3.3.1 Error Analysis

• Match the error type with its definition and impact on results:

  Random Errors ↔️ Fluctuations in measurements that occur randomly, causing results to scatter around the true value

  Systematic Errors ↔️ Errors that occur consistently in the same direction, biasing results away from the true value
• What is a random error?

  Fluctuations in measurements
• What is an example of a source of systematic errors?

  Faulty equipment
• Changes in temperature during an experiment can cause random errors.
• Environmental variations during an experiment can cause fluctuations in results.
• An uncalibrated thermometer consistently reading too high is an example of a systematic error.
• Regularly calibrating instruments is a method for reducing systematic errors.
• When calculating percentage uncertainty, you divide the uncertainty by the measured value.
• A lower percentage uncertainty indicates a more reliable measurement.
• Combining uncertainties allows you to quantify the overall reliability of a result that depends on multiple measured values.
• Random errors in measurements cause results to scatter around the true value
• What are the primary effects of systematic errors on experimental results?

  Biased away from true value
• What is the impact of random errors on experimental measurements?

  Scatter around true value
• Poor technique in experiments can lead to variable measurements
• Error analysis involves identifying, assessing, and quantifying the types of errors present in an experiment
• Identifying and addressing errors improves the reliability and accuracy of experimental outcomes.
• Identifying and addressing both systematic and random errors is crucial for improving experimental outcomes.
• Environmental factors, such as temperature, can be a source of systematic errors.
• What are random errors caused by?

  Unpredictable fluctuations
• Match the error type with its definition:

  Random Errors ↔️ Fluctuations in measurements

  Systematic Errors ↔️ Consistent bias in measurements
• What is a common source of random errors in experiments?

  Poor technique
• Order the methods for reducing random errors:

  1️⃣ Repeated measurements

  2️⃣ Improving technique

  3️⃣ Using more precise instruments
• What is percentage uncertainty a measure of?

  Reliability of an experimental result
• What is the formula used to combine uncertainties when multiple measurements are taken?

  Propagation of errors
• Match the uncertainty type with its definition:

  Absolute Uncertainty ↔️ Range within which the true value likely lies

  Relative Uncertainty ↔️ Uncertainty as a fraction of the measured value

  Percentage Uncertainty ↔️ Uncertainty as a percentage of the measured value
• Systematic errors occur unpredictably and randomly in experiments.

  False
• Systematic errors consistently bias measurements in the same direction
• Calibration is a method for reducing systematic errors by ensuring instruments provide accurate measurements.
• Imprecise instruments can cause random errors in experiments.
• Steps to reduce systematic errors in experiments:

  1️⃣ Calibration of instruments

  2️⃣ Equipment maintenance

  3️⃣ Controlling environmental factors

  4️⃣ Procedural consistency
• Percentage uncertainty is calculated by dividing the uncertainty by the measured value
• A lower percentage uncertainty indicates a more reliable measurement.
• The combined uncertainty is denoted by uc in the propagation of errors formula.
• Understanding different uncertainty types helps communicate data precision.
• If error bars do not overlap, the difference between data points is statistically significant.
• What are the two primary types of errors in error analysis?

  Systematic and random errors
• What is a systematic error?

  Error in the same direction
• Systematic errors arise consistently and bias results in a predictable direction
• What are common sources of random errors?

  Poor technique and imprecise instruments
• Inconsistent use of measuring devices leads to variable measurements