Measurement¶

Notes¶

• Most measurements are indirect: What we actually measure is different what we want to study
• For eg: measuring temperature with mercury thermometer: we look at the difference in mercury height
• Measurement can change the thing that you are measuring

Measurement Stability¶

Temporal & Spatial

Repeated measurements are taken at different times, locations, conditions

• How constant is the sample
• How constant is the measurement process
• How constant is the measurement context

Observation Decomposition¶

Process observation

• Process True Value
• Process Error
• Measurement Error
• Procedure Error
• Sensor Error

Error Components¶

• Systematic errors
• Produces bias
• We try to correct systematic error, but can never be totally free from systematic error
• We can put an upper limit on the expected systematic errors
• Random errors: Can be evaluated statistically, through repeated measurements

Measurement Metrics¶

• Accuracy: 1 - systematic error
• Precision: standard deviation of repeated measurements (random error component)
• Repeatability: standard deviation of repeated measurements under conditions as nearly identical as possible
• Reproducibility: standard deviation of repeated measurements under conditions that vary (different operators, instruments, days, time)

Uncertainty Types¶

• Type A: Process Noise
• Caused by fluctuations in nature that propagate through measurement model
• obtained by statistical analysis of repeated measurements
• Type B: Measurement Noise
• Types
  • Measurement Procedure Noise
  • Incomplete definition of measurement
  • Imperfect realization of procedure
  • Sample not representative
  • Environmental conditions
  • Biases in reading analog scales
  • Instrument resolution
  • Values of constants used in calculations
  • Changes in measuring instrument performance since last calibration
  • Approximations/assumptions in measurement model
  • Sensor Noise
• Evaluated by scientific judgement (Prior experience or data, manufacture’s specs)

Effective Degrees of Freedom¶

When using combined uncertainty , we assume that the measurement is t-distributed

Welch-Satterthwaite approximation $$ \text{DOF}_\text{eff} = \dfrac{(\sum u_i²⁾2}{\sum (u_i^4/\text{DOF}_i)} $$

Replication¶

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