TRANSPARENCY BEFORE RESULTS

Methods, sources and limits

A result is useful when you know how it was obtained.

Conventions in this version

Unweighted arithmetic mean; sample standard deviation with denominator n − 1 or population standard deviation with n.

Quartiles and percentiles use type 7 linear interpolation. Potential outliers lie beyond Q1 − 1.5 IQR and Q3 + 1.5 IQR; no observations are removed. Modes are exact repeated values at the maximum frequency.

Precision and formats

Shared numerical engine: IEEE-754 double precision, compensated sums and centered calculations. Values may be zero or have magnitude from 1e−100 to 1e100, up to 10,000 rows. Very large offsets and tiny differences require caution. Missing selected cells and thousands separators are not supported. Non-negative weights are accepted only by the weighted-mean calculator.

Weighted mean

Weights are relative non-negative importance or frequency values here. This calculator does not implement weighted variance or infer the meaning of the weights.

Simple linear regression

Ordinary least squares with a fitted intercept. RMSE uses n; residual standard error uses n − 2 and needs at least 3 pairs.

Linear association is not causation. Check the scatter plot. No p-values, confidence intervals or significance claims are produced.

Mean confidence interval

The t method assumes independent observations from appropriate sampling. It is exact under normality; large samples may allow an approximation, but strong skew, extreme values or dependence can invalidate it. These assumptions are not tested; systematic errors and instrument calibration are not measured.

The confidence level describes method coverage over repeated samples. It is not the probability that the true mean lies in this computed interval, nor an interval containing that percentage of individual observations.

Spearman rank correlation

Pearson computed on average ranks, accounting for ties. Describes monotonic association, not causation. No p-value or significance test. If either series is constant, ρ is undefined.

Definition references

• NIST: Confidence Limits for the Mean
• SciPy: Spearman rank correlation
• NIST/SEMATECH: Measures of Scale
• NIST/SEMATECH: Box Plot
• R documentation: Sample Quantiles, type 7
• R: Weighted Arithmetic Mean
• NIST: Pearson correlation
• NIST: Linear Least Squares Regression

These are methodological references, not certifications or endorsements of this website. Code, explanations and interface are original to this version. Independently validate results for professional or critical uses.