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Errors and Uncertainties in Biology

Accuracy Accuracy indicates how close a measurement is to the accepted value. For example, we'd expect a balance to read 100 grams if we placed a standard 100 g weight on the balance. If it does not, then the balance is inaccurate.

Precision Precision indicates how close together or how repeatable the results are. A precise measuring instrument will give very nearly the same result each time it is used. The precision of an instrument reflects the number of significant digits in a reading. TRIALMASS(g)TRIALMASS(g) 1100.011100.10 2100.002 399.99399.88 499.994100.02 Average100.00Average100.00 Range±0.01Range±0.11

Precision Precision indicates how close together or how repeatable the results are. A precise measuring instrument will give very nearly the same result each time it is used. The precision of an instrument reflects the number of significant digits in a reading. More precise Less precise TRIALMASS(g)TRIALMASS(g) 1100.011100.10 2100.002 399.99399.88 499.994100.02 Average100.00Average100.00 Range±0.01Range±0.11

Let’s play darts!

Accurate? Precise?

Precise, but poor accuracy

Play again?

Accuracy? Precision?

Both accurate and precise

One more time!

Well?

Poor accuracy and precision

Uncertainty in measurement

An error in a measurement is defined as the difference between the true, or accepted, value of a quantity and its measured value.

Uncertainty in measurement An error in a measurement is defined as the difference between the true, or accepted, value of a quantity and its measured value. In reading any scale the value read is numbers from the scale and one estimated number from the scale and an error of  ½ a division.

The Ruler 0.0mm ± 0.5mm43.4 mm ± 0.5mm Add the uncertainties, therefore 43.4 mm ± 1mm

The Balance The balance is digital and measures to three decimal places: e.g. 24.375g. The uncertainty is  0.0005g, but once again we have to determine two points, the zero (with no mass on the balance) and the mass of the object to be measured. Therefore the uncertainty is  0.001 g. Always use.1 for digital devices

The stopwatch An exception to the uncertainty being half the smallest instrument value is when using a stopwatch. According to the display you can measure time to the nearest 100th of a second (0.01 s) with our stopwatches. Because human reaction time must always be factored in you need to use  second

Data Collection Whenever you record raw data you must include the uncertainty of the measuring device.

Which is more precise? The ruler or the balance?

Which is more precise? The ruler or the balance? The balance has a greater precision than the ruler, it measures to more decimal places and therefore the measurements are closer together.

Which is more precise? The ruler or the balance? The balance has a greater precision than the ruler, it measures to more decimal places and therefore the measurements are closer together. E.g. Balance: 23.456g, 23.453g, 23.458g Ruler: 23.3mm, 23.5mm, 23.6mm

Accuracy and Precision Two students set out to measure the size of a cell that is known to be 100  m in length. Each student takes a number of measurements and they arrive at the following answers:

Accuracy and Precision Two students set out to measure the size of a cell that is known to be 100  m in length. Each student takes a number of measurements and they arrive at the following answers: Student A: 101  m  8  m Student B: 95  m  1  m

Accuracy and Precision Two students set out to measure the size of a cell that is known to be 100  m in length. Each student takes a number of measurements and they arrive at the following answers: Student A: 101  m  8  m Student B: 95  m  1  m Which students measurements are more precise? Which students measurements are more accurate?

Accuracy and Precision Two students set out to measure the size of a cell that is known to be 100  m in length. Each student takes a number of measurements and they arrive at the following answers: Student A: 101  m  8  m Student B: 95  m  1  m Which students measurements are more precise? B Which students measurements are more accurate?

Accuracy and Precision Two students set out to measure the size of a cell that is known to be 100  m in length. Each student takes a number of measurements and they arrive at the following answers: Student A: 101  m  8  m Student B: 95  m  1  m Which students measurements are more precise? B Which students measurements are more accurate? A

Now try the uncertainty practical

41 Dartboard analogy How could you describe the following: Not accurate Not precise Accurate Not precise Not accurate Precise Accurate Precise

Types of errors

There are two types of errors that we are concerned with when looking at our experimental data:

Types of errors There are two types of errors that we are concerned with when looking at our experimental data: Systematic errors

Types of errors There are two types of errors that we are concerned with when looking at our experimental data: Systematic errors Random errors

Systematic errors Result from a defect in an instrument or procedure. E.g. the balance is incorrectly calibrated.

Systematic errors Result from a defect in an instrument or procedure. E.g. the balance is incorrectly calibrated. The systematic error is always in one direction. E.g. the incorrectly calibrated balance always gives readings that are too high by 0.1g.

Systematic errors Result from a defect in an instrument or procedure. E.g. the balance is incorrectly calibrated. The systematic error is always in one direction. E.g. the incorrectly calibrated balance always gives readings that are too high by 0.1g. Comparison to standard samples can help overcome systematic errors. E.g. use a standard of known mass on the balance.

Systematic errors Systematic errors affect the accuracy of the readings.

Random errors Result from random fluctuations in procedures and measuring devices.

Random errors Result from random fluctuations in procedures and measuring devices. Because this error is random in nature it can be too high or too low than the actual value.

Random errors Result from random fluctuations in procedures and measuring devices. Because this error is random in nature it can be too high or too low than the actual value. Random errors can be reduced by taking the average of several replicate measurements.

Random errors An average of the measurements will be more accurate, closer to the actual value.

Random errors An average of the measurements will be more accurate, closer to the actual value. average

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