Experimental Techniques & Vocabulary Flashcards
Accuracy
How close a value is to the true/accepted/literature value
Precision
How close together a series of measurements or calculated values are. How repeatable/reproducible a series of measurements are
*based on the smallest increment of equipment
More precise equipment gives greater confidence about the exact value of a measurement and makes it more likely that a series of repeated measurements will be closer together in value.
Systematic errors
Errors that always affect results in the same direction (making them either too high or too low). Systematic errors generally cause inaccuracies.
Sources can include:
1) equipment (e.g. not properly calibrated/broken)
2) method design/human technique (e.g. failure to zero balance, reading a meniscus not at eye level, recognizing a color change late (reaction time), heat loss to surroundings, a standard/stock solution has been made to an incorrect concentration)
**Increasing the # of repeated measurements will NOT decrease the amount of systematic error because systematic errors always affect measurements in one direction, repeated measurements do nothing to minimize their effects on accuracy.
- sometimes systematic errors can be canceled out in processing, but that is not something to rely on in our lab work (e.g. change in mass or temperature calculations)
Quantifying Inaccuracy
Error and Percent Error are quantitative ways to assess accuracy though % error is a far more useful and common practice.
Error = Lit. value - Experimental value
% Error = IError- lit /Lit. ValueI x 100%
** always positive since it is an absolute value
Random error
Precision in results is affected by random error. In any given trial, random error can affect results in either direction, too high or too low. This leads to values being spread out around the true value or around the average value.
MEASUREMENT UNCERTAINTY is one major source of random error.
Other sources include:
- equipment: The smallest increment limits how certain we can be about any measurement we make with it
- human limitations: our senses and ability can limit how exactly we can repeat something or know smth
- environmental conditions: in an HS lab, different conditions of temp., light, pressure, etc. can vary considerably
- subject variation: specimens or substances may have been exposed to different conditions and therefore may have acquired different properties
**Increasing the # of repeated measurements can lower the effects of random error as the errors will cancel each other out. This means that there is a better chance of the final calculated average being more accurate. Explanation: this happens as random errors can affect measurements in both directions.
*if suggesting repeated trials as an improvement in a lab report always include the caveat that the purpose is to reduce the impact of random error.
Quantifying Random Error (list)
- measurement uncertainty
- total measurement uncertainty
- total random error: half-range uncertainty
- absolute vs. percent uncertainties
Measurement uncertainty
When taking a measurement we generally can estimate a quantitative value of some random error such as those from the equipment and any fluctuations (that is measurement uncertainty)
1)The uncertainty of the measurement is +/- 1 of the instrument’s smallest increment (the manufacturer can also state it)—use this when the instrument provides whole numbers without more precise readings (like a ruler or basic scale/digital instruments).
2) The uncertainty of the measurement is +/- HALF of the smallest increment of the instrument - use when the instrument can show fractions of the smallest unit (like a digital caliper/glassware) or when measuring subjective values.
3) when there is only 1 marking on an instrument, you can use the uncertainty that is printed on the instrument (e.g. pipette and volumetric flask)
4) if a digital instrument is fluctuating, determine the range of fluctuation. Report the measurement in the center of the range and the uncertainty as half of the range of fluctuation. This can also be used to estimate reaction time, by taking the average of many timed trials.
Total measurement uncertainty
When combining different measurements together to create a graph or perform a calculation, the uncertainties from all of the involved measurements must be combined to get a measure of the total measurement uncertainty.
Total Random Error: Half-Range Uncertainty
We can calculate the amount of total random error through a half-the-range calculation, which gives a more complete measure of the total variation in a series of repeated trials when we are not aware of all random errors until after repeated trials have been performed.
Absolute vs. % Uncertainties
Absolute uncertainties must be presented with the same unit as the measurement and be reported to the same # of decimal places as the value they go with.
% Uncertainties are useful because they have NO unit. There is no strict rule about the # of decimal places with % uncertainties, though as a general guideline, anything less than 0.1% uncertainty is very insignificant and CAN be rounded off.
1.0g ± 0.1g = 1.0g ± 10%
Adding and Subtracting With Uncertainties
1) Add the uncertainties (keep the same unit)
2)
I. Round off (*you can decide whether or not you choose to round by normal rules or to always round up so as to never underestimate uncertainty)
ii. matching precision: final calculated values should be rounded to the same precision (# of decimal places) as the uncertainty
Rounding Uncertainties
one digit: only 1 sig. fig.
- sometimes the equipment might give us 2 digits of uncertainty, but in IB chem the expectation is that we round off to 1 digit
matching precision: measurements should be recorded to the same precision (# of decimal places) as the uncertainty
Multiplying & Dividing with Uncertainties
1) % uncertainties
i. Convert the absolute to %.
- to convert: divide the absolute uncertainty by the measurement it goes with and multiply by 100% to make it a %.
2) Total % uncertainty
Add all % uncertainties together
3) Absolute Uncertainty
I. Convert the total % uncertainty into the total absolute uncertainty
- to convert: divide the total % uncertainty by 100%, multiply this decimal by the final calculated value, and give uncertainty the same unit as the final value
Order of Operations
- Within Parentheses: combine addition and subtraction operation uncertainties 1st
- Once combined, continue on with the % uncertainty method for multiplication and division
- Finish by following the rounding-off rules
Half-Range Uncertainties
The approach for getting the uncertainty value as an average value based on multiple repeated trials.
Formula: (max-min value)/2 = half-range uncertainty – round off
*The half-range uncertainty also accounts for any other sources of random error in our method that we didn’t know about and didn’t estimate in advance.
