Performance Benchmark N.12.A.3
Students know repeated experimentation allows for statistical analysis and unbiased
conclusions. E/S
The National Science Education Standards (NSES p. 23) defines scientific inquiry as "the
diverse ways in which scientists study the natural world and propose explanations based on the
evidence derived from their work. Scientific inquiry also refers to the activities through which
students develop knowledge and understanding of scientific ideas, as well as an understanding of
how scientists study the natural world." The Science as Inquiry Standard in NSES includes the
abilities necessary to do scientific inquiry and understanding about scientific inquiry.
Scientific inquiry reflects how scientists come to understand the natural world, and it is at the
heart of how students learn. From a very early age, children interact with their environment, ask
questions, and seek ways to answer those questions. Understanding science content is
significantly enhanced when ideas are anchored to inquiry experiences.
Scientific inquiry is a powerful way of understanding science content. Students learn how to ask
questions and use evidence to answer them. In the process of learning the strategies of scientific
inquiry, students learn to conduct an investigation and collect evidence from a variety of sources,
develop an explanation from the data, communicate and defend their conclusions.
For a complete list of NSTA Position Statements visit
http://www.nsta.org/about/positions.aspx#list
Figure 1. Natural world collage. (from http://www.chemistryland.com/ChemEdArticle/PowerPoint.html)
Science Demands Evidence
Sooner or later, the validity of scientific claims is settled by referring to observations of
phenomena. Hence, scientists concentrate on getting accurate data. Such evidence is obtained by
observations and measurements taken in situations that range from natural settings (such as a
forest) to completely contrived ones (such as the laboratory). To make their observations,
scientists use their own senses, instruments (such as microscopes) that enhance those senses, and
instruments that tap characteristics quite different from what humans can sense (such as
magnetic fields). Scientists observe passively (earthquakes, bird migrations), make collections
(rocks, shells), and actively probe the world (as by boring into the Earth's crust or administering
experimental medicines).
From Science for All Americans Online at
http://www.project2061.org/publications/sfaa/online/chap1.htm
Science places great emphasis on evidence and data, therefore great value is placed on the
development of better instruments and techniques of observation. Additionally, the findings of
any one investigator or group are usually checked by others. Accuracy and precision are two
terms related to the significance of scientific measurements and calculations.
Accuracy is the correctness of a measured or calculated quantity to its actual (true) value. In
scientific investigations, oftentimes the accuracy of the experiment is presented as a percent
error through the following equation:
%error 
accepted value  exp erimentalvalue
x100
accepted value
Precision is the degree to which repeated measurements of the same quantity yield the same or
similar results (often referred to as reproducibility or repeatability of the measurement).
Oftentimes a dartboard and darts are used to model the difference between these two terms.
Aiming at the target, your goal is to hit the bull’s eye (target center) with all five darts. The
resulting patterns provide insight into the meanings of accuracy and precision.
2a
2b
2c
2d
Figure 2a-d. Dart images. (from http://honolulu.hawaii.edu/distance/sci122/SciLab/L5/accprec.html)
Figure 2a. Neither Precise Nor Accurate. This is a random pattern, neither precise nor
accurate. The darts are not clustered together and are not near the bull’s eye.
Figure 2b. Precise, Not Accurate. This is a precise pattern, but not accurate. The darts are
clustered together but did not hit the intended mark.
Figure 2c. Accurate, Not Precise. This is an accurate pattern, but not precise. The darts are not
clustered but their average position is the center of the bull’s eye.
Figure 2d. Accurate and Precise. This pattern is both precise and accurate. The darts are
tightly clustered and their average position is the center of the intended mark.
Adapting the dartboard model to scientific experimentation, poor accuracy among measurements
and calculations arise from procedural or equipment flaws while poor precision results from poor
technique. Individual measurements can be precise without having accuracy. This oftentimes
occurs with an incorrectly used or incorrectly calibrated piece of scientific equipment such as a
balance that was not zeroed prior to massing an object. Repeated measurements of the sample
will yield very similar (if not identical) masses for that sample but will not reflect the true mass
of the sample. However, it is not possible to reliably achieve accuracy in individual
measurements without precision. As in the dartboard model, if the darts are not grouped close to
one another, they cannot all be close to the bull’s eye. (Their average position might be an
accurate estimation of the bull’s eye, but the individual arrows are inaccurate. As in Figure 2c.)
Let’s explore an example using collected data.
A traditional lab experience in an introductory physics class is to determine the acceleration due
to earth’s gravity (gEarth). This investigation used technology and graphical analysis software
(Vernier’s LoggerPro software) to measure the acceleration of a freely falling body (g) using a
Picket Fence and a Photogate.
Trail #1
The slope of a velocity verse time graph yields average acceleration. The analysis box in the
graph above displays a slope value of 10.31 m/s2. The accepted value for acceleration due to
Earth’s gravity (gEarth) is 9.81 m/s2. Substituting the values into the percent error equation for
this one trial yields an error of 5.1%.
%error 
accepted value  exp erimentalvalue
x100
accepted value
9.81

m
m
 10.31 2
2
s
s
x100
m
9.81 2
s
= 5.1%
The same experiment is repeated two more times, indicated in the data table as “Run 2”
and “Latest”.
The acceleration (slope of the best fit line) of Run #1 is 10.31 m/s2, Run #2 is 9.83 m/s2, and
Latest (Run 3) is 9.78 m/s2. The arithmetic mean is calculated to determine the experimental
average acceleration of Earth’s gravity (gEarth). Using the equation below, the experimental
average acceleration due to Earth’s gravity is 9.97 m/s2.
x
x  x
1
n
 x 2  ...  xn
n
Where,
x is the arithmetic mean of all the trials (or samples)
x is the experimental value from a single trial (or single sample)
n is the number of trials (or samples)
x
x
n

10.31
m
m
m
 9.83 2  9.78 2
2
s
s
s
3
gEarth = 9.97 m/s2
Using the average experimental acceleration due to Earth’s gravity from our three trials yields an
error of 1.6%.
%error 
accepted value  exp erimentalvalue
x100
accepted value
9.81

m
m
 9.97 2
2
s
s
x100
m
9.81 2
s
=1.6 %
Increasing the number of trails in our experiment has reduced the error and shown that the
experiment is repeatable and close to the accepted value; in other words accurate.
The average acceleration determined represents a single best value, derived from all the
measurements. The minimum and maximum values give an indication of how much the
measurements can vary from trial to trial; that is, they indicate the precision of the measurement.
One way of stating the precision is to take half of the difference between the minimum and
maximum values and use the result as the uncertainty of the measurement.
For our example, the minimum, average, and maximum values are 9.78 m/s2, 9.97 m/s2, and
10.31 m/s2. The result is g = 10.0 ± 0.25 m/s2. The precision of this experiment is 2.5%.
m
s 2  100%  2.5 0
0
m
10.0 2
s
0.25
Scientists Try to Identify and Avoid Bias
When faced with a claim that something is true, scientists respond by asking what evidence
supports it. But scientific evidence can be biased in how the data is interpreted, in the recording
or reporting of the data, or even in the choice of what data to consider in the first place.
Scientists' nationality, sex, ethnic origin, age, political convictions, and so on may incline them
to look for or emphasize one or another kind of evidence or interpretation. For example, for
many years the study of primates—by male scientists—focused on the competitive social
behavior of males. Not until female scientists entered the field was the importance of female
primates' community-building behavior recognized. Economic factors can also introduce bias
into research. Limited resources may prohibit the scientist from access to the most advanced
techniques and equipment thereby limiting the accuracy and precision of his analysis and
conclusion.
Bias attributable to the investigator, the sample, the method, or the instrument may not be
completely avoidable in every instance, but scientists want to know the possible sources of bias
and how bias is likely to influence evidence. Scientists want, and are expected, to be as alert to
possible bias in their own work as in that of other scientists, although such objectivity is not
always achieved. One safeguard against undetected bias in an area of study is to have many
different investigators or groups of investigators working in it.
Taken from Science for All Americans Online, found at
http://www.project2061.org/publications/sfaa/online/chap1.htm
Same Data Sets Can Result in Alternate (and often very different) Conclusions
Global warming and global climate change are hot topics today. Earth’s climate has changed
through time as discovered through the study of ice cores, tree rings, glacier lengths, ocean
sediments, and studying changes in the Earth’s orbit around the sun. Climate scientists are
analyzing this data in an attempt to determine the causes of global climate change. The fact that
Earth’s climate has changed in the past is not in question, however, the reasons for that change
(especially since the American Industrial Revolution) is. Some scientists attribute rising levels of
CO2 to human causes while others conclude these changes result from Earth’s natural cycles.
Different interpretations of the data sets illustrate scientists’ disagreement in what the data
means.
For more information on past climate change visit
http://www.epa.gov/climatechange/science/pastcc.html
For a detailed discussion of Earth’s atmosphere and the Green House Effect see
TIPS E12A3 Benchmark
Performance Benchmark N.12.A.3
Students know repeated experimentation allows for statistical analysis and unbiased
conclusions. E/S
Common misconceptions associate with this benchmark
1. Students incorrectly think that evidence accumulated carefully will result in sure
knowledge and that scientists are particularly objective.
Facts need to be taken in without bias to reach a conclusion. However, it is both impossible
to make all observations pertaining to a given situation and unattainable to secure all relevant
facts for all time, past, present, and future. With advancements in technology, the precision
and amount of data available to scientists is greater today than ever before. Scientists, like all
observers, hold a multitude of preconceptions and biases about the way the world operates.
Therefore, it is impossible to collect and interpret facts without any bias. Students should be
aware that individuals’ experiences play a role in the interpretation of data and that alternate
interpretations may be valid. Scientists can legitimately hold different explanations for the
same set of observations.
Myth 4 and 8 from McComas, William, "Ten myths of science: Reexamining what we think
we know....," Vol. 96, School Science & Mathematics, 01-01-1996, pp 10. To access this
paper, visit http://www.bluffton.edu/~bergerd/NSC_111/TenMyths.html.
2. Students may not realize that changed theories sometimes suggest new observations or
reinterpretation of previous observations.
Although most students believe that scientific knowledge changes, they typically think
changes occur mainly in facts and mostly through the invention of improved technology for
observation and measurement. One of the strengths of science is that experiments are the
sole route to scientific knowledge and that scientific conclusions are continually reviewed.
From Benchmarks for Science Literacy On-Line by the American Association for the
Advancement of Science (AAAS) found at
http://www.project2061.org/publications/bsl/online/ch15/findings.htm#Ch1
Performance Benchmark N.12.A.3
Students know repeated experimentation allows for statistical analysis and unbiased
conclusions. E/S
Sample Test Questions
1. A student measures the length of a pendulum three times. The measurements were 1.42
meters, 1.43 meters, and 1.45 meters. The actual length of the pendulum was 1.89
meters. What can be said about these measurements?
a. the measurements are accurate
b. the measurements are precise
c. the measurements are both accurate and precise
d. the measurements are neither accurate nor precise
2. What makes a scientific explanation different from a non-scientific explanation?
a. scientific explanations are based on assumptions
b. scientific explanations are predictable
c. scientific explanations cannot be changed
d. scientific explanations are testable
3. The degree to which data matches the true or accepted value is
a. accuracy
b. correlation coefficient
c. precision
d. none of the above
4. A student throws five darts at the bull’s eye (centermost circle) of a target and the
following pattern results. What can be said about the grouping of darts?
a.
b.
c.
d.
the grouping is accurate
the grouping is precise
the grouping is both accurate and precise
the grouping is neither accurate nor precise
5. Students conduct a laboratory investigation to determine the acceleration due to Earth’s
gravity (g). They calculate g to be 8.0 m/s2. The actual (true) acceleration due to Earth’s
gravity is 9.8 m/s2. What is the percent error for their experiment?
a. 7.0%
b. 15%
c. 18%
d. 23%
6. In August 2006, the International Astronomical Union removed Pluto’s status as a planet
and named it a dwarf planet. What prompted the reclassification of Pluto?
a. A new telescope introduced in 2006 allowed scientists to see a better view of
Pluto.
b. Scientists based their decision on known data from Pluto and other objects in the
solar system.
c. A manned mission to Pluto provided evidence to make it a dwarf planet.
d. Scientists were biased to make the solar system have ten planets.
7. Scientists publish the details of important experiments so that
a. their work can be repeated.
b. their experimental procedures can be reviewed.
c. others can try to reproduce the results.
d. all of the above
8. Scientists have observed data that shows the average temperature of the Earth has risen
over the past century. However, there is a debate among some scientists if the
temperature rise is caused by human activity or natural climate change. What is the
source of the global warming debate?
a. Errors in the data collection process.
b. Political bias among scientists and their position.
c. Different interpretations of the same data.
d. Failure of some scientists to publish their data.
9. Pellagra is a disease that first appeared in the United States in the 1820s and was known
as the disease of the four Ds: dermatitis, diarrhea, dementia, and death. There was a
debate among scientists if pellagra was caused by poor diet or an infectious agent. Which
of the following evidence supports the fact that pellagra is caused by a poor diet?
a.
b.
c.
d.
Pellagra was common in the South, especially in mental hospitals,
orphanages, and prisons.
Orphans provided with fresh vegetables, meat, and milk recovered
from Pellagra or never got it.
Staff at institutions (such as hospitals, prisons, and orphanages)
did not develop Pellagra.
Both b. and c.
Performance Benchmark N.12.A.3
Students know repeated experimentation allows for statistical analysis and unbiased
conclusions. E/S
Answers to Sample Test Questions
1. (b)
2. (d)
3. (a)
4. (c)
5. (c)
6. (b)
7. (d)
8. (c)
9. (d)
Performance Benchmark N.12.A.3
Students know repeated experimentation allows for statistical analysis and unbiased
conclusions. E/S
Intervention Strategies and Resources
The following list of intervention strategies and resources will facilitate student understanding of
this benchmark.
1. Accuracy vs. Precision, and Error vs. Uncertainity
A comprehensive review of measurement and error from Bellevue Community College.
Scroll down through the text to participate in a practice quiz reviewing these concepts.
To access the tutorial and practice quiz, go to
http://scidiv.bcc.ctc.edu/Physics/Measure&sigfigs/B-Acc-Prec-Unc.html
2. Visualizing Scientific Data: An Essential Component of Research by Visionlearning
This site contains a wealth of information related to both science process and content
standards. Emphasized here is importance of collecting and analyzing data as a fundamental
component of any scientific endeavor. A simple three step procedure helps with reading any
kind of graph. 1. Describe the graph: What does the title say? What is on the x-axis? What is
on the y-axis? What are the units? 2. Describe the data: What is the numerical range of the
data? What kinds of patterns can you see in the data? 3. Interpret the data: How do the
patterns you see in the graph relate to other things you know?
To access the information on data presentation, go to
http://www.visionlearning.com/library/module_viewer.php?mid=109&l=&c3=
3. Scientific Writing: Peer Review and Scientific Journals by Visionlearning
This article outlines the process of peer review, in which scientists evaluate the value and
credibility of research before allowing it to appear in print. Reviewers consider only the
quality of the science before from the materials and methods used in the experiment to the
data collected and the author’s interpretation.
To access this article visit
http://www.visionlearning.com/library/module_viewer.php?mid=123&l=&c3=
4. Measurements and Calculations from Science Help Online for Chemistry
This site has been designed to aid students who are learning Chemistry, by providing them
with additional lessons, worksheets, and review materials. Each of the lessons on this site
were written by Greg Curran, a Chemistry teacher and the author of Homework Helpers:
Chemistry. Most of the support materials were produced by the students of Fordham
Preparatory School. Specific to assisting with this benchmark is Chapter 2: Measurements
and Calculations, and further exploration of the various chapters will provide resources
across the science disciplines.
To access the Accuracy and Precision background and supporting resources follow
http://www.fordhamprep.com/gcurran/sho/sho/lessons/lesson22.htm
To explore the chapters of this online book and its available resources, go to
http://www.fordhamprep.com/gcurran/sho/sho/review/revindex2.htm