Uncertainty and equipment error


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Uncertainty and equipment error

  1. 1. Uncertainty andEquipment Error by Chris Paine Bioknowledgy
  2. 2. Absolute uncertainty and recording data—   When you record measurements you should also record the (absolute) uncertainty associated with the measurement—  The uncertainty reflects greatest precision, i.e. the smallest unit to which a measurement can be made. This method of quoting uncertainty is called least count
  3. 3. Absolute uncertainty and recording data—  For example measuring a length: —  We measure a length of 213 mm —  The smallest unit on a ruler is 1mm therefore the uncertainty is (±1 mm) —  Therefore as we know the value should be no less than 212 mm and no more than 214 mm —  Therefore we can quote the value as 213 mm (±1 mm)
  4. 4. Uncertainties and recording data—  It is illogical to report values with more decimal places than that indicated by the uncertainty for example: —  9.63 ± 0.6 the last decimal place has no meaning and the number should be reported as 9.6 ±0.6—  If a value 48cm3 is measured to an uncertainty of ±0.5cm3 it should be quoted as 48.0cm3 (±0.5 cm3) – this is an IBO guideline
  5. 5. What about uncertainties in processed data?—  If means and standard deviations are calculated from a data set. Therefore they should be quoted in the same units and the same uncertainty as the data they are calculated from.—  For example: 10 mm (±1 mm) 12 mm (±1 mm) 14 mm (±1 mm)—  Mean = (10 mm + 12 mm + 14 mm) / 3 = 12 mm (±1 mm)—  Standard deviation = 2 mm (±1 mm)
  6. 6. Deciding on the level of uncertainty—  Uncertainty may be quoted on a piece of apparatus or in it’s manual – use that—  If this information is not available use the least count method—  You may choose to increase your uncertainty to reflect the way a piece of equipment is used. Justify this decision in your lab report.—  Time is different, stopwatches depend both on the reaction time of the user and how they are used: —  It takes us 0.1 – 0.3 seconds to start and stop a watch. Therefore the uncertainty is in the region of ±1s —  If you are taking interval measurements, e.g. you observe an investigation every 2 minutes then your uncertainty is the same as your interval ±2 min
  7. 7. Examples of uncertainty—  For example, the school electronic balances measure to 1/100th of a gram e.g. 2.86 g The precision of the electronic balance is ±0.01 g Hence the reading on the electronic balance should be reported as 2.86 g (±0.01 g)—  When using a ruler we can usually be accurate to the nearest mm The implied limits of the measurement 28 mm are 27 mm – 29 mm This can be written as 28 mm (±1 mm), where the ±1 mm is the absolute uncertainty—  N.B. Quote the uncertainty in the column header (e.g. ±0.01 g or ±1 mm) of your data table rather than against each
  8. 8. Be careful of Repeated equipment use—  “I use a 300 mm ruler to measure 970 mm, what is the uncertainty?” “To measure the length I must of used the ruler 3 times (300 mm + 300 mm + 270 mm)” “Hence the uncertainty in my measurements is 3 times as big (1 mm + 1 mm + 1 mm)” “Therefore my measurement is 970 mm (±3 mm)” N.B. In reality the investigator should have made a better choice of equipment, e.g. 1m ruler
  9. 9. Be careful of Repeated equipment use—  “I am carrying out a vitamin C titration in a 50cm3 burette with an uncertainty of ±0.05cm3. My starting volume reads 48cm3. When I finish my titration the volume reads 35.6cm3.” “The volume I used in the titration is 12.4cm3 (48cm3 – 35.6cm3)” “I took two reading from the burette therefore my uncertainty doubled to ±0.1cm3 (±0.05cm3 + ±0.05cm3)” “Therefore my volume is 12.4cm3 (±0.1cm3)”
  10. 10. Systematic Error—  Analysis of systematic error looks at how rigorously your method controlled, varied and measured the different variables—  One aspect is equipment error, i.e. was the equipment choice and use appropriate?—  Ideally equipment errors ideally should be below 5%
  11. 11. Equipment Error—  Although it is optional to assess equipment errors it is highly recommended—  For each different use of equipment calculate the % error—  Calculate the error on the smallest quantity measured. The smallest quantity will generate the largest error.—  Ideally equipment errors ideally should be below 5%—  Repeated calculations can be useful to illustrate cases where only a couple of measurements break the 5% error rule. Use your judgment.
  12. 12. Calculating % equipment errors—  Use a table to organise the calculations—  The table enhances the evaluation therefore add to the evaluation section of the lab report Measuring Uncertainty Smallest % Error Instrument amount and use measured (= uncertainty x 100 / amount measured)
  13. 13. Example Calculations—  13 mm was the smallest length measured—  1 mm the uncertainty—  % Equipment Error = uncertainty x 100 / amount measured—  = 1 mm x 100 / 13—  = 6.7 %
  14. 14. Evaluation - What if an Equipment Error is greater than 5%?—  Recommend a change to a more accurate named example of measuring equipment—  Suggest than larger (suggest an amount) amounts are measured/sampled to bring error below 5%
  15. 15. Evaluation – what if equipment errors are below 5%?—  It’s not necessary to suggest a change, but still comment on it to show that you’ve critically evaluated your equipment use.
  16. 16. Design - make sure you are measuring the right amounts—  If % Equipment Error = uncertainty x 100 / amount measured—  Then amount measured = uncertainty x 100 / % Equipment Error—  Therefore smallest amount measured ≥ uncertainty x 20