Exact descriptive statistics
Expected: Mean 5; sample variance 32/7
Observed: Mean 5; variance 4.571428571428571
passMeasurement, Data Analysis & Uncertainty Lab
Understand what your measurements support. Import readings, inspect their distribution, fit a calibration curve, and trace uncertainty from the inputs to your result. Start with a guided example or bring your own CSV. Everything runs locally in your browser.
Choose an experiment
Follow the rows in order, or open the analysis you need. Every experiment includes equations, assumptions, validation, guided questions, and exports.
Repeated Measurements & Data Explorer
Import CSV or use repeated instrument readings to compare mean, scatter, standard error, confidence intervals, histograms, and unusual observations.
Calibration, Regression & Residuals
Fit linear, polynomial, or exponential measurement models, examine residuals, and distinguish confidence intervals for a fitted response from prediction intervals.
Type A, Type B & Expanded Uncertainty
Build an explicit uncertainty budget for repeated measurements, apply a known correction, and see why averaging does not eliminate calibration uncertainty.
Analytical Uncertainty Propagation
Follow exact sensitivity coefficients through engineering equations and inspect how input correlation changes combined and expanded uncertainty.
Monte Carlo Uncertainty & Model Comparison
Propagate input distributions with a reproducible seed, compare output statistics with first-order uncertainty, and interpret empirical coverage intervals.
What the results mean
Sample standard deviation describes the scatter of individual observations. Standard error describes random uncertainty in their mean when the readings are independent. A confidence interval for that mean has different assumptions and a different purpose from a prediction interval for a future reading.
Measurement uncertainty also includes information outside the sample, such as a calibration certificate or instrument resolution. Convert those specifications to standard uncertainties, identify their sensitivities, then combine them. The lab keeps the uncertainty budget visible so a precise average does not hide a systematic limitation.
For a nonlinear equation, Monte Carlo can reveal asymmetry or higher-order effects missed by local linearization. Its empirical coverage interval describes simulated output values. Its simulation standard error describes finite-run numerical error. Increasing the number of simulations does not improve the underlying instrument.
Use your own measurements
Upload comma, semicolon, or tab-delimited text with up to 10,000 data rows and 16 columns. Put units in square brackets in the header, such as Voltage [mV], or assign them after import. Preview the original cells, map X and Y, and explicitly choose how missing values are handled.
A flagged point stays in the dataset. If an investigation justifies excluding it, record the reason. Saved project JSON and annotated CSV preserve the original rows and inclusion decisions. A portable project restores the dataset, units, fit settings, and budget without requiring an account.
Generate readings in the Instrumentation Lab, then use its transfer action to analyze that exact sequence here. Existing measurement summaries can also be imported as CSV; confirm their mapped columns and units.
Numerical validation7/7 published benchmark checks passReviewed 2026-09-16
View benchmark details
Small-sample Student t interval
Expected: 95% critical value with 9 df = 2.2621571628
Observed: 2.262157162798201
passScaled QR calibration
Expected: Y = 1 + 2X, evaluated at X = 2.5 gives 6
Observed: Y = 6; RMSE 0
passType A/B combination
Expected: uc = sqrt(1/3 + 0.01)
Observed: 0.5859465277082316
passTemperature differences
Expected: 0 °C = 273.15 K, but u = 1 °C becomes 1 K
Observed: Value 273.15 K; uncertainty 1 K
passCorrelated analytical propagation
Expected: Sum uncertainty sqrt(7)
Observed: 2.6457513110645907
passSeeded Monte Carlo comparison
Expected: Exact replay; output SD within 4% of sqrt(7)
Observed: SD 2.668657048095092; identical replay true
passAssumptions, limits, and references
The models support engineering learning with explicit mathematical checks. Regression treats X as exact and is unweighted. Correlated sampling is limited to jointly normal inputs. Monte Carlo is bounded to 100,000 samples and does not automatically certify percentile convergence. Your experimental design, distribution assumptions, and physical model remain part of the analysis.
Methods draw on NIST/SEMATECH confidence interval guidance, NIST Technical Note 1297, and JCGM 101 on Monte Carlo propagation. These references do not imply external certification.