Test Sub-page for Upper Tolerance Limit

This sub-page of the Data Analysis page displays results of specific tests on the data values from the Data Entry Sub-page.

This page contains the following controls / displays:

Normal Distribution Test

Significance Level

Choose a 1%, 5%, or 10% significance level for the associated normality test. VSP conducts a Shapiro-Wilk normality test if there are fewer than 50 selected data values; otherwise a Lilliefors normality test is conducted.

Nonparametric Upper Tolerance Limit (UTL)

If the data set contains \(n\) values, where \(n\) is computed according to the formula on the Nonparametric UTL page, then the nonparametric UTL is the largest of those \(n\) values. VSP takes the largest value from the data entry page and uses it as the nonparametric UTL. If this value exceeds the action level, then VSP accepts the null hypothesis that the site is dirty (less than 100P% of the population \(\leq\) action level).

Parametric Upper Tolerance Limit (UTL)

The parametric UTL is calculated using the formula \( UTIL_{P, \alpha} = \bar x + t_{n-1,Z_P \sqrt{n}, 1- \alpha^S} \) (see Parametric UTL page for details of the formula). If the parametric UTL exceeds the action level, then VSP accepts the null hypothesis that the site is dirty (less than 100P% of the population \(\leq\) action level).