1.1e Measurement and Uncertainty Flashcards
All numbers in science can be broken down into 2 types:
measurements (continuous)
integers (discrete)
All measurements must contain…
uncertainty
Uncertainty is expressed as a
+/-
Reading error (defn)
is the amount of error expected from taking a measurement. It is intrinsic to the measuring device
Reading error on an analog device is …
half the smallest increment of the device
Reading error on a digital device is …
the smallest decimal place shown
Estimated error (defn)
the amount of error expected due to what is being measured and the limitations of the situation. It is usually much larger than the reading error. It comes from thinking about the measurement being taken.
Random Error (defn)
is the error that comes from taking trials. The random variation in reading or estimating the uncertain digit of the measurement.
Random Error is expected to follow what kind of distribution?
Bell Curve a.k.a Normal or Gaussian distribution
Standard deviation (defn)
the average difference between each measurement and the mean. It is a measure of the spread in the data.
Data error (defn)
equal to twice the standard deviation. It includes 95% of the data and excludes the 5% that are outliers.
Upper Limit (defn)
the mean + the data error
Lower limit
the mean - the data error
Absolute Uncertainty (defn)
half the range in the data ((max-min)/2)
absolute uncertainty
any uncertainty expressed in units like cm, kg, etc. (as opposed to %).
% Uncertainty
any uncertainty expressed as a % of the mean value
% uncertainty (defn)
the ratio of the absolute uncertainty to the mean value
Why do we take trials?
to know the mean better
Why do we want to know the mean?
the mean is the best estimate of the true value
How many trials is enough?
- a minimum of 5 is required to calculate the standard deviation
- when taking more trials will no longer change the mean given the precision of the measurements
- when we are convinced that the running mean will no longer change by taking more trials
Can we say two values are different from each other when the means are different?
No. The overlap of the uncertainties must be taken into account.
What is the name of the test to tell if two sets of data overlap?
t-test (unpaired)
A t-test tells us…
the probability that the amount of overlap occurred by chance, given the mean values and the data error
accuracy (defn)
the correctness of a value
accuracy (example)
a student determined pi to be 3.15, when the actual value is 3.14. Their results were fairly accurate.
precision (defn)
- how specifically and narrowly a value is known
- tied to decimal place
- tied to data error
accurate, but not precise (example)
a student got a value of pi of 3.1 +/-2.6. Although the mean was close, the range of possible answers was very wide, including anything from 0.5 to 5.7!
accurate and precise (example)
a student achieved 3.14+/-0.01. The value is correct and 95% certain to be between 3.13 and 3.15.
not accurate and not precise (example)
a student got a value of 6.5 +/-2.4 for the value of pi. The value is far off the accepted value of 3.14. The range of values, 4.1 to 8.9 is very broad and also doesn’t include the actual value.
Not accurate but precise
A student got a value of 5.62+/-0.02 for pi. The value is off the accepted value by a lot, although it is know to be between 5.60 and 5.64.
Systematic error (defn)
when all the values (trials or cases) are incorrect by the same amount.
• associated with a y-intercept shift
systematic error (examples)
- zero errors on a balance (reads 0.12g before something is placed on it - all masses will be large by 0.12g)
- calibration errors (thermometer reads 1.2°C when placed in an ice bath - all temperatures will read 1.2°C higher than they actually are)
