1. Error Error is the difference between a measured or calculated (reported) value and the true value. Scientists recognize that errors are present in their professional lives and must be able to: 1. Identify types of errors 2. Numerically express the magnitude of errors 3. Recognize the confidence that may be placed in a printed number

2. Why are errors important? Two measurements of body temperature before and after a drug is administered 38.2  C and 38.4  C Is temperature rise significant? – It depends on the associated errors (38.2  0.01)  C and (38.4  0.01)  C - significant (38.2  0.5)  C and (38.4  0.5)  C – not significant

3. Simple Error Analysis Suppose a rod of unknown length is measured with a standard meter stick. Spend 5 minutes as a team completing this exercise: What can be said about the length of the rod is reported as: 7 to 8 cm 7.5 to 7.6 cm 7.57 to 7.59 cm?

4. Systematic Errors Systematic Errors - errors that can be attributed to some regular outside occurrence. Scientists must be aware of the presence of systematic errors and eliminate those possible and try to quantify and correct for those remaining.

5. Systematic Errors The error associated with systematic errors can be corrected if the source and magnitude are known. Repeating measurements will not eliminate or reduce systematic errors.

6. Systematic Errors Constant throughout a set of readings. May result from equipment which is incorrectly calibrated or how measurements are performed. measurements are performed. Cause average (mean) of measured values ause average (mean) of measured values to depart from correct value. to depart from correct value. Difficult to spot presence of systematic cult to spot presence of systematic errors in an experiment. errors in an experiment.

7. Random Errors Accidental (Random) Errors – errors that occur in a random nature. The presence of accidental errors is evident by the scatter in measured data.

8. Random Errors It is impossible to predict the magnitude and sign of the accidental error present in any one measurement. Repeating measurements and averaging the results will reduce the random error in the average.

9. Random Errors An error that varies between successive Ar measurements measurements Equally likely to be positive or negative Equally likely to be positive or negative Always present in an experiment Always present in an experiment Presence obvious from distribution of values obtained obtained Can be minimised by performing multiple Can be minimised by performing multiple measurements of the same quantity or by measurements of the same quantity or by measuring one quantity as function of second measuring one quantity as function of second quantity and performing a straight line fit of the data data Sometimes referred to as reading errors

10. What type of error is: The produce scale at the grocery store has water on it. (The water runs off the produce) The timekeeper sneezes at the moment the runners cross the finish line. Gasoline sloshed from your tank prior to the pump shutting off (mpg calculation). Measuring with a 100 ft tape that is actually 99.01 ft. Press the wrong key(s) on a calculator during a long calculation.

11. Definitions There are three ways to numerically describe error: 1) True error = Reported value – True value 2) Fractional error = True error / True value 3) Percent error = Fractional error * 100%

12. An example: Calculate the true error, fractional error and percent error for:

13. Quoting results and errors Generally state error to one significant figure (although if one or two then two significant figures may be used). significant figures may be used). Quote result to same significance as error Quote result to same significance as error When using scientific notation, quote value and error with the same exponent value and