Random & Systematic Errors (DP IB Physics): Revision Note

Random & Systematic Errors

• Measurements of quantities are made with the aim of finding the true value of that quantity

  • In reality, it is impossible to obtain the true value of any quantity as there will always be a degree of uncertainty

• The uncertainty is an estimate of the difference between a measurement reading and the true value

• The two types of measurement errors that lead to uncertainty are:

  • Random errors

  • Systematic errors

Random Errors

• Random errors cause unpredictable fluctuations in an instrument’s readings as a result of uncontrollable factors, such as environmental conditions

• This affects the precision of the measurements taken, causing a wider spread of results about the mean value

• To reduce random error:

  • Repeat measurements several times and calculate an average from them

Reading Errors

• When measuring a quantity using an analogue device such as a ruler, the uncertainty in that measured quantity is ±0.5 the smallest measuring interval

• When measuring a quantity using a digital device such as a digital scale or stopwatch, the uncertainty in that measured quantity is ±1 the smallest measuring interval

• To reduce reading errors:

  • Use a more precise device with smaller measuring intervals and therefore less uncertainty

Both rulers measure the same candy cane, yet Ruler B is more precise than Ruler A due to a smaller interval size

Systematic Errors

• Systematic errors arise from the use of faulty instruments or from flaws in the experimental method

• This type of error is repeated consistently every time the instrument is used or the method is followed, which affects the accuracy of all readings obtained

• To reduce systematic errors:

  • Instruments should be recalibrated, or different instruments should be used

  • Corrections or adjustments should be made to the technique

Systematic errors on graphs are shown by the offset of the line from the origin

Zero Errors

• This is a type of systematic error which occurs when an instrument gives a reading when the true reading is zero

  • For example, a top-ban balance that starts at 2 g instead of 0 g

• To account for zero errors

  • Take the difference of the offset from each value

  • For example, if a scale starts at 2 g instead of 0 g, a measurement of 50 g would actually be 50 – 2 = 48 g

  • The offset could be positive or negative

Precision

• Precise measurements are ones in which there is very little spread about the mean value, in other words, how close the measured values are to each other

• If a measurement is repeated several times, it can be described as precise when the values are very similar to, or the same as, each other

  • Another way to describe this concept is if the random uncertainty of a measurement is small, then that measurement can be said to be precise

• The precision of a measurement is reflected in the values recorded – measurements to a greater number of decimal places are said to be more precise than those to a whole number

Accuracy

• A measurement is considered accurate if it is close to the true value

  • Another way to describe this concept is if the systematic error of a measurement is small, then that measurement can be said to be accurate

• The accuracy can be increased by repeating measurements and finding a mean of the results

• Repeating measurements also helps to identify anomalies that can be omitted from the final results

The difference between precise and accurate results

Representing precision and accuracy on a graph

Reliability

• Reliability is defined as

  A measure of the ability of an experimental procedure to produce the expected results when using the same method and equipment

• A reliable experiment is one which produces consistent results when repeated many times

• Similarly, a reliable measurement is one which can be reproduced consistently when measured repeatedly 

• When thinking about the reliability of an experiment, a good question to ask is

  • Would similar conclusions be reached if someone repeated this experiment?

Validity 

• The validity of an experiment relates to the experimental method and the appropriate choice of variables

• Validity is defined as 

  A measure of the suitability of an experimental procedure to measure what it is intended to measure

• It is essential that any variables that may affect the outcome of an experiment are identified and controlled in order for the results to be valid

• For example, when using Charles’ law to determine absolute zero, pressure must be kept constant

• When thinking about the validity of an experiment, a good question to ask is

  • How relevant is this experiment to my original research question?