Principles of Vegetation Measurement & Assessment and Ecological Monitoring & Analysis

## Accuracy and Bias

Accuracy of Assessment

### Accuracy, Precision, and Bias

When we present an error (e.g. ± 5cm) with a measurement (e.g., 180 cm) it does not mean a mistake, but rather due to experimental limitations there is uncertainty of ± 5cm in the quoted value.

The term accuracy refers to the closeness of a measurement or estimate to the TRUE value.

The term precision (or variance) refers to the degree of agreement for a series of measurements.

There are two common measures:

• The clustering of samples about their own average is called the standard deviation.

• The reproducibility of an estimate in repeated sampling is called the standard error.

Bias refers to the tendency of measures to systematically shift in one direction from the true value and as such are often called systematic errors. Such errors are often caused by poorly calibrated instruments. In contrast, random errors are  produced by the statistical fluctuations observed when measuring a quantity. These result in a spread of observed measurements about a center value.

### Expressing Uncertainty

Some things in life are relatively certain. If you buy a 6-pack of soda, you can expect to get 6 cans of soda (barring some unforeseen problem).  Thus, if you ordered 13 6-packs of soda you would probably get 6 cans per park plus or minus (+) 0 cans.  Or, your average would be 6 + 0 cans of soda per pack.

However, few things in measuring vegetation are certain. We commonly use averages to express what is called a "central tendency."  In the example of the target and arrows above, we are relatively accurate if the average of our shots (i.e., the central tendency) is near the bulls eye.  An estimate of uncertainty (or, spread of data) is an expression of our precision.

For example one might examine 50 plots and count the number of sagebrush plants in each plot and calculate an average. The average number of plants per plot might be 4.5 + 0.5 plants.  The 0.5 represents the precision through an estimate of standard deviation or standard error (For more info on how to make calculations, visit College of Natural Resources Student Learning Center - Statistics - Lesson 3).  We will use estimates of precision and spread of data throughout this course.

A NOTE OF CAUTION -- avoid excessive units created by calculators and spreadsheets.  In the example above we measured 50 plots and I noted that there were 4.5 + 0.5 plants/plot. Actually, when I finished the calculations in my spreadsheet there were 4.423 plants per plot.  But, I made the informed decision to round to the nearest half plant (0.5 plant).  The number 4.423 insinuates that I could recognized fractions of a plant to 1/1000th (i.e., 0.001).  Sorry, I just can't envision 1/1000th of a plant and I don't think it would be very useful to try to make decisions based on 1000ths  of a plant. Especially because I only measured 50 plots. Just because you can calculate numbers with many units beyond the decimal doesn't mean you should.  Here are a few guidelines:

• Avoid rounding numbers while making calculations -- you can lose accuracy if you do.

• When reporting numbers, round to the unit level that you think you could realistically measure and recognize in nature.

• Also, think about the unit level that would be useful to make management decisions or conclusions about differences between sites.

 Summary Questions What is meant by the terms accuracy and  precision?   What are a few errors in field measurement that could create a random error in your data? Advanced Questions: Consider the example that you find out that a class of 20 students who you asked to report to you the height of a special shrub have been taking measurements with broken yard sticks that are missing 5" off one end. You are told each stick has increments down to the nearest inch and that the group of twenty is pleased that all their measurements are within 15 inches of each other. Explain the different sources of errors in this measurement and explain whether they would be random or systematic. Consider the following scenario: An area of sagebrush steppe was split into two parts A and B and twenty years later students measure the average height of Big Sagebrush in each half. They find that the height in Area A is 4' ± 6" and in Area B is 3' ± 8". Explain if these results suggest whether in the twenty year time period different management practices have been conducted in each part? Consider the following scenario: A forester measures the heights of grand fir at two locations X and Y. The mean height of X is 80' and Y is 78'. Explain whether you can conclude that the trees in X definitely have a larger mean height?