Friction Test Statistics Helper

Statistical summary

The mean is the primary estimate; the cards below describe uncertainty and observed scatter.

Enter a minimum of two and a maximum of 10,000 measurements from repeated friction runs. Use either dimensionless coefficients of friction or one consistent friction-force unit; do not mix quantities or units. Coefficients are normally nonnegative. Signed force values must use one consistent direction convention.
Select a two-sided 90%, 95%, or 99% confidence level for the mean. The calculator updates automatically; Analyze also recalculates explicitly.
Read the mean as the primary estimate. Use sample standard deviation and range for observed scatter, standard error and the Student-t interval for uncertainty in the mean, and coefficient of variation only when the mean is meaningfully different from zero.
Use the 95% repeatability limit only when all runs were made under repeatability conditions: the same method, operator, apparatus, location, and a short time interval.
Load example restores the example dataset. Clear resets the measurement field and shows the minimum-input warning.
Correct any warning before interpreting results. Do not use this summary for mixed test conditions, time-series drift, dependent observations, specification limits, reproducibility between laboratories, or strongly non-normal small samples.

For measurements x_i (all in the same unit), sample count n ≥ 2, sample mean x̄, sample standard deviation s, and selected confidence level 1 − α:

x̄ = Σx_i / n — arithmetic mean, in the input unit.
s = √[Σ(x_i − x̄)² / (n − 1)] — sample standard deviation with Bessel’s correction, in the input unit.
SE = s / √n — standard error of the mean, in the input unit.
CI = x̄ ± t_{1−α/2,n−1} × SE — two-sided mean interval; t is the Student-t critical value with n − 1 degrees of freedom.
CV = 100s / |x̄| — coefficient of variation in percent. It is not reported when |x̄| ≤ 8εn max|x_i|, where ε is IEEE-754 machine precision; this scale-relative rule prevents round-off cancellation from producing an unbounded CV.
R = max(x_i) − min(x_i) — observed range, in the input unit.
r = 2.8s — 95% repeatability limit screening estimate, in the input unit, only when s represents repeatability standard deviation.

Sample standard deviation uses n – 1; the confidence interval uses Student’s t distribution.
The 95% repeatability limit is shown as 2.8 × sample standard deviation. Interpret it as repeatability only when the runs were made under repeatability conditions.
Coefficient of variation is useful only when the mean is meaningfully different from zero according to the scale-relative rule above.
Coefficients of friction are normally nonnegative. For signed force values, use one consistent direction convention. The mean and confidence interval preserve the selected sign; standard deviation, standard error, range, and repeatability limit remain nonnegative.
Inspect the run sequence and test conditions before treating a compact summary as evidence of stability; drift and outliers can be hidden by aggregate statistics.
See NIST guidance on confidence limits and ISO 5725-2 for repeatability terminology.