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Forfirst
exams2009
International Baccalaureate
PhysicsInternal Assessment
Guide
Kari Eloranta
2013
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CONTENTS
Contents ii
Preface iii
1 Introduction 1
1.1 General Information . . . . . . . . . . . . . . . . . . . . . . 2
2 Design 5
2.1 Design Criterion . . . . . . . . . . . . . . . . . . . . . . . . . 5
Summary of Design Aspect 1 . . . . . . . . . . . . . . . . . . 7
Summary of Design Aspect 2 . . . . . . . . . . . . . . . . . . 7
Summary of Design Aspect 3 . . . . . . . . . . . . . . . . . . 8
3 Guidelines for Data Collection and Processing 11
3.1 Data Collection and Processing (DCP) . . . . . . . . . . . . 11
Summary of DCP Aspect 1 . . . . . . . . . . . . . . . . . . . 12
DCP Aspect 1 Explained . . . . . . . . . . . . . . . . . . . . 12Instrumental Uncertainty . . . . . . . . . . . . . . . . . . . 14
Summary of DCP Aspect 2 . . . . . . . . . . . . . . . . . . . 15
DCP Aspect 2 Explained . . . . . . . . . . . . . . . . . . . . 16
Summary of DCP Aspect 3 . . . . . . . . . . . . . . . . . . . 21
4 Guidelines for Conclusion and Evaluation 25
Conclusion and Evaluation . . . . . . . . . . . . . . . . . . . . . . 25
Summary of CE Aspect 1: Concluding . . . . . . . . . . . 27
CE Aspect 1 Concluding" Explained . . . . . . . . . . . . . 27
Summary of CE Aspect 2: Evaluating procedure(s) . . . . 31
CE Aspect 3: Improving the investigation" . . . . . . . . . 32Summary of CE Aspect 3: Improving the investigation" . 32
CE Aspect 3: Improving the investigation" Explained . . . 32
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PREFACE
This is the first draft of my new "Physics Internal Assessment Guide".
You should use it alongside with the IBOs Physics Guide whenever you
are engaged in practical work.
As this is only the first draft, there will probably be quite many errors,
inconsistencies and omissions in the material. I hope that there are not
too many, so that you find the material useful.I appreciate any feedback and corrections you can offer.
Develop a passion for learning. If you do, you will never
cease to grow.
Anthony J. DAngelo
In Jyvskyl, 1 January 2013
Kari Eloranta
Teacher of Physics
Jyvskyln Lyseon lukio International Baccalaureate
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1INTRODUCTION
This little guide explains the process of internal assessment in physics
in some detail. It serves as your secondary source of information, as you
work on your practicals.
Figure 1.1: Your teacher will be monitoring your performance during the
two year course in physics, and give you a mark on your manipulative
skills ( Dacopeland).
The internal assessment is assessed according to the sets of assess-
ment criteria, and achievement level descriptors. For each criterion,
there are three descriptors that describe your level of achievement. In-
ternal assessment comprises 24% of your final assessment.
1
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2 Introduction
Officially assessed work reports are divided into two groups. Thefirst
is a design practical, where you design a physical experiment at school
during a double lesson, and finalise the work at home. The second is a
combined Data Collection and Processing, and Conclusion and Evalua-
tion practical, where you make the measurements at school, and writethe work report at home.
Note!
The work report must be printed and returned in a week from the
day of a practical. During the week, your teacher can comment on
your work once. When you return your work report, you should take
two copies of your work: one for yourself, and one for the school
archives. No electronic, or late returns will be accepted.
1.1 General Information about Internal As-
sessment Criteria and Aspects
Internal Assessment is criterion-related. It means that you will be as-
sessed in relation to identified assessment criteria, and not in relation to
the work of other students.
Your practical work is assessed according to sets of assessment crite-
ria, and achievement level descriptors in the Physics Guide, First Exams
2009. For each assessment criterion, there are three descriptors that de-scribe your level of achievement. The same internal assessment criteria
are used for both Higher and Standard Level.
Your teacher aims to find, for each criterion, the descriptor that matches
your achievement level most accurately. Each aspect is assessed as c
(complete, 2 marks), p (partial, 1 mark) and n (none at all, 0 marks). To
earn complete in any aspect, your work does not necessarily have to be
perfect. It is enough to reach the level described.
There are five assessment criteria that are used to assess your prac-
tical work in physics:
Design (D),
Data Collection and Processing (DCP),
Conclusion and Evaluation (CE),
Manipulative Skills (MS), and
Personal Skills (PS)
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1.1. General Information 3
Note!
Design, Data Collection and Processing, and Conclusion and Evalu-
ation are each assessed twice. Manipulative Skills is assessed sum-
mativelyover your two year course in physics. Personal skills is as-sessed once only during the group 4 project.
There are three aspects in each of the assessment criteria. The max-
imum mark for each criterion is 32= 6 marks representing three com-pletes. Since the first three criteria are assessed twice, and last two once,
the maximum marks are 263+26= 48.Your teacher assesses your work, and adds your marks together to
to determine the final mark out of 48 for the IA component. The result
is then scaled at IBCA to give a total out of 24% of your total marks in
physics.
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2DESIGN
2.1 Design Criterion
In design, you have to plan a physical measurement and following anal-
ysis from scratch. Design prompts are open-ended tasks, where teacher
gives you very little information. It is a challenging creative process, in
which you have to understand the nature of physical measurement in
detail.
Figure 2.1: Which kind of experiment would you design relating to the
formation of soap bubbles ( Brocken Inaglory)?
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6 Design
There are three aspects in the Design criterion.
Figure 2.2: The Design criteria from the Physics, first exams in 2009
guide ( IBO).
In design, your teacher gives you an open-endedinvestigation. Based
on the teacher prompt, your first task is to devise a proper quantitative
research question. In the question, you have to have an independent
variable that affects the value ofthe dependent variable.
Independent and Dependent Variable
A variable that is manipulated in the experiment is called an inde-
pendent variable. The result of the manipulation leads to the mea-
surement of the dependent variable.
You have to choose from several independent variables that provide
a suitable basis for the experiment. Your teacher is not allowed to tellyou how to select the relevant independent variable, and how to collect
and analyse the data.
Note!
If you need to carry out the designed practical in practise, you
should design an experiment that lends itself to a proper graphi-
cal analysis, where you can draw a line of best fit, and calculate the
associated uncertainties.
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2.1. Design Criterion 7
As we study how the changing value of the independent variable af-
fects the measured value of the dependent variable, we try to keep other
variables constant during the measurement.
Controlled Variable
A controlled variable is one that should be held constant so as not
to obscure the effect of the independent variable on the dependent
variable.
Summary of Design Aspect 1: Defining the Problem and Selecting
Variables
Design Aspect 1 is about stating a research question and recording vari-
ables.
In Design Aspect 1: Recording raw data you should
choose an independent variable.
choose a dependent variable, if it is not included in the
teacher prompt.
list all relevant controlled variables.
state a quantitative research question.
In your work report you need to clearly identify your variables as
the dependent (measured), independent (manipulated or free to roam
(time)), and controlled (constants). A relevant controlled variable is the
one that can reasonably be expected to affect the outcome.
Summary of Design Aspect 2: Controlling Variables
Design Aspect 2 is about designing a method for the effective control of
the variables.
In Design Aspect 2: Controlling Variables you should
explain, how the value of independent variable is manipu-
lated.
explain, how the value of dependent variable is measured.
explain carefully the control of variables.
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8 Design
You should pay special attention to explaining how the control of
variables is achieved. For example, it is not enough to state that the
length of a thread was measured, but also to explain how it was mea-
sured.
If the control of relevant variables is not practically possible, you
should try to monitor the values. For example, if ambient temperature
is relevant to your measurement, but you cannot control the class room
temperature, you should record the temperature in each measurement.
Summary of Design Aspect 3: Developing a Method for Collec-
tion of Data
Design Aspect 3 is about designing a method by which you can have
enough relevant data for graphical analysis.
In Design Aspect 3: Developing a Method for Collection of Data
you should
make repeated measurements, if just possible.
explain, how many measurement points you intend to have.
decide the suitable range of data.
consider boundary conditions.
explain, how the data is manipulated.
explain, how data analysis is carried out including propaga-
tion of error.
What sufficient relevant data constitutes depends on the context.
If you record discrete values, you should have at least five measurement
points. If you measure the dependent variable as a function of time, the
duration of the experiment should be long enough.
If realistic, you should make repeated measurements. For example,
to measure the period of a simple pendulum, it is not enough the mea-
sure the period of one oscillation. Instead, you should measure the time
for a number of oscillations (for example ten), and from that value cal-
culate the time for one oscillation with the associated uncertainty.
The range of data is important. For example, in a pendulum exper-
iment, the thread length could range from 20.0 cm to 170.0 cm in steps
of 30.0 cm. This way the range is large enough, and you collect enough
measurement points (in this case six).
The laws of physics have a limited range in which they can be ap-
plied. That is why you have to often consider the boundary conditions
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2.1. Design Criterion 9
of the experiment. For example, for a simple pendulum, the oscillatory
motion is harmonic only when the release angle is under 10. So, we
measure the period for the constant 10 release angle.
Note!
In design, you should consider the time constraints and other re-
sources as well: the designed investigation should be doable in a
double lesson with the equipment the school has.
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3GUIDELINES FOR DATA COLLECTION
AND PROCESSING
3.1 Data Collection and Processing (DCP)
In Data Collection and Processing (DCP) you have to record and pro-
cess raw data, and present processed data with uncertainties in graphi-
cal form.
Figure 3.1: When position of a cart is measured by the position sensor,
the position is a dependent, and time an independent variable.
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12 Guidelines for Data Collection and Processing
There are three aspects in Data Collection and Processing.
Figure 3.2: The Data collection and processing criteria from the
"Physics, first exams in 2009 guide ( IBO).
Summary of DCP Aspect 1: Recording Raw Data
Data Collection and Processing Aspect 1 is about recording appropriate
quantitative raw data with associated uncertainties.
In DCP Aspect 1: Record raw data you should
record raw data with units and uncertainties in a table.
record enough data in an appropriate range.
round uncertainties to one significant figure.
explain the reasoning behind the uncertainties.
represent measured values and uncertainties with the same
precision.
DCP Aspect 1 Explained
Raw data is the actual data measured. Table 3.1 is an example of how
raw data with uncertainties should be recorded.
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3.1. Data Collection and Processing (DCP) 13
Table 3.1: Raw data in a simple pendulum experiment. l is the length of
thread, and ti time for ten oscillations in trial i.
l/cm
0.5cm t1/s
0.4s t2/s
0.4s t3/s
0.4s
20.1 9.1 9.0 9.3
49.8 13.6 13.9 14.0
80.7 17.6 18.3 18.1
110.1 21.1 20.8 21.3
142.2 23.8 24.0 23.5
169.8 26.2 25.9 26.4
Note!The symbols of quantities, units and uncertainties are recorded in
the first row of the table.
Table 3.2: All data is recorded with units and uncertainties.
l/cm0.5cm t1/s0.4s t2/s0.4s t3/s0.4s
l/cm means that all values of length l are divided by the unit cm. As
a result, you do not repeat the unit in numerical values of a column . All
uncertainties must be rounded to one significant figure.
Note!
You should always record uncertainties, explain the reasoning be-
hind them, and explain, if an uncertainty may be neglected.
For example, it is not enough to say, there is uncertainty in man-
ual timing due to reaction time, but also to estimate the magnitude ofuncertainty (for example, 0.2 s).
Occasionally, an uncertainty is so small that it may be neglected. As
an example, consider a position sensor. Since the device records po-
sition as function of time, and the instrumental uncertainty in time is
0.01 s, the uncertainty in time may be neglected.
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14 Guidelines for Data Collection and Processing
Instrumental Uncertainty
Instrumental uncertainty
The accuracy of a digital device is called the instrumental uncer-tainty.
You will find the instrumental uncertainty of digital measurement
devices from the manual of a device. If a manual is missing, you may
assume that the uncertainty is the precision of the digital device. For ex-
ample, if mass is measured by a digital scale as 76.3 g, you may estimate
the uncertainty as 0.1 g.
Note!
In a physics extended essay the instrumental uncertainty of digitaldevices should always be checked from the manual.
Usually, the instrumental uncertainty of analogue devices must be
estimated. If you are using a graduated scale, the instrumental uncer-
tainty may be estimated as the smallest division in the scale. For exam-
ple, if you measure the height of a box as 7.3 cm by a ruler divided into
millimetres, the instrumental uncertainty is 0.1 cm (the precision of the
instrument).
From the accuracy of a measurement device, the uncertainty in the
measurement can be estimated.
Note!
The uncertainties in data are recorded on the first row of a table.
Note!
A common mistake is to record values with greater precision than
uncertainty.
For example, time is wrongly recorded as 5.12 s, when uncertainty in
manual timing is 0.2s. Instead, the time should be rounded to tenthsof a second to match the precision of the uncertainty ((5.10.2) s).
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3.1. Data Collection and Processing (DCP) 15
Table 3.3: In each column, the precision of data is constant, and matches
the precision of uncertainty.
l/cm0.5cm20.1
49.8
80.7
110.1
142.2
169.8
l/cm0.5cm20.1
49.8
80.7
110.1
142.2
169.8
t1/s0.4s9.1
13.6
17.6
21.1
23.8
26.2
t1/s0.4s9.1
13.6
17.6
21.1
23.8
26.2
Summary of DCP Aspect 2: Processing Raw Data
In DCP Aspect 2: Processing raw data you should
represent processed data and propagated uncertainties with
units in a table.
round propagated uncertainties to one significant figure.
represent processed values and propagated uncertainties
with the same precision.
draw the best fit line
calculate the slope of the best fit line
represent the equation of the best fit line
To meet the criteria in Data Collection and Processing Aspect 2, you
need to process the raw data correctly. This includes all arithmetic oper-
ations, transforming data into a form suitable for graphical representa-
tion, constructing the coordinate axes, plotting the data, and determin-
ing the best fit line and its slope.
If the dependent variable should be directly proportional to the in-
dependent variable, you have to plot the data on a proper coordinate
system, draw the line of best fit, and calculate the slope of the line. Then,
the raw data has been processed.
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16 Guidelines for Data Collection and Processing
Note!
Processing the raw data without a graph line does not earn com-
plete in Aspect 2.
In many cases, especially at Higher Level, the raw data is not linear.
In such a case the processing of raw data includes also the linearisation
of data. Then, you plot the processed data, draw the line of best fit, and
calculate the slope of the line for the linearised data.
DCP Aspect 2 Explained
In a repeated experiment we have to calculate the average of measure-
ment values. In Internal Assessment, you are allowed to use a simple
method of finding the uncertainty in the average.
Uncertainty in the Average
The uncertainty in the average is
x= xmax xmin2
(3.1)
where xmax is the maximum and xmin the minimum value in the
sample.
This method of calculating the uncertainty in the average exagger-
ates the uncertainty a little. If you want to use a more scientific method,
you can use the standard error of the mean.
Standard Error of the Mean
The standard error of the mean is defined as
= sN
(3.2)
where sisthe standard deviation of the sample and N is the number
of measurements.
You should calculate the standard deviation with a calculator, or us-
ing a spreadsheet. Refer to the Users Manual for detailed instructions of
how to do it.
Note!
Use of Standard Error of the Mean is compulsory in Physics Ex-
tended Essays.
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3.1. Data Collection and Processing (DCP) 17
Linearisation of Data
Typically, we want to have a linear relationship between the variables to
be able to draw a line of best fit.
Note!
If data is not linear, we need to linearise it for graphical analysis, and
propagate uncertainties.
As an example, consider the equation of the period T of simple pen-
dulum.
Period T of Simple Pendulum
The period of simple pendulum is
T= 2
l
g(3.3)
where l is the length of the cord, and g is the acceleration due to
gravity.
As you can see, period T is proportional to the square root of length
l. Since period T is not directly proportional to length l of the pendu-
lum, we have to linearise Equation 3.3 by a variable interchange.
Squaring both sides of Equation 3.3 gives
T2 = 42
gl (3.4)
which is an equation of a straight line in a (l, T2) coordinate system
whose slope is m= 42g
. So, for linearisation, we have to calculate the
square of the period T2, mark the measurement points to a (l, T2) coor-
dinate system, and draw a line of best fit for the processed data.
Because we calculated the square of the period, we need to prop-
agate uncertainties. Because in multiplication fractional uncertaintiesadd, the fractional uncertainty in the period squared T2 is 2 T
T.
Graphing
After having processed the raw data, you have to use a regression tool,
such as Logger Pro, for graphical analysis. In the simple pendulum ex-
periment the uncertainty in the measurement of length is negligible. As
a result, only vertical error bars are drawn.
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3.1. Data Collection and Processing (DCP) 19
0
1
2
3
4
5
6
7
20 40 60 80 100 120 140 160 180
l
cm
T2s2
T2 = 0.041l0.055
Figure 3.4: The period squared T2 as a function of lenght l.
Note!
You have to state the equation of the best line. If the dependent vari-
able should be directly proportional to the independent variable,
the y-intercept is a measure of a systematic error in the experiment.
The equation of the best fit line is T2 = 0.041l0.055, where the y-intercept is b=0.055s2. The value is so small that it might be a resultof the mathematical algorithm of the spreadsheet program used, rather
than an indication of a systematic error in the experiment.
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20 Guidelines for Data Collection and Processing
Outliers
Occasionally, a point with error bars may not fall on a line even if it
should. Such a point is called an outlier. In your work report, you have
to consider all outliers, and act accordingly.
Typical reasons for outliers include
You have underestimated uncertainties. In this case you
have to correct the uncertainties, and repeat the process with
longer error bars.
Real physical behaviour. For example, you have exceeded
the range in which linear model is valid. Such points should
not be included in the linear fit.
An error in measurement has occurred. For example, a valueis not recorded correctly, or a malfunction of a device has oc-
curred. Such a point may be left out of the process.
You have mistyped a data point. If the correct value is known,
retype the point, or leave it out.
In all cases, you have to clearly explain your reasoning in the treat-
ment of the outlier. If you decide to leave a point out, you have to make
sure you have enough data left. In the graph above, the best fit line goes
through the error bars, and no further action is needed.
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3.1. Data Collection and Processing (DCP) 21
Summary of DCP Aspect 3: Presenting Processed Data
Aspect 3 is about presenting the processed data appropriately including
units and uncertainties. To achieve complete in DCP Aspect 3, you need
to
In DCP Aspect 3: Presenting processed data you should
determine appropriate scales for the graphs.
mark the measurement points with error bars when the error
bars are not negligible.
explain where uncertainties are not significant.
draw the minimum fit line and maximum fit line.
represent the equation of the minimum andmaximum fit line
clearly in context with the lines.
label the axes with units appropriately.
label the tables, diagrams and graphs and add captions to
them.
represent processed values and (propagated) uncertainties
with the same precision.
Minimum and Maximum Fit Lines
To find the uncertainties in the slope, you have to draw a minimum and
maximum fit line. The process should be carried out manually in the
data processing software used.
Note!
To draw a minimum and maximum fit line, you may use only the
first and last measurement points.
The minimum fit line gives the minimum value of the slope.
It goes through the highest error bar point of the first value,
and through the lowest error bar point of the last value.
The maximum fit line gives themaximum value of theslope.
It goes through the lowest error bar point of the first value,
and through the highest error bar point of the last value.
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22 Guidelines for Data Collection and Processing
Here are the minimum and maximum fit lines for our example data.
0
1
2
3
4
5
6
7
20 40 60 80 100 120 140 160 180
l
cm
T2s2
Max
fit: T
2 =0.0
42l
0.060
Min
fit: T
2 =0.0
39l
0.08
Figure 3.5: The minimum (green) and maximum (red) fit lines in the
simple pendulum experiment.
0
1
2
3
4
5
6
7
20 40 60 80 100 120 140 160 180
l
cm
T2s2
Max
fit: T
2 =0.0
42l
0.060
Min
fit: T
2 =0.0
39l
0.08
Figure 3.6: First and last points with error bars magnified. Red line is the
maximum fit, and green the minimum fit line.
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3.1. Data Collection and Processing (DCP) 23
Uncertainty in the Final Result
Once you have drawn the lines, you calculate the uncertainty in the
slope of the best fit line.
Uncertainty in the slope of the best fit line
The uncertainty in the slope of the best fit line is
mbest =mmaxmmin
2(3.5)
where mmaxis the slope of the maximum fit line, and mmin the slope
of the minimum fit line.
The uncertainty in the best fit line of the simple pendulum experi-
ment becomes
mbest=mmaxmmin
2
= 0.0422s2 cm10.0390s2 cm1
2
0.002s2 cm1
If the slope is used in the calculation of the final result, we have to
propagate the uncertainty to the final result as well. The slope of the
best fit line in the simple pendulum experiment is
mbest = 4
2
g (3.6)
from where it follows that the acceleration due to gravity is
g= 42
mbest= 4
2
0.041s2 cm1 9.6ms2. (3.7)
The uncertainty in the acceleration due to gravity is
g= mbestmbest
g= 0.002s2 cm1
0.041s2 cm19.629ms2 0.5ms2. (3.8)
Thus, according to the data acquired in the simple pendulum exper-iment, the acceleration due to gravity is
g= (9.60.5)ms2
Data collection and processing is a relatively straightforward pro-
cess, and you should have little difficulty in learning the skills needed
to achieve high marks in it.
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4GUIDELINES FOR CONCLUSION AND
EVALUATION
Conclusion and Evaluation
In Conclusion and evaluation you have to state a conclusion, evaluate
weaknesses and limitations in the experiment, and suggest improve-
ments.
Figure 4.1: Students in Ouagadougou, Burkina Faso, discussing physics.
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26 Guidelines for Conclusion and Evaluation
In writing Conclusion and evaluation, you should divide your text
into clear paragraphs for fluent communication. In order to be able
to write good conclusion and evaluation, you need to understand the
physics of the experiment, and the main principles of experimental re-
search.There is no single way of writing proper conclusion and evaluation.
In these instructions we propose a way of dividing your text into clearly
organised paragraphs. This way, conclusions and evaluations are easier
to read. It is also easier for you to make sure that you have considered
all necessary factors.
There are three aspects in Conclusion and evaluation.
Figure 4.2: The Conclusion and evaluation criteria from the "Physics,
first exams in 2009 guide ( IBO).
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Conclusion and Evaluation 27
Summary of CE Aspect 1: Concluding
Conclusion and evaluation criteria Aspect 1 is about stating a justified
conclusion with uncertainties, and analysing the reliability of data.
In CE Aspect 1: Concluding you should
Restate the final result with the associated uncertainty.
State the fractional uncertainty from the processed data.
Comment on the accuracy of the result.
Compare the result with the text book or literature value (if
applicable).
Fully reference the literature consulted (if applicable).
Discuss the linearity of data (if applicable).
State the systematic error with units and its direction (if ap-
plicable).
Discuss the random errors encountered.
Discuss observations, trends and patterns revealed by the
data.
CE Aspect 1 Concluding" Explained
Step 1: Stating the result
In the first paragraph of conclusion and evaluation you restate the ex-
perimental result with the associated uncertainty, and compare it with a
fully referenced literature value.
In my experiment, the value for the acceleration due to gravity was
found to be
g= (9.60.5)ms2 (4.1)The accepted value in Jyvskyl1 being g = 9.82ms2. The frac-tional uncertainty is 5%.
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28 Guidelines for Conclusion and Evaluation
In comparing your result with the reference value you should:
state the absolute or fractional difference between the values.
consider the uncertainty in the reference value (if applicable).
check, does the probable range of the experimental value
overlap include the reference value.
check, if the reference value has an associated uncertainty,
does the probable range of the experimental value overlap the
probable range of the reference value.
According to the IBO, a percentage error should be compared with
the total estimated random error as derived from the propagation of un-certainties.
In the absence of a reference value, you should comment on the reli-
ability of the result, based on how accurate the measurements were, and
how reliable the process was in the experiment.
Step 2: Analysing the graphs
In analysing the graphs, your first task is to comment on the observed
trends, such as linearity of the data.
You should check from the graph:
do the measurement points fall on a line?
does the line go through all error bars?
is there any indication of a systematic error?
are there any outliers?
is there anything else worth noting?
If the measurement points fall very nearly on a line, the associated
random errors are small. If the points deviate from the line clearly, but
the line nevertheless goes through the error bars, the data is consistent
with the line.
Note!
If the graph is a straight line where the line goes through all the error
bars, you should state that the data is linear.
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Conclusion and Evaluation 29
If the data does not follow the expected trend, reasons for it need
to be considered. The most common case is the one, where the data is
expected to be linear, but it is not.
Typical reasons for non-linear data include
The data should not be linear in the first place. For example,
in uniformly accelerated motion, the distance travelled h is
proportional to the time t squared (h= 12
at2 where a is the
acceleration).
The changes in ambient or internal physical conditions has
affected the results. For example, the electric current I in a
conductor is not directly proportional to the potential differ-
ence V across the component, because of the increasing tem-
perature of the component (non-ohmic behaviour).
The range of the linear model has been exceeded. For ex-
ample, the spring force F is not directly proportional to the
displacement x from the equilibrium position, because the
string has been stretched beyond its linear range (Hookes law
F=k x). Or air resistance opposes motion so much that thefalling object is not in a free fall anymore.
The physics of the experiment has been misunderstood. For
example, in a falling ball experiment the falling height should
be directly proportional to the final speed squared, not just
final speed.
If your data is not linear, you should goback to DCP and check, if it is
possible to linearise the data, and does it make sense to do so. If not, you
should try to find and analyse the reasons for the non-linear behaviour.
If there are any outliers, you need to ponder upon the reasons for
them. The instructions for the treatment of outliers are in Section 3.1.
Systematic error in a linear graph
If the dependent variable should be directly proportional to the inde-
pendent variable, the best fit line should go through the origin. Usually,
however, the line does not go through the origin exactly, indicating a
systematic error in the data.
Note!
You should state the systematic error in the data with units, and try
to find out the reason for it.
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30 Guidelines for Conclusion and Evaluation
Systematic errors are most often caused by:
by the software algorithm in a linear fit.
systematic misuse of a measurement device. For example, azero-offset error in a scale.
systematic misreading of a scale. For example, reading a
thermometer at an angle, measuring volumes in a graduated
cylinder at an angle, and misreading a scale in a multimeter.
Forgetting to add or subtract a fixed value from measure-
ment results. For example, forget to add atmospheric pres-
sure to overpressure values in using gas laws, and not to sub-
tract background radiation in studying the activity of a ra-
dioactive sample.
A small deviation from the origin is most often caused by the algo-
rithm the measurement software uses. In this case you should clearly
state that the systematic error is most probably caused by the algorithm
of the measurement software.
If the systematic error cannot be accounted for bysoftware, you must
try to find a reason for it. Systematic errors are sometimes hard to detect.
Note!
Remember that a repeated experiment does not reduce the effect ofa systematic error unless the source of the error is removed.
Random errors
In the conclusion you should also comment on the random errors en-
countered. You should pay special attention to unexpected random er-
rors in the data, such as random errors caused by fluctuating reading
in a multimeter. A more detailed analysis of random errors goes to the
Aspect 2: Evaluating procedure(s)".
According to physics syllabus, conclusions that are supported by the
data can be acceptable even if they appear to contradict accepted theo-
ries. In such a case, however, you have to be extremely careful, and dou-
ble check you work to verify that you have not just missed something
obvious.
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Conclusion and Evaluation 31
Summary of CE Aspect 2: Evaluating procedure(s)
Conclusion and Evaluation criteria Aspect 2 is about evaluating the strengths
and weaknesses of the experiment.
In CE Aspect 2: Evaluating procedure(s) you should
Comment on the overall quality of the process.
Identify weaknesses and limitations in the process.
Go through the sources of uncertainty in the decreasing order
of importance.
Discuss all sources of uncertainty that affect the accuracy of
the measurement.
Discuss the method of measurement in detail, and identify all
relevant weaknesses.
Appreciate whether the limitations cause a systematic or ran-
dom uncertainty.
First, you should comment on overall quality of the experimental
procedure, and data collected.
Was the experiment suitable for its intended purpose?
What were the major limitations in the experiment.
You should go through the significant weaknesses, limitations, and
sources of uncertainty in the process in decreasing order of importance.
In the first paragraph in evaluating the procedures, you analyse the ma-
jor weakness in the experiment. In the second paragraph the second
most important weakness and so on.
In analysing weaknesses you should consider the equipment and
time management well, such as instrumental uncertainty, and did the
equipment fit well with the experiment. If time management affected
your measurements, you should comment on that as well.
It is important that you show some appreciation of the significance
of each weakness and source of uncertainty. You must also have some
appreciation of whether each factor would cause a systematic or a ran-
dom uncertainty.
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32 Guidelines for Conclusion and Evaluation
CE Aspect 3: Improving the investigation"
In Conclusion and evaluation Aspect 3 you have to suggest realistic im-
provements in respect of identified weaknesses and limitations. This
includes the description of how the experimental procedure could beimproved for better accuracy of the experimental result.
Summary of CE Aspect 3: Improving the investigation"
In CE Aspect 3: Improving the investigation" you should
Address the weaknesses and limitations identified in CE As-
pect 2.
Suggest realistic improvements.
Suggest exactly what should be done to reduce random un-
certainties.
Suggest exactlywhat should be done to reduce systematic un-
certainties
CE Aspect 3: Improving the investigation" Explained
The ways of improving the weaknesses and limitations identified in
Aspect 2 include
Improving the accuracy of the measurement by using more
accurate instruments. For example, using a more accurate
multimeter or scale.
Improving the external and internal physical factors relat-
ing to the accuracy of the experiment. For example, in mea-
suring the thermal capacity of an object, insulating the sys-
tem better from its surroundings to reduce thermal energy
losses to the surroundings.
Improving the measurement process. For example, change
the measurement location from outdoors to indoors to elim-
inate the effect of wind.
An easy way of improving the accuracy of a measurement is to use
more accurate instruments. Ideally, you should suggests instruments
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Conclusion and Evaluation 33
that are available at your school. As an example, consider a case, where
the position of a rolling ball on the floor was measured as a function of
time by using manual timing and 5 metres long tape measure. Using a
position sensor instead would improve both the accuracy of the mea-
surement of time, and the accuracy of the measurement of position.It is always best the state exactly which instrument you would use,
and how much it would improve the accuracy of the measured quantity.
To improve the accuracy of the measurement of time
and position, I would use Vernier Motion Detector 2
http://www.vernier.com/files/manuals/md-btd.pdf . As a re-
sult, the instrumental uncertainty in time would be reduced to
t=0.01s, and that of position tos=0.001m.
You may use the Internet in finding information about the instru-
ments. For example, you find information about Vernier accessories at
http://www.vernier.com/support/manuals/ .
Improving the external and internal physical factors relating to the
accuracy of the experiment is not always easy. For example, many physics
experiments are carried out in ordinary classroom conditions. When
many people work at the same time in the class, the class room tem-
perature tends to rise. As a result, it is difficult to control the class room
temperature. Or, to eliminate the effect of air resistance, it would be nice
to perform an experiment in a vacuum. But that would be impossible in
most practical cases.
Improving the measurement process is most often relevant, when
as a result of the measurement process, uncertainties are exceptionally
high. For example, the uncertainty is away too high, if you measure the
falling time manually. Once again, using a position sensor reduces the
uncertainty to the minimum. Or if you want to measure the resistivity of
the material a twisted wire is made of, you can improve the uncertainty
in measuring the length by using a straighter wire.
http://www.vernier.com/files/manuals/md-btd.pdfhttp://www.vernier.com/files/manuals/md-btd.pdfhttp://www.vernier.com/support/manuals/http://www.vernier.com/support/manuals/http://www.vernier.com/support/manuals/http://www.vernier.com/files/manuals/md-btd.pdf