Home / Statistical Tools / Analysis Tools / Tolerance Interval / Normal Method
Normal Method¶
The normal method assumes the sample comes from a normal distribution. The bounds are built from the sample mean and standard deviation, scaled by a tolerance factor \(k\):
The tolerance factor accounts for both the requested population coverage \(P\) and the confidence level \(C\). Quantum XL computes it exactly rather than from a tabulated or approximated value, so the interval attains the requested confidence precisely. The one-sided and two-sided factors are computed differently. The Math Details page gives the exact formulas.
When to use it¶
The normal method is appropriate when a normal distribution is a reasonable model for the data. Use the normal probability plot and the Anderson-Darling statistic in the output to judge this. When the points follow the reference line and the Anderson-Darling p-value is not small, the normal interval is usually the tighter and more informative of the two. When the data clearly depart from normality, prefer the Nonparametric Method.
See the Math Details for the exact tolerance factor formulas and References.