SkarpChapter 4 of 10
Measuring Biology: Accuracy, Precision, and Error
Look closely at your measurements to see how small errors can change big conclusions—and how careful technique keeps your data trustworthy.
Why Measurement Quality Matters in Biology
Small Numbers, Big Consequences
In biology, big conclusions often depend on small differences: a 5% drop in enzyme activity, a 0.2 g change in mouse mass, a 0.1 pH shift. If measurements are off, conclusions can be wrong.
Link to Earlier Modules
You have seen how to design good experiments and work safely. Those skills only pay off if your measurements are trustworthy and recorded correctly.
What You Will Learn
You will learn to distinguish accuracy from precision, recognize systematic vs random error, and record data with appropriate significant figures and units.
Your Goal
By the end, you should be able to look at a data table and ask: Are these measurements believable? Are they recorded correctly? What kinds of error might be present?
Accuracy vs Precision: The Core Ideas
Definitions
Accuracy is how close your measurements are to the true value. Precision is how close your measurements are to each other, regardless of the true value.
Accurate and Precise
If a 1.00 g weight gives 0.99, 1.01, 1.00, 1.00 g, the data are both accurate (near 1.00) and precise (clustered together).
Precise but Inaccurate
Readings 0.80, 0.81, 0.80, 0.79 g are precise but not accurate: values are tightly grouped but far from the true 1.00 g.
Neither Accurate nor Precise
Readings 0.9, 1.1, 0.8, 1.2 g are scattered and off from the true value, so they are neither accurate nor precise.
Why It Matters
Modern biology papers are expected to discuss both accuracy (via calibration, controls) and precision (via error bars, standard deviation, confidence intervals).
Classify Accuracy and Precision
For each scenario, decide whether the measurements are: accurate and precise, precise but not accurate, accurate but not precise, or neither.
- A pH meter is used to measure a standard buffer that is exactly pH 7.00. You get: 6.99, 7.00, 7.01, 7.00.
- What is this?
- A micropipette is set to 100 µL. You repeatedly weigh dispensed water (assuming 1.00 g/mL) and calculate the volume: 95, 95, 95, 95 µL.
- What is this?
- You count cells in a hemocytometer. The true concentration is 1.0 × 10^6 cells/mL. Your counts (converted to concentration) are: 0.8, 1.4, 0.9, 1.3 × 10^6 cells/mL.
- What is this?
- You measure the absorbance of a DNA standard that should be 1.0 AU. You get: 0.98, 1.02, 0.99, 0.97 AU.
- What is this?
Write down your answers before checking the solution below.
Suggested answers (check yourself):
- Accurate and precise
- Precise but not accurate
- Neither accurate nor precise
- Accurate and reasonably precise
Systematic vs Random Error
Systematic Error
Systematic error is a consistent, repeatable error in one direction. It shifts all measurements away from the true value and mainly harms accuracy.
Example of Systematic Error
A balance not zeroed reads 0.05 g when empty. Every mass is 0.05 g too high. The data can look precise but are all biased.
Random Error
Random error is unpredictable variation between measurements, caused by noise, small technique differences, or environment. It mainly harms precision.
Example of Random Error
When reading a meniscus, tiny changes in eye position cause slight over- or under-reading, making values scatter around the true volume.
Fixing Errors
Reduce systematic error by calibration and controls. Reduce random error by better technique, standardized procedures, and more replicates.
Biology Lab Scenarios: Spot the Error Type
Pipette Calibration Drift
A 1000 µL pipette actually delivers 920 µL every time. This is a systematic error: a consistent bias that makes all concentrations lower than expected.
Inconsistent Incubation Times
Incubation times vary from 9 to 11 minutes instead of exactly 10. This introduces random error, increasing scatter in enzyme activity measurements.
Dirty Cuvette
A cuvette with fingerprints is used for all readings. Dirt scatters light in a similar way each time, causing mainly systematic error in absorbance.
Counting Colonies
Small differences in plating and mixing make colony counts vary between plates. This is mainly random error, handled with replication and statistics.
Significant Figures and Units: Recording Data Correctly
Why Sig Figs Matter
Significant figures show how precisely you measured something. Do not report more digits than your instrument can justify, or you will overstate your precision.
Instrument Limits
If a balance reads to 0.001 g, 2.437 g is appropriate. Writing 2.4370 g suggests extra precision you do not actually have.
Sig Fig Basics
Non-zero digits are significant. Zeros between non-zero digits are significant. Leading zeros are not. Trailing zeros after a decimal point are significant.
Calculation Rules
For multiplication/division, match the least number of significant figures. For addition/subtraction, match the least number of decimal places.
Units Are Essential
Always record units: g, mL, °C, cells/mL, etc. Use SI units and consistent prefixes (milli-, micro-, nano-) across your dataset.
Reporting Uncertainty
Modern guidelines expect you to pair means with uncertainty (e.g., 2.43 ± 0.07 µmol/min) using compatible significant figures and units.
Practice: Sig Figs and Units
Work through these and compare with the suggested answers.
- A spectrophotometer shows an absorbance of `0.234`. How should you record it in your notebook?
- a) 0.2
- b) 0.23
- c) 0.234
- d) 0.2340
- You measure the length of a root with a ruler marked every 1 mm and read 5.6 cm. What is a reasonable way to record this?
- a) 5.6 cm
- b) 5.60 cm
- c) 5.600 cm
- You weigh a tube: empty = 1.235 g, with sample = 3.456 g. What is the sample mass (with correct sig figs)?
- Raw subtraction: 3.456 g − 1.235 g = 2.221 g
- Considering decimal places, your answer should be:
- a) 2.2 g
- b) 2.22 g
- c) 2.221 g
- You pipette 250 µL of a solution. Which recording is best?
- a) 0.25 mL
- b) 250 µL
- c) 0.250 mL
Suggested answers (check yourself):
- c) 0.234 (matches instrument precision)
- a) 5.6 cm (you can justify one decimal place with 1 mm markings)
- c) 2.221 g (both inputs have 3 decimal places, so keep 3)
- b) 250 µL (clear and uses a standard volume unit for pipettes)
Quick Check: Accuracy, Precision, and Error
Test your understanding with this question.
You are measuring the concentration of a protein standard that is known (from an external certified lab) to be 2.00 mg/mL. Your five measurements are: 1.62, 1.63, 1.61, 1.62, 1.63 mg/mL. Which statement best describes your results?
- They are accurate but not precise.
- They are precise but not accurate, suggesting a systematic error.
- They are neither accurate nor precise.
- They are both accurate and precise; any difference from 2.00 mg/mL is random noise.
Show Answer
Answer: B) They are precise but not accurate, suggesting a systematic error.
All measurements cluster tightly around 1.62–1.63 mg/mL, so they are precise. However, they are consistently lower than the true 2.00 mg/mL, indicating a systematic error (bias) that reduces accuracy.
Key Term Review
Use these flashcards to reinforce the main terms before you move on.
- Accuracy
- How close a measurement is to the true or accepted value. High accuracy means low systematic error.
- Precision
- How close repeated measurements are to each other. High precision means low random variation.
- Systematic error
- Consistent, repeatable error that shifts all measurements in the same direction, affecting accuracy (bias). Often caused by miscalibration or flawed procedure.
- Random error
- Unpredictable variation between measurements due to chance factors like instrument noise or small technique differences. Mainly affects precision.
- Significant figures
- Digits in a number that carry meaningful information about its precision. Determined by the measurement instrument and used to avoid overstating certainty.
- Units
- Standard quantities (e.g., g, mL, °C, mol/L, cells/mL) attached to measurements. Essential for interpreting biological data and ensuring comparability.
- Calibration
- Process of adjusting or checking an instrument against a known standard to minimize systematic error and ensure accurate measurements.
Key Terms
- Units
- Standardized quantities (such as grams, liters, meters, seconds) used to express and compare measurements in science.
- Accuracy
- The degree to which a measured value agrees with the true or accepted value; high accuracy implies low systematic error.
- Precision
- The degree to which repeated measurements under unchanged conditions show the same results; high precision implies low random error.
- Calibration
- The act of comparing and adjusting an instrument's readings to match a known standard, to improve measurement accuracy.
- Random error
- Unpredictable fluctuations in measurements caused by uncontrollable variables, leading to scatter around the true value.
- Systematic error
- A consistent, directional error arising from faulty equipment, calibration, or procedures, which biases measurements away from the true value.
- Significant figures
- Digits in a numerical value that are considered reliable and meaningful, reflecting the precision of the measurement.