BS ISO 16269-8:2004

Foreword
Introduction
1 Scope
2 Normative references
3 Terms, definitions and symbols
  3.1 Terms and definitions
  3.2 Symbols
4 Prediction intervals
  4.1 General
  4.2 Comparison with other types of statistical interval
      4.2.1 Choice of type of interval
      4.2.2 Comparison with a statistical tolerance interval
      4.2.3 Comparison with a confidence interval for the mean
5 Prediction intervals for all observations in a further
  sample from a normally distributed population with unknown
  population standard deviation
  5.1 One-sided intervals
  5.2 Symmetric two-sided intervals
  5.3 Prediction intervals for non-normally distributed
      populations that can be transformed to normality
  5.4 Determination of a suitable initial sample size, n,
      for a given maximum value of the prediction interval
      factor, k
  5.5 Determination of the confidence level corresponding
      to a given prediction interval
6 Prediction intervals for all observations in a further
  sample from a normally distributed population with known
  population standard deviation
  6.1 One-sided intervals
  6.2 Symmetric two-sided intervals
  6.3 Prediction intervals for non-normally distributed
      populations that can be transformed to normality
  6.4 Determination of a suitable initial sample size, n,
      for a given value of k
  6.5 Determination of the confidence level corresponding
      to a given prediction interval
7 Prediction intervals for the mean of a further sample
  from a normally distributed population
8 Distribution-free prediction intervals
  8.1 General
  8.2 One-sided intervals
  8.3 Two-sided intervals
Annex A (normative) Tables of one-sided prediction interval
        factors, k, for unknown population standard deviation
Annex B (normative) Tables of two-sided prediction interval
        factors, k, for unknown population standard deviation
Annex C (normative) Tables of one-sided prediction interval
        factors, k, for known population standard deviation
Annex D (normative) Tables of two-sided prediction interval
        factors, k, for known population standard deviation
Annex E (normative) Tables of sample sizes for one-sided
        distribution-free prediction intervals
Annex F (normative) Tables of sample sizes for two-sided
        distribution-free prediction intervals
Annex G (normative) Interpolating in the tables
Annex H (informative) Statistical theory underlying the tables
Bibliography

Specifies methods of determining prediction intervals for a single continuously distributed variable.

This part of ISO16269 specifies methods of determining prediction intervals for a single continuously distributed variable. These are ranges of values of the variable, derived from a random sample of size n, for which a prediction relating to a further randomly selected sample of size m from the same population may be made with a specified confidence. Three different types of population are considered, namely: normally distributed with unknown standard deviation; normally distributed with known standard deviation; continuous but of unknown form. For each of these three types of population, two methods are presented, one for one-sided prediction intervals and one for symmetric two-sided prediction intervals. In all cases, there is a choice from among six confidence levels. The methods presented for cases a) and b) may also be used for non-normally distributed populations that can be transformed to normality. For cases a) and b) the tables presented in this part of ISO16269 are restricted to prediction intervals containing all the further m sampled values of the variable. For case c) the tables relate to prediction intervals that contain at least m - r of the next m values, where r takes values from 0 to 10 or 0 to m - 1, whichever range is smaller. For normally distributed populations a procedure is also provided for calculating prediction intervals for the mean of m further observations.