Lab Report Grading Ru
ic
Grading Criteria
Objective
The objective should be concise and should not go into detail regarding the
ackground theory or include any equations.
Clearly states the scientific concept tested and key parameters being
measured in the student’s own words.
Data
Relevant data tables and graphs included.
Units included everywhere and significant figures paid attention to.
Analysis and regression methods discussed.
Sample calculations included. Student’s alge
a shown where appropriate.
Analysis
Well-motivated responses to observational and comprehension questions.
Exceptional synthesis of material across the parts of the lab and interpretation
going beyond the lab manual questions.
E
or
Reasonable estimates for uncertainties used for each measurement. Every measurement
has an e
or included.
Co
ect e
or calculations are shown, i.e. the e
or propagation is co
ect.
Sources of e
or in the experimental process identified and effects on results shown.
Conclusion
Should be concise, respond to experimental objectives, and expand on it.
Summarizes all key results (with numbers where necessary) and discusses major problems
encountered (if any).
Organization
Clarity and coherence. The lab report should be neat, concise, coherent, clear
and complete.
The lab report has max 3 pages, excluding figures, graphs, tables, objectives, etc. Has
co
ect formatting (font size min 12, double spaced)
Presentation
Sections, graphs, equations, tables, and any relevant items should be properly
labelled and/or numbered.
Introduction to Labs and Uncertainty
1. Introduction
There is no such thing as a perfect measurement. All measurements have e
ors and
uncertainties, no matter how hard we might try to minimize them. Understanding
possible e
ors is an important issue in any experimental science. The conclusions we
draw from the data, and especially the strength of those conclusions, will depend on
how well we control the uncertainties.
Let’s consider an example: You’re trying to measure something and from theory,
you know the expected value should be 2.3. You make two measurements and get two
very different values: 2.5 and 1.5. We can see immediately that 2.5 is rather close
to the expected value while 1.5 is quite far off. However, we have not taken e
o
into account. Each measurement has a certain amount of uncertainty, or wiggle room.
Basically, there’s an interval su
ounding your measurement where the true value is
expected to lie. If your measurements give experimental uncertainties of 0.1 and 1.0
espectively, the new measured values may be expressed 2.5 ± 0.1 and 1.5 ± 1.0. The
expected value falls within the range of the second measurement, but not the first!
Analyzing data and e
or in experiments is essential in making conclusions about
the physical laws we are testing. The advent of computers and software made to
manipulate large data sets has revolutionized scientist’s ability to make conclusions
from experimental data. In this lab course, we will be using Microsoft Excel to record
data sets from the experiments and determine experimental uncertainties in calculated
quantities. We will learn to use excel to propagate uncertainties and plot e
or bars
with our data. You can download a personal copy of Microsoft Excel with your student
email address from Office 365 Education 1. Please note the sections introducing new
Excel tools pertain to the newest version of Excel. If you are using a personal laptop
with a different version of Excel, you are responsible for adapting the instructions to
your version of Excel.
The purpose of this introduction is to give some basic information about statistics
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1
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Introduction to Labs and Uncertainty
and uncertainty. The techniques studied here will be essential for the rest of this two-
semester lab course. These tools are important in order to a
ive at good judgments
in any field (like medicine) in which it is necessary to understand not just numerical
esults, but the uncertainties associated with those results.
2. Theory
2.1 Types of Uncertainties
Uncertainty in a measurement can arise from three possible origins: the measuring
device, the procedure of how you measure, and the observed quantity itself. Usually
the largest of these will determine the uncertainty in your data.
Uncertainties can be divided into two different types: systematic uncertainties and
andom (statistical) uncertainties2.
Systematic Uncertainties
Systematic uncertainties or systematic e
ors always bias results in one specific direc-
tion. They will cause your measurement to consistently be higher or lower than the
accepted value.
An example of a systematic e
or follows. Assume you want to measure the length
of a table in cm using a meter stick. However, the stick is made of metal that has
contracted due to the temperature in the room, so that it is less than one meter long.
Therefore, all the intervals on the stick are smaller than they should be. Your numerical
value for the length of the table will then always be larger than its actual length no
matter how often or how carefully you measure. Another example might be measuring
temperature using a mercury thermometer in which a bu
le is present in the mercury
column.
Systematic e
ors are usually due to imperfections in the equipment, imprope
or biased observation, or the presence of additional physical effects not taken into
account. (An example might be an experiment on forces and acceleration in which
there is friction in the setup and it is not taken into account!)
In performing experiments, try to estimate the effects of as many systematic e
ors
as you can, and then remove or co
ect for the most important. By being aware of
the sources of systematic e
or beforehand, it is often possible to perform experiments
with sufficient care to compensate for weaknesses in the equipment.
2If you were to engage in further research, random uncertainty is typically refe
ed to as statistical
uncertainty.
2
Introduction to Labs and Uncertainty
Random Uncertainties
In contrast to systematic uncertainties, random uncertainties are an unavoidable result
of measurement, no matter how well designed and cali
ated the tools you are using.
Whenever more than one measurement is taken, the values obtained will not be equal
ut will exhibit a spread around a mean value, which is considered the most reliable
measurement. That spread is known as the random uncertainty. Random uncertainties
are unbiased – meaning it is equally likely that an individual measurement is too high
or too low.
From your everyday experience you might be thinking, “Stop! Whenever I measure
the length of a table with a meter stick I get exactly the same value no matter how
often I measure it!” This may happen if your meter stick is insensitive to random
measurements, because you use a coarse scale (like mm) and you always read the
length to the nearest mm. But if you would use a meter stick with a finer scale, or if
you interpolate to fractions of a millimeter, you would definitely see the spread. As a
general rule, if you do not get a spread in values, you can improve your measurements
y using a finer scale or by interpolating between the finest scale marks on the ruler.
How can one reduce the effect of random uncertainties? Consider the following
example. Ten people measure the time of a sprinter using stopwatches. It is very
unlikely that each of the ten stopwatches will show exactly the same result. Even if
all of the people started their watches at exactly the same time (unlikely) some of
the people will have stopped the watch early, and others may have done so late. You
will observe a spread in the results. If you average the times obtained by all ten stop
watches, the mean value will be a better estimate of the true value than any individual
measurement, since the uncertainty we are describing is random, the effects of the
people who stop early will compensate for those who stop late. In general, making
multiple measurements and averaging can reduce the effect of random uncertainty.
Remark : We usually specify any measurement by including an estimate of the
andom uncertainty. (Since the random uncertainty is unbiased we note it with a ±
sign). So if we measure a time of 7.6 seconds, but we expect a spread of about 0.2
seconds, we write as a result:
t = (7.6± 0.2) s (1)
indicating that the uncertainty of this measurement is 0.2 s or about 3%.
2.2 Accuracy and Precision
An important distinction in physics is the difference between the accuracy and the
precision of a measurement. Accuracy refers to the closeness of a measured value to
a standard or known value. For example, if in lab you obtain a weight measurement
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Introduction to Labs and Uncertainty
of 3.2 kg for a given substance, but the actual or known weight is 10 kg, then you
measurement is not accurate. In this case, your measurement is not close to the known
value.
Precision refers to the closeness of two or more measurements to each other. Using
the example above, if you weigh a given substance five times, and get 3.2 kg each time,
then your measurement is very precise. Precision is independent of accuracy. You
can be very precise but inaccurate, as described above. You can also be accurate but
imprecise.
For example, if on average, your measurements for a given substance are close to the
known value, but the measurements are far from each other, then you have accuracy
without precision.
A good analogy for understanding accuracy and precision is to imagine a basketball
player shooting baskets. If the player shoots with accuracy, his aim will always take
the ball close to or into the basket. If the player shoots with precision, his aim will
always take the ball to the same location which may or may not be close to the basket.
A good player will be both accurate and precise by shooting the ball the same way
each time and each time making it in the basket.
2.3 Numerical Estimates of Uncertainties
For this laboratory, we will estimate uncertainties with three approximation techniques,
which we describe below. You should note which technique you are using in a particula
experiment.
Upper Bound (Analog)
Most of our measuring devices in this lab have scales that are coarser than the ability
of our eyes to measure.
Figure 1: Measuring Length
For example in the figure above, where we are measuring the length of an object
against a meter stick marked in cm, we can definitely say that our result is somewhere
etween 46.4 cm and 46.6 cm. We assume as an upper bound of our uncertainty, an
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Introduction to Labs and Uncertainty
amount equal to half this width (in