Lecture 2 - Accuracy, Precision, and Bias
Topics:
1.
2.
3.
4.
5.
6.
Accuracy, precision, and bias.
30-300 rule.
Significant digits.
Rounding.
Measurement systems.
Converting between units and systems.
Handouts/Readings:
1. Definitions handout
2. Measurement systems handout
3. Metric-US system conversion table
Assignment:
Complete problem set #1 before next Monday's (Jan. 28) lecture.
Notes:
Some definitions:
Population - is the total number of objects in a given area and
time period.
Sample - is the portion of the population that is measured.
Parameter - is a population characteristic. It is the value that
would be obtained for the characteristic of the population of
interest if every object in the population were measured. Ex. -
average tons of biomass per acre, total number of trees in a
forest.
Sample estimate - is the value of the parameter as estimated
from the population sample.
Accuracy - indicates the closeness of a measurement to the true
value. When we make measurements we want to know how
accurate they are - i.e., how close is the value we obtained by
measuring to the actual value of the parameter we measured.
Bias - refers to systematic errors that may result from faulty
measurement procedures, instrument errors, flaws in the
sampling procedure, errors in computations, mistakes in
recording, etc.
Ex. - If for some reason the measured value(s) is
consistently too high or too low, it is said to be biased.
Bias is often hard to detect, and consequently the accuracy of a
set of measurements can be very difficult to ascertain.
Precision - the degree of agreement in a series of measurements.
If the same result is obtained each time then the value obtained
is said to be 'precise'; as agreement decreases the measurements
become 'less precise'.
It is possible to have very precise measurements that are not
accurate. Think of a target bull's-eye as the true value of the
population parameter and the individual shots at the target as
sample estimates of the parameter (Show overhead -- Figure
2.2.1 - Shiver and Borders).
Least reading - refers to the smallest graduation of a particular
measurement instrument (show overhead -- ruler overhead).
Precision of a continuous variable will never be perfect. The
implied precision usually is equal to plus or minus half the least
reading of the measuring device.
The 30-300 rule: helps you to determine the least reading of
the instrument required to make the measurements.
- The # of units from the smallest to the largest expected
reading should fall between 30 and 300 (show overhead).
Significant digits
A significant digit is any digit denoting the true size of the unit
at its specific location in the overall number. The significant
figures in a number are the digits reading from left to right
beginning with the first nonzero digit and ending with the last
digit written, which may be a zero (show overhead).
Numbers used in natural resource measurements and inventories
arise from pure numbers, direct measurements, or from
computations using pure numbers and values from direct
measurements.
Pure numbers – are the result of a count in which a number is
exact, or they can be the result of some definition. Ex. - # of
sides on a square, the value of pi, the number of meters in a
kilometer.
Direct measurements – are obtained by using a measuring
instrument and the numerical values obtained are only
approximations. The number of significant digits used indicates
the precision of the approximation.
Ex. – The height of a tree could be measured to the nearest one,
tenth, or hundredth of a foot and recorded as 8, 7.6, 7.60,
respectively. Each measurement implies an increasing standard of
precision.
 8 feet lies somewhere between 7.5 and 8.5
 7.6 feet lies somewhere between 7.5 and 7.7
 7.60 feet lies somewhere between 7.595 and 7.605
It is incorrect to record more significant digits than were
observed or omit significant zeros in decimals.
Rounding
When a number contains more significant digits than are desired
or can be used, the number can be rounded off to the point that
it expresses the count in terms of a larger unit, which is some
multiple of 10 larger than the original counting unit. In this
process the portion of the number to the right of the new right
end position becomes a remainder.
 If the remainder is less than half the new counting
unit, it is ignored and the right end digit is left
unchanged.
Ex. – round the value 50,422 lb to the nearest thousand
pounds - (remainder 422 is less than half of 1000, so no
change – answer is 50,000 lb).
 If the remainder is greater than or equal to half the
new counting unit, the right end digit is increased to
be the next higher value.
Ex. – round the value 608.6 g to the nearest gram (remainder 0.6 is greater than or equal to half of 1, so
increase – answer is 609 g).
Significant digits in arithmetic operations
Rules for multiplication or division (see overhead):
1. Determine the number of significant digits in the number
with the fewest significant figures. Round off all the other
numbers until they have one more significant digit than the
one with the fewest.
2. Multiply or divide as usual.
3. Round off the product or quotient to the number of
significant figures possessed by the original number with
the fewest significant digits.
Rules for addition or subtraction (see overhead):
1. Arrange the numbers in a column so that their decimal
points line up.
2. Find the column farthest toward the left, which contains
a nonsignificant digit.
3. Round off all the numbers until their right-most
significant digit is in the column found in step 2.
4. Add or subtract as usual.
5. Round off the sum or difference so that it has the same
number of significant digits as has the item, which had
its right-most significant digit farthest to the left when
the numbers were arranged in a column.
Measurement systems and conversions
English versus Metric system (see measurement systems
overhead).
Both measurement systems are used in natural resource
management in the United States. Until the US adopts the
metric system as its defacto system we need to know both
systems and how to convert between the two.
The English system is still used extensively in US forestry,
however the metric system is used in Canadian forestry. You
have to know how to work in and between both systems.
Converting between systems is not difficult (see conversions
overhead).
You can also use the cross-multiplication method (show example).