STATISTICS IN LESSON 3.

The second way we could summarize this data is graphically by creating a box plot or a histogram. This method would provide information on the distribution of fuel loadings. WE WILL GO OVER HOW TO CREATE THESE TYPES OF GRAPHICAL SUMMARIES AS WELL AS OTHERS IN LESSON 3.

Example

Consider an experiment where tree growth rates were increased by 25 percent following a forest thinning operation on 10 sites compared to tree growth rates on 10 sites which were not thinned. Inferential statistics allows us to decide if the increased growth rates are due to chance or are real.

There are primarily two ways to use inferential statistics:

1. The first is to estimate a parameter about a population.
2. The second is to test a hypothesis.