CSEC Essential Distinction: Understanding the difference between accuracy and precision is fundamental to experimental physics and is frequently tested in CSEC exams. These concepts determine how you evaluate measurements, instruments, and experimental results. According to the textbook: “We judge the accuracy of the result obtained for the value of a quantity by the closeness or otherwise of the result to the ‘true’ value. We judge the precision… by the width of the range of values within which the true value lies.”
The Fundamental Difference
Definition: How close a measurement is to the true or accepted value.
Key Question: “Is my result correct?”
Depends on: Systematic errors, calibration, correct technique
Improve by: Calibrating instruments, eliminating systematic errors, using correct method
Example: A clock that shows the exact correct time is accurate.
Definition: How close repeated measurements are to each other (reproducibility).
Key Question: “Can I get the same result again?”
Depends on: Random errors, instrument design, skill of experimenter
Improve by: Using better instruments, reducing random errors, improving technique
Example: A clock that consistently shows 8:05 every day (even if wrong) is precise.
Imagine shooting arrows at a target. The bullseye represents the true value.
Accurate but NOT Precise
Close to bullseye but scattered
Precise but NOT Accurate
Grouped together but far from bullseye
Both Accurate AND Precise
Grouped together at bullseye
Neither Accurate NOR Precise
Scattered and far from bullseye
Accuracy in CSEC Physics Experiments
CSEC Perspective: “A satisfactory result for the value of a quantity is one that is near to the ‘true’ value or the ‘accepted’ or ‘expected’ value of that quantity.” In your SBA work, accuracy is assessed by how close your experimental result is to the theoretical or accepted value.
Factors Affecting Accuracy
- Systematic errors: Consistent errors that affect all measurements in the same way
- Instrument calibration: Whether instruments are properly zeroed and calibrated
- Experimental technique: Correct procedure and methodology
- Environmental conditions: Temperature, pressure, humidity if not controlled
- Parallax errors: Not reading instruments perpendicularly
Scenario: Measuring ‘g’ using a pendulum. The accepted value is 9.81 m/s².
- Accurate result: 9.80 m/s² (close to accepted value)
- Inaccurate result: 11.2 m/s² (far from accepted value)
Improving accuracy: Use small angles (<10°), ensure rigid support, minimize air resistance, use long pendulum to reduce timing errors.
Precision in CSEC Physics Experiments
CSEC Definition: “The precision of an instrument is the maximum error there can be in measuring the size of a quantity with that instrument.” Precision relates to the smallest division on an instrument and the reproducibility of measurements.
Factors Affecting Precision
- Instrument design: Quality and sensitivity of measuring device
- Smallest division: Value of the smallest scale marking
- Random errors: Unpredictable variations in measurements
- Experimenter skill: Consistency in technique and reading
- Environmental stability: Fluctuations in conditions during measurements
Instrument Precision Examples
| Instrument | Precision | Explanation |
|---|---|---|
| Metre rule (mm markings) | 1 mm | Smallest division is 1 mm |
| Vernier caliper | 0.1 mm | Can measure to 0.1 mm |
| Micrometer screw gauge | 0.01 mm | Most precise common length instrument |
| Digital stopwatch | 0.01 s | Displays to hundredths of a second |
| Laboratory thermometer | 0.5°C | Typically has 0.5°C divisions |
| Burette | 0.1 cm³ | Can measure to 0.1 cm³ (0.1 mL) |
Key Point: The micrometer is 10 times more precise than the vernier caliper, which is 10 times more precise than a metre rule.
Scenario: Measuring the diameter of a wire with different instruments:
- Metre rule: 0.5 cm (one reading)
- Vernier caliper: 0.56 cm (more precise – to 0.01 cm)
- Micrometer: 0.557 cm (most precise – to 0.001 cm)
Precision demonstration: If 5 measurements with a micrometer give: 0.557 cm, 0.558 cm, 0.557 cm, 0.556 cm, 0.558 cm → these are precise (close to each other).
Improving Accuracy and Precision in Your SBA Work
1. Calibrate instruments before use (zero ammeters, thermometers)
2. Eliminate systematic errors (parallax, zero errors)
3. Use correct experimental technique
4. Control environmental conditions where possible
5. Compare with accepted values when available
1. Use more precise instruments (micrometer vs ruler)
2. Take multiple readings and calculate mean
3. Reduce random errors through careful technique
4. Use digital instruments for consistent readings
5. “Spread the error” by measuring multiple items
Measure many items together, then divide. Examples:
• Measure 20 oscillations of a pendulum, divide by 20 for period
• Measure total thickness of 100 pages, divide by 100 for one page
• Measure total mass of 50 ball bearings, divide by 50
This reduces the impact of measurement uncertainty on individual items.
⚠️ Common CSEC Exam Confusions
- Thinking precision means accuracy: A precise instrument can give inaccurate results if not properly used or calibrated.
- Confusing instrument precision with measurement precision: A precise instrument used poorly gives imprecise measurements.
- Believing digital instruments are always accurate: Digital displays can be precise (consistent) but inaccurate if poorly calibrated.
- Assuming more decimal places means better accuracy: Reporting 2.45678 cm from a ruler with 1 mm precision is misleading – the extra digits suggest false precision.
- Forgetting that precision depends on the instrument’s smallest division: The last digit in a measurement should reflect the instrument’s precision.
Accuracy, Precision, and Significant Figures
CSEC Connection: The degree of significance (significant figures) in your results should reflect the precision of your measurements. If you use a metre rule (precision = 1 mm), don’t report a length as 15.236 cm – this suggests 0.001 cm precision which the rule cannot provide. Report as 15.2 cm instead.
| Situation | Appropriate Significant Figures | Reason |
|---|---|---|
| Metre rule measurement (mm precision) | 3 sig figs (e.g., 15.2 cm) | Can estimate to 0.1 cm (1 mm) |
| Vernier caliper measurement | 3-4 sig figs (e.g., 1.56 cm) | Precision to 0.01 cm (0.1 mm) |
| Micrometer measurement | 4 sig figs (e.g., 0.557 cm) | Precision to 0.001 cm (0.01 mm) |
| Digital stopwatch | 3-4 sig figs (e.g., 2.45 s) | Displays to 0.01 s |
| Analogue thermometer (0.5°C divisions) | 3 sig figs (e.g., 24.5°C) | Can estimate to 0.1°C |
Applying These Concepts in Your SBA Reports
SBA Assessment Insight: Examiners look for evidence that you understand accuracy and precision. In your practical reports, you should:
- State the precision of instruments used
- Discuss factors affecting accuracy in your experiment
- Explain steps taken to improve both accuracy and precision
- Use appropriate significant figures in your results
- Comment on the accuracy of your final result compared to accepted values
- Suggest improvements for better accuracy/precision
In the “Discussion” section of your report:
“The precision of the metre rule used was 1 mm, so all length measurements were recorded to the nearest 0.1 cm. To improve accuracy, we ensured the rule was vertical and read at eye level to avoid parallax error. The main limitation affecting precision was reaction time when timing oscillations; to minimize this, we timed 20 oscillations and divided by 20. Our calculated value of g was 9.75 m/s², which compares reasonably with the accepted value of 9.81 m/s², suggesting good accuracy. The percentage difference was 0.6%, indicating satisfactory experimental technique.”
CSEC Exam Practice
Explanation: The measurements are close to each other (range: 15.2-15.4 cm), showing good precision (reproducibility). However, they are all about 0.2-0.4 cm higher than the actual value (15.0 cm), showing poor accuracy. This suggests a systematic error, such as a zero error in the ruler or parallax error.
Explanation: The micrometer has the smallest scale division (typically 0.01 mm), compared to the vernier caliper (0.1 mm) and metre rule (1 mm). The textbook states: “Whereas the screw gauge would allow a reading to the nearest 0.001 cm, the vernier caliper will give a reading to only 0.01 cm. We could say that the screw gauge is ten times more precise than the vernier caliper.”
Explanation: If the balance reads to the nearest 1 g, the maximum error is ±0.5 g. The actual mass could be as low as 140 – 0.5 = 139.5 g or as high as 140 + 0.5 = 140.5 g. As stated in the textbook: “The ‘limits of error’ or the ‘limits of uncertainty’ of the reading for the mass are ±0.5 g… The mass is somewhere in the range (139.5–140.5 g).”
Group A: 9.81, 9.82, 9.80, 9.81 m/s²
Group B: 8.5, 9.1, 10.2, 8.9 m/s²
Group C: 11.2, 11.3, 11.2, 11.2 m/s²
Group D: 9.79, 9.78, 9.80, 9.79 m/s²
Which group has (i) the most accurate results, (ii) the most precise results?
Explanation:
(i) Accuracy: The accepted value of g is 9.81 m/s². Group D’s results (9.79-9.80) are closest to this value.
(ii) Precision: Group C’s results (11.2-11.3) are closest to each other (most reproducible), even though they’re inaccurate.
Group A is both accurate and precise. Group B is neither accurate nor precise.
1. Zero error: Not zeroing the instrument before use
2. Poor technique: Applying too much pressure, misreading the scale
3. Calibration issues: Instrument not properly calibrated
4. Wrong use: Using instrument outside its designed range
5. Systematic errors: Consistent errors in measurement method
Precision refers to reproducibility, not correctness. A micrometer can consistently give the same wrong measurement if there’s a systematic error.
Explanation:
Time for 10 oscillations = 14.0 s ± 0.4 s (reaction error both starting and stopping)
Time for 1 oscillation = 1.40 s ± 0.04 s
Maximum error = 0.08 s (2 × 0.04 s)
The error is about 0.1 s, so we should express the result to the nearest 0.1 s.
1.40 s rounded to nearest 0.1 s = 1.4 s
As the textbook explains: “The degree of significance must therefore reflect this fact and so we must express the time for one swing to the nearest tenth (0.1) of a second and not to the nearest 0.01s.”
🎯 CSEC Summary: Accuracy = closeness to true value. Precision = reproducibility of measurements. A good experiment aims for both. Your SBA marks depend on demonstrating understanding of both concepts through proper instrument use, appropriate significant figures, and thoughtful error discussion.
Quick Reference Guide
- Accuracy: “Am I right?” → Systematic errors → Improve by calibration
- Precision: “Can I repeat it?” → Random errors → Improve by better instruments/technique
- Instrument precision: Value of smallest scale division
- Significant figures: Should match measurement precision
- SBA requirement: Discuss both accuracy and precision in your reports
- Common confusion: Precise ≠ Accurate (a clock can be consistently wrong)