Introduction to Measuring in Biology
In Biology, we aren't just looking at pretty cells under a microscope; we are often measuring things like the volume of oxygen produced by a plant or the mass of a piece of potato. But how do we know if our measurements are actually "good"? In this chapter, we explore how to describe the quality of our data using three key concepts: accuracy, precision, and uncertainty. Understanding these will help you evaluate your practical work in the Practical Endorsement (PAGs) and ace your written exams!
1. Accuracy vs. Precision: The Dartboard Challenge
Many people use these words to mean the same thing, but in Biology A Level, they have very specific meanings. A great way to remember the difference is to imagine throwing darts at a board.
Accuracy
Accuracy refers to how close a measurement is to the true value. If the "true" concentration of a glucose solution is \(0.5\text{ mol dm}^{-3}\) and your result is \(0.49\text{ mol dm}^{-3}\), your measurement is very accurate.
Precision
Precision refers to how close repeated measurements are to each other. It is about consistency. If you measure the same leaf three times and get \(5.2\text{ cm}\), \(5.2\text{ cm}\), and \(5.1\text{ cm}\), your results are precise because they are very similar.
The Analogy:
• Accurate and Precise: All your darts hit the bullseye.
• Precise but NOT Accurate: Your darts are all bunched together, but they are in the bottom left corner instead of the center.
• Accurate but NOT Precise: Your darts are scattered all over the board, but their average position is the center.
Key Takeaway
Accuracy is about being "correct" (hitting the target), while precision is about being "consistent" (hitting the same spot repeatedly).
2. Understanding Uncertainty
No piece of equipment is perfect. Uncertainty is the "doubt" that exists about any measurement. It is the range in which the true value is likely to lie.
Where does uncertainty come from?
Every piece of apparatus has a limit to how small it can measure. This is called its resolution. For example, a standard ruler has a resolution of \(1\text{ mm}\).
The "Half-Division" Rule
As a general rule for OCR Biology, the uncertainty of a single reading is usually plus or minus (\(\pm\)) half of the smallest graduation on the scale.
Example:
If you use a thermometer where the smallest lines are \(1.0\text{ }^\circ\text{C}\) apart:
The uncertainty is \( \pm 0.5\text{ }^\circ\text{C} \).
If you record a temperature of \(25.0\text{ }^\circ\text{C}\), the true value is somewhere between \(24.5\text{ }^\circ\text{C}\) and \(25.5\text{ }^\circ\text{C}\).
Common Pitfall: Rulers and Burettes
Don't worry if this seems tricky, but some instruments require two readings. For a ruler, you align the "zero" (reading 1) and then look at the length (reading 2). Because there is a \(\pm 0.5\text{ mm}\) uncertainty at both ends, the total uncertainty for the length is \(0.5 + 0.5 = 1.0\text{ mm}\).
Quick Review
Uncertainty is often written as a margin of error, such as \(20\text{ cm}^3 \pm 0.5\text{ cm}^3\).
3. Calculating Percentage Error
To understand how much the uncertainty actually matters, we calculate the percentage error. This tells us what proportion of our measurement might be "wrong."
You must recall this formula for your exam:
\( \text{Percentage Error} = \frac{\text{Uncertainty}}{\text{Measured Value}} \times 100 \)
Step-by-Step Example
Imagine you are measuring \(5.0\text{ cm}^3\) of enzyme solution using a pipette that has an uncertainty of \(\pm 0.05\text{ cm}^3\).
Step 1: Identify the uncertainty (\(0.05\)).
Step 2: Identify the measured value (\(5.0\)).
Step 3: Plug them into the formula:
\( \text{Percentage Error} = \frac{0.05}{5.0} \times 100 = 1\% \)
How to reduce percentage error
There are two ways to make your results more reliable:
1. Use a larger measurement: Measuring \(100\text{ cm}^3\) with the same equipment will result in a much lower percentage error than measuring \(1\text{ cm}^3\).
2. Use higher-resolution equipment: Switch from a measuring cylinder (uncertainty \(\pm 0.5\)) to a pipette (uncertainty \(\pm 0.05\)).
Key Takeaway
The smaller the measurement you take, the higher the percentage error will be for that specific piece of equipment.
4. Anomalies and Limitations
When evaluating your practical results (Module 1.1.4), you need to look out for anomalies. These are data points that do not fit the overall trend or pattern of the results.
What should you do with an anomaly?
• If you spot it during the experiment: Repeat the measurement.
• If you spot it after the experiment: Identify it, but do not include it when calculating your mean (average).
Limitations in Procedures:
In your exam, you might be asked how to improve precision or accuracy.
• To improve accuracy: Calibrate equipment or use a colorimeter instead of "judging by eye."
• To improve precision: Use equipment with a higher resolution (smaller divisions) to reduce uncertainty.
Summary Checklist
Quick Review:
• Accuracy: How close you are to the truth.
• Precision: How close your repeats are to each other.
• Uncertainty: The \(\pm\) range of a measurement.
• Percentage Error Formula: \( \frac{\text{Uncertainty}}{\text{Value}} \times 100 \).
• Anomalies: Weird results that should be excluded from the mean.
Note: For more information on how to round your final answers after calculating error, see the chapter on "Units, standard form and significant figures."