Replicate Statistics for a Lab Result

The formula

This is the expression the tool evaluates. Every term is named underneath, with the unit it must be supplied in.

How the result is derived

Step by step, from the values you type to the figure on screen.

1. The 13 inputs are read from the form on every keystroke: Specimens Measured, Specimen 1, Specimen 2, Specimen 3, Specimen 4, Specimen 5, Specimen 6, Specimen 7, Specimen 8, Specimen 9, Specimen 10, Specimens the Method Requires and Specification Minimum.
2. Each value is checked against the accepted range in the input table below. A value outside its range stops the calculation rather than producing a misleading figure — the results blank out and a message appears.
3. The validated values are substituted into the expression above, which resolves Coefficient of Variation together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Mean, Standard Deviation (n-1), Range, Standard Error of the Mean, t Used for 95%, 95% Confidence Half-Width, Mean Could Be As Low As, Lower Bound Minus Specification and Specimens Short of the Method — come from the same pass, so they always describe the same case as the headline figure.
5. Results are rounded for display only. The full-precision value is used throughout the chain, so reading a rounded intermediate figure back into the tool by hand can shift the last digit.

What each input means

Where to read each value on the floor, the unit it must be in, and the range the tool accepts.

What the tool returns

The headline figure and every supporting value it is built from.

Worked example

The tool loads with this case already solved — the Coefficient of Variation shown above is its answer. Change one value and the difference from this baseline is the sensitivity of the result to that variable.

How to use it

1. Work through the input groups in order — Readings and Against the method. The defaults are a realistic case, so you can change one value at a time and watch what moves.
2. There is no calculate button. Every figure recalculates as you type or drag, which is what makes this usable for a what-if sweep rather than a single answer.
3. Read Coefficient of Variation in the dark results panel — that is the headline figure, expressed in %.
4. Check the supporting rows underneath (Mean, Standard Deviation (n-1), Range, Standard Error of the Mean, t Used for 95%, 95% Confidence Half-Width, Mean Could Be As Low As, Lower Bound Minus Specification and Specimens Short of the Method) before acting on the headline — they are where an implausible input usually shows itself first.
5. Reset to defaults returns every field to the reference case, which is the quickest way to check whether a surprising result came from the tool or from an input you had changed earlier.

Where this is used

• Process planning — establishing Coefficient of Variation before a trial is booked, so machine time and material in Textile Testing & Quality Control are committed against a calculated figure rather than an estimate.
• Costing and quotation — Coefficient of Variation is an input to the cost sheet, and quoting from a worked number rather than a remembered one is what keeps a margin intact.
• Troubleshooting — when the floor result drifts from plan, entering the measured values (starting with Specimens Measured) shows how much of the gap in Coefficient of Variation each variable explains.
• Teaching and study — the accepted ranges bracket normal Textile Testing & Quality Control practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Assumptions and limits

• The standard deviation is the sample form, dividing by n-1, because these specimens are a sample of the fabric and not the whole of it. The confidence half-width uses the t value for n-1 degrees of freedom rather than 1.96: at five specimens the correct interval is 42% wider than the normal approximation, and reporting the narrow one is the commonest error on a student worksheet. Read the lower bound against the specification, not the mean - a mean that clears the minimum with a lower bound beneath it has not demonstrated compliance.
• Every input is bounded to the range normal practice occupies (Specimens Measured 2 to 10 no., Specimen 1 -1000000 to 1000000 units and Specimen 2 -1000000 to 1000000 units, and so on for the rest). Those bounds are guard rails against typing errors, not a claim that the formula fails one unit outside them.
• The calculation is deterministic: the same inputs always give the same result. It carries no allowance for machine condition, operator skill, ambient conditions or lot-to-lot material variation unless an input above explicitly represents one.
• Nothing is sent anywhere. The maths runs in your browser, so the numbers you type never leave the page.

Questions people ask