CE 304 Calibration Curve Report I uploaded the lab data and lab lecture read them to know everything about the experiment. Also I uploaded the Technical Wr

CE 304 Calibration Curve Report I uploaded the lab data and lab lecture read them to know everything about the experiment. Also I uploaded the Technical Writing for the report you MUST follow the steps in the technical writing to know exactly how to write the report. Spectrophotometer
Wavelength
Total # of test
Group A
Group B
Colorimeter
Wavelength
Total # of test
500 nm
24
Conc. (mg/L)
100
100
100
250
250
250
500
500
500
1000
1000
1000
100
100
100
250
250
250
500
500
500
1000
1000
1000
Abs
0.211
0.217
0.218
0.562
0.569
0.576
1.172
1.177
1.175
2.134
2.142
2.144
0.228
0.226
0.223
0.567
0.568
0.575
1.161
1.183
1.183
2.148
2.180
2.181
Group A
Group B
Unknown Sample
Total # of test
520 nm
24
Conc. (mg/L)
100
100
100
250
250
250
500
500
500
1000
1000
1000
100
100
100
250
250
250
500
500
500
1000
1000
1000
Abs
0.182
0.182
0.183
0.516
0.515
0.518
1.049
1.058
1.055
1.929
1.962
1.972
0.186
0.185
0.185
0.518
0.518
0.519
1.057
1.059
1.057
1.975
1.979
1.974
6
Group A, B
1
2
3
4
5
6
Average =
Abs at
500 nm
520 nm
0.873
0.817
0.876
0.821
0.874
0.820
0.918
0.826
0.919
0.825
0.919
0.827
0.897
0.823
1. Run the regresion analysis according to
tests) from each equipment.
2. Report the required values such as slope
(refer the lecture slide examples)
3. The significant digits: use the scientific e
hundredth digits for most of the factors in
value can be down to thousandth digits.
4. See the plotting example (in the next sp
value can be down to thousandth digits.
4. See the plotting example (in the next sp
to plot the calibration curve equation line
1. Convert the Abs. from each test with
the calibration curve equation.
2. Take the average of the
concentration values and calculate the
standard deviation. Report the
averagred concentration with standard
analysis according to the results (24
uipment.
ed values such as slope, intercepts… etcs.
de examples)
gits: use the scientific expression to
r most of the factors in this lab report. R^2
to thousandth digits.
example (in the next spreadsheet) for how
to thousandth digits.
example (in the next spreadsheet) for how
on curve equation line with the
Spectrophotometer
Wavelength
Total # of test
Group C
Colorimeter
Wavelength
Total # of test
500 nm
12
Conc. (mg/L)
100
100
100
250
250
250
500
500
500
1000
1000
1000
Abs
0.224
0.227
0.224
0.567
0.575
0.572
1.178
1.176
1.176
2.183
2.181
2.183
Group C
Unknown Sample
Total # of test
520 nm
12
Conc. (mg/L)
100
100
100
250
250
250
500
500
500
1000
1000
1000
Abs
0.175
0.171
0.170
0.500
0.501
0.499
1.036
1.036
1.034
1.943
1.950
1.949
6
Group C
1
2
3
Average =
Abs at
500 nm
520 nm
0.920
0.806
0.918
0.805
0.919
0.806
0.919
0.806
1. Run the regresion analysis according to the
from each equipment.
2. Report the required values such as slope, int
(refer the lecture slide examples)
3. The significant digits: use the scientific expre
hundredth digits for most of the factors in this
value can be down to thousandth digits.
4. See the plotting example (in the next sprea
to plot the calibration curve equation line with
1. Convert the Abs. from each test with
alysis according to the results (12 tests)
values such as slope, intercepts… etcs.
examples)
use the scientific expression to
ost of the factors in this lab report. R^2
housandth digits.
(in the next spreadsheet) for how
urve equation line with the
Example only
Copper metal calibration curve
Conc. (mg/L)
100
100
200
200
400
400
800
800
Abs.
0.103
0.107
0.235
0.228
0.467
0.462
0.935
0.941
From above Table, we can plot a scatter plot as shown on the right.
If after regressional analysis, we obtained the intercept and slope values as the following,
Intercept
X Variable 1 (slope)
-9.870E-03
1.186E-03
we can use them to plot the calibration curve with this equation
Y (Abs.) = slope*X(Conc.)+intercept.
With given any value of X (it should be in the range of the experimental concentrations), then we can c
X
Conc. (mg/L)
100
125
150
175
200
225
250
275
300
325
350
400
450
Y
Abs.
0.109
0.138
0.168
0.198
0.227
0.257
0.287
0.316
0.346
0.375
0.405
0.464
0.524
With the Table on the left, we can add
500
550
600
650
700
750
800
0.583
0.642
0.702
0.761
0.820
0.879
0.939
Copper calbiration curve
1
0.9
0.8
0.7
Abs.
0.6
0.5
0.4
0.3
0.2
Exp. data
0.1
0
0
200
400
600
Concentration (mg/L)
Copper calbiration curve
1
0.9
Exp. data
0.8
Calibration Curve
0.7
Abs.
0.6
0.5
0.4
0.3
800
1000
0.3
0.2
0.1
0
0
200
400
600
Concentration (mg/L)
800
1000
Lab 1 Calibration Curve and
Linear Regression Analysis
CE 304 Spring 2019
Dr. Kevin Wang
1
Outline
•
•
•
•
•
Introduction
Objectives
Equipments
Experimental Procedures
Data Analysis
– Regression analysis
– Confidence Interval
2
Introduction
The Water Cycle
3
Monitor how a fluid is transported
Groundwater Tracing
Measuring Flows in Open
Channels
http://www.openchannelflow.com/blog/article/methods-ofmeasuring-flows-in-open-channels
http://www.globalunderwaterexplorers.org/node/798
Know the residence time, flow velocities
4
How to do measurement?
• Take a series of things
whose values are known
and compare them to the
thing with the value you
want to know
• The unknown must be
within range of the
measuring device you are
using
Example
• Weight
• Length
How do we measure tracer dye?
5
Beer-Lambert Law (Beer’s Law)
A
T
I0
I
The complementary
color of the solution
(observed)
yellowish-green
yellow
organge
red
purple
violet
blue
greenish-blue
bluish-green
The transmitted The wavelength (nm) of ε
color of the
the transmitted color of
c
solution (I)
the solution
violet
400-435
d
blue
435-480
greenish-blue
480-490
bluish-green
490-500
greenish-blue
500-560
yellowish-green
560-580
yellow
580-595
organge
595-610
red
610-750
Absorption
Transmission T = I⁄I0
Intensity of the light going to the flow cell
Intensity of the light that has passed the
flow cell
extinction coefficient: how strong does a
specific substance absorb light?
concentration of the substance
length of the beam path through the cell,
cell length
http://chemistry.tutorvista.com/inorganicchemistry/concentration-of-a-solution.html
http://www.teamcag.com/support/theory/chroma/hplc_bas_at/detectors/detectio
nPrinciple.html
6
Objectives
• Develop a statistically significant calibration
curve for both a spectrophotometer and a
colorimeter to measure concentrations of a
tracer dye for use in contaminant transport
studies.
7
Equipments
Hach DR900 Colorimeter
Wavelengths: 420, 520, 560 and 610 nm
Hach DR4000-UV
Spectrophotometer
Ultraviolet and Visible spectrum
wavelength: 190 to 1100 nm.
(500 nm)
www.hach.com
http://img.medicalexpo.com/images_me/photog/84321-10100225.jpg
8
Experimental Procedures
•
•
•
•
•
http://chemistry.tutorvista.com/inorganicchemistry/concentration-of-a-solution.html
Blank solution: tap water
Standard solutions :
100, 250, 500 and 1000 mg/L
Set up the wavelength value, Calibrate
(zero) the equipment
Measure the Abs. of each concentration
(triplicates)
Measure the Abs of unknown sample
(triplicates)
Absorption spectrum of the red dye
9
Abs = m C(mg/L) + K
For many analytical
techniques, we need to
evaluate the response of
the unknown sample
against a set of standards
(known quantities).
10
Linear regression
• The coefficient of determination, R², which indicates the
percentage of variance in the dependent variable that is
accounted by variability in the independent variable
• The regression equation is the formula for the trend or fit
line which enables us to predict the dependent variable (y)
for any given value of the independent variable (x)
• The regression equation has two parts – the intercept and
the slope
• The intercept is the point on the vertical axis where the
regression line crosses.
• The slope is the change in the dependent variable for a one unit
change in the independent variable. The slope tells us the
direction and magnitude of change.
11
Regression Analysis
Dependent variable (Y)
The basic regression line concept,
DATA = FIT + RESIDUAL
Residuals
Y = mX + b
Independent variable (X)
To be precise, standard deviation is used
to represent the “error”
• Determine the the value
of m, b and their
uncertainties.
• The uncertainty (error) of
the regression, that is
Ypredict-Yexp is the function of
X*m + b
• From the regression error,
the error due to the “m”
and “b” can be further
calculated.
http://www.chem.utoronto.ca/coursenotes/analsci/stats/ErrRegr.html#errint
12
What can we do with the “error”?
13
Confidence Interval (CI)
• A 99% confidence
interval is a range of
values that you can be
99% certain contains
the true mean of the
population.
• If 99%confidence
interval contains zero,
then the effect will not
be significant at the
0.01 level.
14
Data Analysis (I)
• Use the Regression function (under Tools, Data Analysis menu
of Excel) to generate the output tables and determine the
regression equation for absorbance as a function of
concentration (these tables should be included in the
appendix of the report, but only a summary table of the
relevant information should be provided in the results section
of the main report).
• Examine the regression output table to determine whether
the intercept is significant based on the 99% confidence
interval for the intercept (if the 99% CI includes the value of
zero, the intercept is not statistically significant and should be
eliminated from the regression analysis).
15
Data Analysis (II)
• If the intercept is not significant, run the regression
analysis again by selecting the value of zero for the
intercept. Examine the regression output table to
report the final relationship, the coefficient of
determination (R2), and the 99 % CI for the slope.
• The final regression lines can be shown on the plot of
the data. For each regression, the summary tables in
the results should show the estimated values for the
slope and intercept, the 99% confidence intervals for
the slope and intercept, and the coefficient of
determination (R2).
16
Examples
Spectrophotometer Absorbance vs. Concentration (at 500 nm)
2.5
Absorbance
2
1.5
1
How to plot this line?
0.5
0
0
200
400
600
800
1000
1200
Concentration (mg/L)
Figure 1: Linear relationship between Absorbance and
Concentration using Spectrophotometer
Table 1: Summarized Regression Results for Spectrophotometer
Model
m
(99% CI)
Intercept
(99% CI)
R2
With intercept
Abs=mC+b
.00228
(.00223,.00233)
-.00748
(-.03832,.02335)
.9985
Without intercept
Abs=mC
.00227
(.00224,.00230)
N/A
.9994
17
Table A 1: Regression analysis output from Spectrophotometer data with intercept
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
0.9992
0.9985
0.9984
0.0318
24
ANOVA
df
Regression
Residual
Total
Intercept
X Variable 1
SS
1
22
23
14.545
0.022
14.568
Coefficients Standard Error
-0.00748
0.01094
0.00228
0.00002
MS
14.545
0.001
t Stat
-0.68413
119.76079
F
Significance F
14342.647
1.830E-32
P-value
0.50103
0.00000
Lower 95%
Upper 95% Lower 99.0% Upper 99.0%
-0.03017
0.01520
-0.03832
0.02335
0.00224
0.00232
0.00223
0.00233
at 500 nm
Reject intercept
18
Table A 2: Regression analysis output from Spectrophotometer data with intercept=0
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.9997
R Square
0.9994
Adjusted R Square
0.9560
Standard Error
0.0315
Observations
24
ANOVA
df
Regression
Residual
Total
Intercept
X Variable 1
SS
1
23
24
40.825
0.023
40.848
Coefficients Standard Error
0
#N/A
2.268E-03
1.117E-05
Significance
MS
F
F
40.8247 41208.50403 1.679E-37
0.0010
t Stat
#N/A
2.030E+02
P-value
Lower 95% Upper 95% Lower 99.0% Upper 99.0%
#N/A
#N/A
#N/A
#N/A
#N/A
6.327E-39 0.002245 0.002291
0.002237
0.002300
at 500 nm
Abs. = 2.268×10^-3 *Conc.
Conc. = XXXX * Abs.
19
Data Analysis (III)
• Format, significant digits
• Show how you decide the equations (with or without intercept)
based on the results of the linear regression analysis
• Apply the equations (one measure at wavelength = 500 nm and one
measure at wavelength = 520 nm) and calculate the concentration
of tracer in the unknown samples.
• Show the final equation in the form of
C (mg/L) = a Abs + b
(b can be zero or any value, depending on the results of your
regression analysis)
• These are the final equations that will be used in later experiments
for determining tracer concentrations for complete mix and plug
flow reactors.
20
Lab1 Schedule
• Group A: 2 pm (7 students)
• Group B: 2:40 pm (6 students)
• Group C: 2 pm (7 students) Friday.
• Results from Group A to C will be shared,
students in the same lab section will analyze
the same data.
21
Water Resources and Environmental
Engineering Laboratory
Writing Scientific and Engineering Reports
CE 304 SP2019
Technical Writing
Kevin Wang
Outline
•
•
•
•
Introduction
Structure of a technical report
Writing by Sections
Tips for report writing
How Engineers Spend Their Time: Early Career
25-50
______%
Engineering: Designing, measuring,
calculating, problem-solving
______%
Communicating: Writing reports, letters,
50-75
memos, proposals; giving presentations,
talking to colleagues, supervisors, and
clients
3
https://ibrahimelsawy.files.wordpress.com/2012/02/communication-engineer1.jpg
General Structure of a scientific
Writing
• In scientific writing, IMRaD (Introduction,
Methods, Results, and Discussion,
Conclusion) refers to a common organization
structure
Structure of a scientific /engineering
Report
•
•
•
•
•
•
•
•
•
Title Page
Table of Contents
Abstract
Introduction
Methods and Procedures
Results and Discussion
Summary and Conclusions
References
Appendices
Abstract
Brief trajectory (objectives, major findings, conclusion) of the report
Introduction
Background information, importance of the work,
objectives, scope of works
Methods and Procedures
Exp. Procedures
Data Analysis
The steps and equipments Equations, theories, statistic
you used in the lab
tools
Results and Discussion
Visually and textually represents research findings
Interpret the findings: Primary results vs secondary
results; Results vs. theories , Sources of error,
Conclusions
Summary of goals, results and discussion, implication of
the findings
6
Procedures and Methods
How did you do it?
• Experimental Procedures and Methods
– History of work completed
– Make use of illustrations
– Flow chart
Do not provide a step by step set of instructions
that are found in the lab manual!
• Methods of Data Analysis
– Formulas, equations, theory, statistics
Results and Discussion
• Results:
What did you find?
– Present data collected to support objectives
(Tables & Graphs)
– Use sub-headings to keep results of the same type
together, which is easier to review and read
– For the data, decide on a logical order that tells a
clear story and makes it and easy to understand
Results and Discussion
• Discussion:
What does it all mean?
– Discuss results with regard to objectives, explain the
data and significance of the information in the tables
and graphs.
– How do these results relate to the original question or
objectives outlined in the Introduction section?
– Do the data support your hypothesis? Comparison of
results with theory or accepted formulas should be
discussed.
– Sources of error should be addressed with respect to
your findings and the significance of these errors with
respect to the objectives of the lab
Results and Discussion
• Discussion:
What does it all mean?
– Discuss weaknesses and discrepancies. If your
results were unexpected, try to explain why
– Is there another way to interpret your results?
– What further research would be necessary to
answer the questions raised by your results?
– Explain what is new without exaggerating
Conclusions
• Summary of goals
• Summary of Results
– Findings from the data
You should provide a clear scientific
justification for your work in this
section
The Conclusion should concisely
provide the key message(s) the author
wishes to convey
• Implication of the findings
• Summary of recommendations
– Improve the data quality (accuracy or precision)
– Improve the experimental methods
A common error in this section is repeating the abstract, or just listing
experimental results.
Introduction
Why did you do it?
• Background (1st)
What did you do?
– Explain the importance of this lab in Engineering
practice.
• Objectives (2nd)
– State the practical objectives of the lab.
• Scope of works (3rd)
– Provide an overview of the how the objectives
were achieved, that is, what will be done in this
lab.
Move from general to specific: problem in real world / research topics
/ textbook –> your experiment.
Abstract
what you did and what the
important findings in your
research were.
• Single page alone! (requirement for the report format
in this class)
• What information should be provided in the Abstract?
– Objectives and Background Statement (1-2 sentences,
What did you investigate? Why?)
– Scope of work(1-2 sentences, What did you do?)
– Highlight Significant Findings (2 to 3 sentences, What did
you find out?)
– State major conclusions and significance. (1-2 sentences,
What do your results mean? So what?)
– One to two paragraphs total (150-300 words)
Abstract
• What to avoid:
– Do not include references to figures, tables,
equations, or sources.
– Do not include information not in report.
– Using jargon, uncommon abbreviations and
references
References and Appendix
• References
– Provide a bibliographic list of references used in the
lab report.
• Appendix (starting from an new page)
– Original data from lab, calculations (or at least one
complete set of well documented sample
calculations),
– Any other related information which supports the lab
report, but does not fit in the main report.
– All information and data needed to develop the
results of the lab or project should be presented
either in the main report or the appendix.
How to start it?
• Suggested writing order:
1.
2.
Perform all required data analysis
Have all the Figures, Tables, or Equations ready
Methods and Procedures
Write down the Exp. Steps ASAP after the lab
3.
Results and Discussion / Appendices
Put your answers for application problems in Appendices
4.
5.
6.
Conclusions
Introduction
Abstract
Major findings should be mentioned
7.
References
But we are not finished yet!
• This is just the “first draft” of your report!
Check ! Check ! Check!
Check List (attach this Table in the last page of your first two reports)
Items
Title page (format)
Table of Contents (format)
Structured abstract (Objectives, important findings and conclusion), single page alone
Introduction (Importance, objectives, scope of work)
Experimental Procedures and Data Analysis Methods
Results and discussion (rational thinking, present your data or results in a logical order, sub headings)
Conclusion
Figure legends
Captions for Figure (bottom) and Table (above)
Significant digits (round up to hundredths decimal for most of data) or scientific expression
References are superscript in text.
Text is 12 point, double-spaced.
Text is in Microsoft Word.
Acronym use is limited.
Report has been checked for spelling and grammar.
The report file name should be named in the following way: first name last name_lab#
Answers for Application questions (N/A if there is no application question)
Tips for Report Writing (I)
• Avoid vague generalizations
– “good data”, “very high temperature”, “good R2 values”
• Use Headings and Subheadings
Example: In Lab
– Spectrophotometer,
– Colorimeter
• Avoid the use of personal pronouns such as “we” or “I”
– Passive voice
– Student measured the absorbance of unknown samples with colorimeter.
– The absorbance of unknown samples were measured with colorimeter.
• Tense
–
–
–
–
Past tense to describe what was done
Past tense for results obtained
Past tense to describe findings, with present tense to interpret results
Present tense to refer to figures, tables and graphs
• Avoid long c…
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