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.

TRIAL MASS(g) TRIAL MASS(g)

1 100.01 1 100.10

2 100.00 2 100.00

3 99.99 3 99.88

4 99.99 4 100.02

Average 100.00 Average 100.00

Range ±0.01 Range ±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

TRIAL MASS(g) TRIAL MASS(g)

1 100.01 1 100.10

2 100.00 2 100.00

3 99.99 3 99.88

4 99.99 4 100.02

Average 100.00 Average 100.00

Range ±0.01 Range ±0.11

Let’s play darts!

Let’s play darts!

Let’s play darts!

Let’s play darts!

Accurate? Precise?

Precise, but poor accuracy

Play again?

Play again?

Play again?

Play again?

Play again?

Accuracy? Precision?

Both accurate and precise

One more time!

One more time!

One more time!

One more time!

One more time!

Well?

Poor accuracy and precision

Uncertainty in measurement

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 ± 0.5mm 43.4 mm ± 0.5mm

Add the uncertainties, therefore 43.4 mm ± 1mm

The Balance

The balance 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

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

Types of errors

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 errorsRandom errors

Systematic 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

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