Repeated Measurements & Data Explorer | Neutron STEM Lab

1 · Choose your data

Start with an example or your measurements

All analysis stays in this browser. Original cells and row IDs are retained when you change units or exclude a reading.

Import CSV or paste a table

CSV fileDelimiter First row contains column names

CSV text

Up to 2 MB, 10,000 readings, and 16 columns. Use a decimal point; quote fields containing commas. Units in square brackets are detected. Empty and nonnumeric values are shown in the preview.

Save or restore an analysis project

Restore project JSON

Project JSON preserves original cells, units, mappings, exclusions and reasons, fit settings, and the uncertainty budget. Annotated CSV includes every original row; formula-like text is escaped for spreadsheets. Use JSON for exact restoration.

2 · Map columns and choose the method

What do you want to measure?

X columnY measurementY standard uncertainty columnX display unitY display unitInvalid mapped rowsRegressionPolynomial degreeConfidence level

Statistics and regression use the same included rows with valid mapped values. Error bars show ±1 standard uncertainty in Y; regression remains unweighted and treats X as exact.

Assign original column units

These labels describe the values in your original file. Assigning a label does not convert raw values. Use the display-unit controls above to convert values without changing the original data.

Uncertainty budget for the mean

Type A is s/√n. Add independent Type B components in the current Y display unit. Enter a half-width for rectangular/triangular distributions, standard uncertainty directly, or certificate expanded uncertainty with its k. A known correction changes the mean; its remaining uncertainty belongs in this budget.

Known additive correctionOutput coverage factor k

Resolution half-width = display step/2. Avoid counting quantization twice when repeated scatter already captures it. k = 2 is often approximately 95% for near-normal output with sufficient information; it is not an exact coverage guarantee.

Ready. Check the columns and analyze the example, or import your own data.

3 · Inspect, compare, and explain

Your analysis

Data plot

Measurements and model

Run the current setup to draw this plot. Use the buttons above to zoom and pan.

Regression and calibration

Evaluate fit at X

Residuals: observed minus fitted

Run the current setup to draw this plot. Use the buttons above to zoom and pan.

Residual data by original row

Row	X	Residual

First 100 residuals shown. Download the analysis results for all rows.

Uncertainty of the corrected mean

Independent components combine in quadrature. The statistical confidence interval above covers the population mean under the sampling assumptions; expanded measurement uncertainty also includes the Type B budget.

Inspect original readings

Rows outside Q1 − 1.5 IQR or Q3 + 1.5 IQR are flagged for investigation after analysis. This is a descriptive rule, not proof of an error. A zero IQR can flag any departure from the central value. No row is automatically deleted.

Reason to record when excluding a row

Measurements

Instrument readings

Included readings: —
Sample mean: —
Sample standard deviation: —
Standard error of the mean: —

Theory

Equations and model

Describe a sample without hiding missing data

The sample mean summarizes location. The sample variance uses n−1 because the mean was estimated from the same readings. A single observation can have a mean but cannot estimate sample scatter. Missing and nonnumeric mapped values are listed or rejected according to your selected policy.

x̄ = Σxᵢ/ns² = Σ(xᵢ − x̄)²/(n − 1)SEM = s/√n

Confidence and screening

A Student t interval describes uncertainty in the population mean under the stated sampling assumptions. It does not include unknown calibration bias. Quantiles use linear interpolation between ordered observations. IQR fences are a reason to investigate unusual data, not a deletion rule.

CI = x̄ ± t((1 + confidence)/2, n − 1) · s/√nIQR = Q3 − Q1; fences = Q1 − 1.5 IQR, Q3 + 1.5 IQR

Validation

Independent checks

Sampling adequacyNot run

At least two included readings are required to estimate scatter and the standard error.

Expected: —
Simulated: —
Error: —
Tolerance: 0%

Run the experiment to perform this check.

Selected method is definedNot run

Check the selected analysis prerequisites, without treating mathematical validity as proof of physical adequacy.

Expected: —
Simulated: —
Error: —
Tolerance: 0%

Run the experiment to perform this check.

Engineering interpretation

Run the experiment to generate an engineering interpretation.

Assumptions and limitations

Assumptions

Observations used for standard error and Student t intervals are independent and sampled from a stable process; small-sample t intervals assume normal observations.
Regression is unweighted, includes an intercept, and treats X as exact. Errors have constant variance in the fitted space.
The uncertainty budget components are independent. The uncertainty of a mean is distinct from the scatter of individual readings.
Declared original units describe the raw cells. Display conversion changes presentation, not those raw cells.

Limitations

Import is bounded to 2 MB, 10,000 data rows, 16 columns, and 1,000 characters per cell. Missing values are never interpreted as zero.
Polynomial degree is limited to 1–5; fits need more observations than coefficients and distinct X values. Exponential fitting requires Y > 0.
IQR fences identify unusual values descriptively; they do not diagnose faults or delete readings. A zero IQR can flag every departure from the central value.
Weighted fitting, uncertainty in X, inverse calibration, and automatic model selection are not included. Do not infer validity from R² alone.
A chosen k is not an automatic confidence guarantee. Correlated budget components should be handled in the propagation experiment.

Local experiment export

Save your measurements and setup

Exports are generated in your browser. No account or server upload is required.

Settings JSON: Current parameters and instrument controls, including waveform, output enable, scope coupling, timebase, trigger, and cursors when present. Data labs also include the dataset, mappings, exclusions, budget, or propagation setup.
Measurements CSV: Completed instrument readings with labels, units, and descriptions.
Plot PNG: The current canvas-based scope, transient, sweep, or statistics visualization when available.
Summary: Markdown report with objectives, setup, measurements, validation, interpretation, assumptions, and graded guided concept-check results.

Ready to export the current local experiment state.

Learning objectives

What this experiment should establish

Distinguish individual-reading scatter from uncertainty in the estimated mean.
Map CSV columns and units while preserving original observations.
Use plots and IQR flags to investigate data quality without automatically deleting readings.

Check your understanding

Questions to answer from the experiment

Which quantity estimates the uncertainty of the mean of n independent repeated readings?
Why use Student t instead of a fixed 1.96 multiplier for a small sample?
A point falls outside the 1.5 IQR fences. What should you do first?
The readings drift steadily with time. Which statement is most defensible?

Continue learning

Sources and model review

Reviewed 2026-09-16. The educational model exposes its assumptions and validation; source references do not imply external certification.

NIST/SEMATECH: Confidence limits for the mean — Student t confidence intervals and sampling assumptions.
NIST Technical Note 1297 — Type A/B, combined standard uncertainty, expanded uncertainty, and reporting.
JCGM 101: Propagation of distributions using a Monte Carlo method — Distribution propagation and numerical interpretation. This lab uses a bounded fixed sample count, not an adaptive convergence certification.