1. Statistics
Introduction

2. Significant Digits and Rounding Off
Only record and report actual digits observed
It is fine to let your calculator carry all the digits it wants until you get to the final answer.
Once arrived upon, report the answer using rounded digits. For instance, we will measure trees to the nearest inch. When reporting average size, please do not write ” just use 20”

3. Statistics
the art and science of gathering, describing, analyzing, summarizing and interpreting data to give us new information and knowledge

4. Statistics and Sampling
In everyday life, at work or at home, decisions are made based on the facts available.
In forestry and in this class, examples of these decisions would be:
How much to charge for a timber sale?
What tree growth can be expected in the next 50 years?

5. Reasons to Sample Reduced Cost
For populations having an extremely large number of individuals (like forest trees), measuring each individual would be impractical. Neither the time nor the money is available to do such an inventory. Additionally, the inventory costs of doing such an inventory would exceed the value of the sale.
Greater Speed
Sampling reduces the magnitude of the job, allowing the task to be completed in a shorter period of time. Not many timber sales would make it to market if the volume is measured on all of the trees and it takes ten months to do the sale prep work.
Greater Scope
Sampling provides the ability to study a larger area and include diverse information about the population. Additional information such as species present in the population, type of defect, or other conditions in the population can be included when sampling is used.
Greater Accuracy
Often overlooked is the quality of work suffers when budgets and resources are stretched too thin. Good measurements on a sample of individuals provide more reliable information than bad measurements on the entire population.

6. Populations and Parameters
Population – the total of all individuals or units that information is desired about.
Unit – the object information is gathered on
i.e. a tree or a plot
Value – the property observed on a unit.
i.e. species, height, diameter or volume per acre
Parameters describe populations
i.e. size, total, mean, variation

7. Variables
An attribute, property or characteristic of an individual that varies from unit to unit.
Variables of interest in forestry include tree diameters, heights, or volumes

8. Accuracy vs. Precision
Accuracy = the success of estimating the true value of a quantity
Precision refers to the clustering of sample values about their own average

9. Bias
A systematic distortion in the data which may be caused by poor measurements, bad sample selection or incorrect estimation procedures.
This could be caused by defective or improperly calibrated equipment or measuring procedures. Also by user error - failing to correct for declination, slope, etc.

10. Accuracy, Bias and Precision

11. Bias can be measured

12. Probability Probability of an event happening =
Number of ways it can happen
Total number of outcomes

13. Coin Toss Example
A balanced coin flipped in an unbiased way results in heads or tails (each with an equal 50% chance)
Chance of heads = one/two possible outcomes
What if the last 4 coin flips were heads, what is the chance of the next flip resulting in tails?

14. Probability of Failure
Know the odds!
Example when rolling a die, the chance of your number coming up equals 1/6 (or 16.6%)
More importantly the chance of numbers that you didn’t pick to show up is – 1/6 (or 83.3%)