Experimental Data Flashcards
Notations like mega pico etc
learn off
Types of data
Quantitative
Qualitative
Quantitative data
eg.
length = 1.24m
24 types of paints used
fram is manufactured o alpha brass
Qualitative data
eg.
it is a sad painting
masterful brush strokes
SI unit of: mass length time electrical current temperature luminous intensity amount of substance
kg m s A K cd mol
femto f
x 10 ^ -15
pico p
x 10 ^ -12
nano n
x 10 ^ -9
micro μ
x 10 ^ -6
milli m
x 10 ^ -3
centi c
x 10 ^ -2
kilo k
x 10 ^ 3
mega M
x 10 ^ 6
giga G
x 10 ^ 9
tera T
x 10 ^ 12
tabulating data
book pg 13
sensors
detect energy
transdurcers
convert energy from one form to another
is a microphone a sensor or a transducer?
-detects and converts sound energy to electrical energy - it is both
is a loudspeaker a sensor or a transducer?
-converts electrical energy to sound energy - a transducer
sensors and energy
no sensor is sensitive to only one form of energy
Measurement instrument
a measurement system
scientific instruments
- high quality measurement systems
- due to high accuracy + low uncertainty
how measurement systems work
- transducer/sensor provides input to instrument
- instrument manipulates (amplify, filter, convert to digital representation) input signal to provide useful output
The correct device has:
req accuracy
stability
robustness
appropriate cost
types of quantities
static
dynamic
static quantities
slowly varying quantities
eg. a building height
dynamic quantitites
rapidly varying quantities
eg. sound, temperature
performance characteristics of instruments
- range
- span
- linearity
- non-linearity
- hysteresis
- resolution
- repeatability
- accuracy
range
min and max values of input or output variables
span
maximum variation of input or output variables
eg. thermometer with range -40C to 100C, span is 140C
linearity
extent to which input values and output values lie on (or near) a straight line
non-linearity
a more complex relationship between input and output
hysteresis
some instruments have different loading and unloading performance
(some sensors behave differently during loading and unloading, eg. due to friction between components in instrument)
resolution
smallest change in a variable to which the instrument will respond.
repeatability
measure of the closeness of agreement between a number of readings taken consecutively of a variable, before the variable has time to change.
accuracy
difference between the indicated value and the actual value.
If instrument preforms with ideal linear behaviour then relationship between input and output can be expressed as:
y = Ax
Drift
eg. a change to ambient temp may cause a drift in output of instrument which is not due to a change in measured variable
Impact of drift
- zero drift
- sensitivity drift
calibration
process of validating a measurement technique or instrument
-compare performance of instrument w/ known standard
static calibration
- to obtain static characteristics of an instrument
- establish relationship between input (measurand) + output
- hold all inputs steady
- vary measurand + record output
standards
primary
secondary
primary standards
standards are complex and expensive, usually held by government agencies. Such as the National Institute of Standards and Technology in the US.
secondary standards
less expensive and less accurate.
eg. from National Laboratories, Universities
Tertiary Standard
In house calibration
Sig figures rules
- count all figures eg. 6.12 has 3 sig figs
- for decimals with lots of zeroes, counta ll digits to right of 1st non-zero eg. 0.001246 has 4 sig figs
check notes
multiplying or dividing sig figs
- result should have same number of sig figs as number with least sig figs
eg. 3.7 x 3.01 = 11.137 = 11
adding or substracting sig figs
numbers round the result to the same number of significant digits as that number with the least number of significant digits
eg. 11.24 + 13.1 = 24.34 = 24.3
Types of rounding
Truncation
Round to nearest even
Ceiling
Flooring
Sig figs - what does 6.124 mean?
number is between 6.123 and 6.125
uncertainties: writing them
eg.
(15. 5 +- 0.5)°C
truncation
round towards zero, discard least sig figures
eg: truncated to 4 sig figures:
- 672 = 45.67
- 45812 = 45.45
Round to nearest even
If LSD > 5 increment next LSD
If LSD < 5 truncate LSDs
tie breaking rule for when x is half way between 2 integers
check otes
how to decide how many sig figs
depends on precision and accuracy
accuracy
describes how well a measurement agrees with a known standard.
accurate if readings close to ‘true’ value
precision
describes the degree of certainty about the measurement.
precise if readings closely grouped
measured value and its uncertainty
must always have same no. of digits after decimal place
eg
g=(9.802 +- 0.0001)[m/s2]
Resolution uncertainty
check slides 3
use of mean
often used to smooth out the variation
best estimate, but still uncertain
we can’t know the TRUE value
but reasonable to assume that true value lies within range of extremes (in between max and min values)
mean (𝑥̅) formula
check slides 3
calculating uncertainty in the mean
- calculate range (largest - smallest value)
- divide range by number of measurements
- only quote one sig figure eg. 0.0825 = 0.08
- quote mean to same number of decimal places as uncertainty
random errors
- measurements subject to random errors, cause measurement to fluctuate above and below true value
- best approach is to take repeated measurements
- determine uncertainty from spread
- mean is best estimate of true value
deviation of one measurement from mean formula
𝑑ᵢ =𝑥ᵢ − 𝑥̅
Spread - Variance formula
in lecture slides 4
units of variance are square of those of the measurand
standard deviation
measure of how much indiv measurements are likely to vary from mean value
reduce uncertainty
more measurements (increasing n)
standard deviation of the means
standard error in the mean
-know how to use formula
relationship between standard error in mean and standard deviation formula
σ𝑥̅ =σ/√𝑛
Adding measurements with uncertainty
-Uncertainty in computed measurement is the SUM of the uncertainties in the individual measurements
(X +- △X) + (Y +- △Y) = (X + Y) +- (△X + △Y)
subtracting measurements with unceratainties
Uncertainty in computed measurement is the SUM of the uncertainties in the individual measurements.
(X +- △X) - (Y +- △Y) = (X - Y) +- (△X + △Y)
uncertainties not subtracted
multiplying two measurements with uncertainties
(X +- △X)(Y +- △Y)
do algebraically, and get
XY(1 +- △X/X +- △Y/Y)
Fractional uncertainty in X
Fractional Uncertainty in Y
△X/X
△Y/Y
what x y △x and △y stand for
X and Y = measurements
△X and △Y = uncertainties in the measurements
dividing two measurements with uncertainties
(X +- △X)/(Y +- △Y)
=
X/Y(1 +- △X/X +- △Y/Y)
graphing measurements w/ uncertainties
eg. on table label it as
Time (s) +- 5s
error bars
indicate the size of uncertainties
-error bars can be presented going in both axises for one dot/measurement
check slides 4
reasons to fit a line on a graph
- show a trend
- allow values to be read from our graph at a point which we did not directly measure
interpolate
an estimation of a value within two known values in a sequence of values
extrapolate
an estimation of a value based on extending a known sequence of values or facts beyond the area that is certainly known
finding fit line
Use Least Squares Method
Why use least squares method
minimises sum of squares of the vertical direction
equation of line
yᵢ𝒸 = mxᵢ + c
xᵢ = particular point yᵢₒ = observed value (measured value) yᵢ𝒸 = calculated value from equation of line
partial differentiation
know how to do it
Derivations to learn (chap 6 of book)
- least squares line fitting formula
- centroid
standard error formula
slides 5
least squares line and standard erorr
least squares line has smallest standard error fo all possible lines through data
coefficient of determination
r², measure of how well line fits the data
-formula
outliers
should never be simply discarded without justification
assumptions of least squares line fitting method
- uncertainty in independent variable is taken to be negligible
- random uncertainty is only in dependent variable
- uncertainty is same in each measurement. If not, use Weighted Least Squares fit
simple way to check answer of least squares line fits
the centroid, which is the point given by (𝑥̅,𝑦̅), must lie on the least squares line fit.
sig figures to report in line fit equation
-can use diff between measured values of y and those which are calculated using our line fit
-formulas to estimate uncertainty in m and c
-
technical report sections
- title
- abstract
- introduction
- experimental method
- results
- discussion
- conclusions
- references
abstract
An overview of the experiment and its findings. Why you did the experiment, what your results show and why is that significant.
what is in an abstract
- what you set out to do and why
- how you did it
- what you found
- recommendations
what is not in an abstract
- introduction
- plan of activities
- extracts from main body with no context
- repeat of conclusions
introduction
- Describe background + goals of experiment.
- should place the experiment in context of what is known from existing literature.
- Describe theory relevant to experiment.
experimental method
- be a description of what was done
- observations of what was done, incl observations of what happened.
- purpose: allow reader to critically examine way in which experiment was conducted + analyse results in context of what happened.
conclusion
acknowledgements
acknowledge assistance from colleagues through discussion, borrowing equipment or even financial support to complete the work
scientific literature
Scientific literature is published in peer reviewed journals.
peer reviewed journals
These are publications which release a new edition several times per year. A researcher will conduct an experiment and write a detailed document (known as a research paper) reporting the results.
purpose of referencing
is expected that we will draw on the ideas and research that has gone before us. However it is expected that we will give credit to the people who have produced this knowledge that we are using. If we do not it is as if we are trying to claim their work as our own. This is plagiarism and is a very serious offence in all technical/scientific writing.
qualitative data
is information that describes something. It is often subjective and responses will vary depending on the outlook of an individual. For example an individual may describe a sound as annoying or pleasant but this may or may not useful in predicting the responses of a community of people.
quantitative data
data expressing a certain physical quantity, amount or range. There is a measurement unit associated with the data, e.g. metres, in the case of the height of a building
