
PREDICTION LIMITSName:
with t denoting the percent point function of the t distribution. In this formula, the only value from the new observations is the sample size. That is, it can be applied before the new data is actually collected. The number of observations for the new sample is entered with the command
If NNEW is not defined, then a value of 1 is used. This prediction interval is based on the assumption that the underlying data is approximately normally distributed. However, this prediction interval is fairly robust against nonnormality unless either the original sample size or the new sample is small or the departure from normality is severe (in particular, the data is not too skewed). Note that this includes the case of a prediction interval for a single future observation.
<SUBSET/EXCEPT/FOR qualification> where <y> is the response variable; and where the <SUBSET/EXCEPT/FOR qualification> is optional. If LOWER is specified, a onesided lower prediction limit is returned. If UPPER is specified, a onesided upper prediction limit is returned. If neither is specified, a twosided limit is returned. If the keyword LOGNORMAL is present, the log of the data will be taken, then the normal prediction limits will be computed, and then the computed normal lower and upper limits will be exponentiated to obtain the lognormal prediction limits. Similarly, if the keyword BOXCOX is present, a BoxCox transformation to normality will be applied to the data before computing the normal prediction limits. The computed lower and upper limits will then be transformed back to the original scale. This syntax supports matrix arguments for the response variable.
PREDICTION LIMITS <y1> ... <yk> <SUBSET/EXCEPT/FOR qualification> where <y1> .... <yk> is a list of 1 to 30 response variables; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax will generate a prediction interval for each of the response variables. If LOWER is specified, a onesided lower prediction limit is returned. If UPPER is specified, a onesided upper prediction limit is returned. If neither is specified, a twosided limit is returned. If the keyword LOGNORMAL is present, the log of the data will be taken, then the normal prediction limits will be computed, and then the computed normal lower and upper limits will be exponentiated to obtain the lognormal prediction limits. Similarly, if the keyword BOXCOX is present, a BoxCox transformation to normality will be applied to the data before computing the normal prediction limits. The computed lower and upper limits will then be transformed back to the original scale. This syntax supports matrix arguments for the response variables.
PREDICTION LIMITS <y> <x1> ... <xk> <SUBSET/EXCEPT/FOR qualification> where <y> is the response variable; <x1> .... <xk> is a list of 1 to 6 groupid variables; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax performs a crosstabulation of the <x1> ... <xk> and generates a prediction interval for each unique combination of the crosstabulated values. For example, if X1 has 3 levels and X2 has 2 levels, six prediction intervals will be generated. If LOWER is specified, a onesided lower prediction limit is returned. If UPPER is specified, a onesided upper prediction limit is returned. If neither is specified, a twosided limit is returned. If the keyword LOGNORMAL is present, the log of the data will be taken, then the normal prediction limits will be computed, and then the computed normal lower and upper limits will be exponentiated to obtain the lognormal prediction limits. Similarly, if the keyword BOXCOX is present, a BoxCox transformation to normality will be applied to the data before computing the normal prediction limits. The computed lower and upper limits will then be transformed back to the original scale. This syntax does not support matrix arguments.
PREDICTION LIMITS Y1 SUBSET TAG > 2 MULTIPLE PREDICTION LIMITS Y1 TO Y5 REPLICATED PREDICTION LIMITS Y X
LET NNEW = 3
LET A = LOWER PREDICTION LIMIT Y
LET A = SUMMARY LOWER PREDICTION LIMIT YMEAN YSD N The first two commands specify the significance level and the number of new observations. The next four commands are used when you have raw data. The last four commands are used when only summary data (mean, standard deviation, sample size) is available. In addition to the above LET command, builtin statistics are supported for 20+ different commands (enter HELP STATISTICS for details).
SKIP 25 READ ZARR13.DAT Y SET WRITE DECIMALS 5 LET NNEW = 5 . PREDICTION LIMITS Y LOWER PREDICTION LIMITS Y UPPER PREDICTION LIMITS YThe following output is generated TwoSided Prediction Limits for the Mean Response Variable: Y Summary Statistics: Number of Observations: 195 Sample Mean: 9.26146 Sample Standard Deviation: 0.02278 Number of New Observations: 5 TwoSided Prediction Limits for the Mean  Confidence Lower Upper Value (%) Limit Limit  50.0 9.25448 9.26843 80.0 9.24818 9.27473 90.0 9.24440 9.27851 95.0 9.24110 9.28181 99.0 9.23461 9.28831 99.9 9.22697 9.29594 OneSided Lower Prediction Limits for the Mean Response Variable: Y Summary Statistics: Number of Observations: 195 Sample Mean: 9.26146 Sample Standard Deviation: 0.02278 Number of New Observations: 5 OneSided Lower Prediction Limits for the Mean  Confidence Lower Value (%) Limit  50.0 9.26146 80.0 9.25275 90.0 9.24818 95.0 9.24440 99.0 9.23724 99.9 9.22912 OneSided Upper Prediction Limits for the Mean Response Variable: Y Summary Statistics: Number of Observations: 195 Sample Mean: 9.26146 Sample Standard Deviation: 0.02278 Number of New Observations: 5 OneSided Upper Prediction Limits for the Mean  Confidence Upper Value (%) Limit  50.0 9.26146 80.0 9.27016 90.0 9.27473 95.0 9.27851 99.0 9.28567 99.9 9.29379Program 2: SKIP 25 READ GEAR.DAT Y X SET WRITE DECIMALS 5 LET NNEW = 3 REPLICATED PREDICTION LIMITS Y XThe following output is generated TwoSided Prediction Limits for the Mean Response Variable: Y Factor Variable 1: X 1.00000 Summary Statistics: Number of Observations: 10 Sample Mean: 0.99800 Sample Standard Deviation: 0.00434 Number of New Observations: 3 TwoSided Prediction Limits for the Mean  Confidence Lower Upper Value (%) Limit Limit  50.0 0.99598 1.00001 80.0 0.99404 1.00195 90.0 0.99275 1.00324 95.0 0.99152 1.00447 99.0 0.98870 1.00729 99.9 0.98432 1.01167 TwoSided Prediction Limits for the Mean Response Variable: Y Factor Variable 1: X 2.00000 Summary Statistics: Number of Observations: 10 Sample Mean: 0.99910 Sample Standard Deviation: 0.00521 Number of New Observations: 3 TwoSided Prediction Limits for the Mean  Confidence Lower Upper Value (%) Limit Limit  50.0 0.99668 1.00151 80.0 0.99435 1.00384 90.0 0.99280 1.00539 95.0 0.99133 1.00686 99.0 0.98794 1.01025 99.9 0.98268 1.01551 TwoSided Prediction Limits for the Mean Response Variable: Y Factor Variable 1: X 3.00000 Summary Statistics: Number of Observations: 10 Sample Mean: 0.99540 Sample Standard Deviation: 0.00397 Number of New Observations: 3 TwoSided Prediction Limits for the Mean  Confidence Lower Upper Value (%) Limit Limit  50.0 0.99355 0.99724 80.0 0.99177 0.99902 90.0 0.99060 1.00019 95.0 0.98947 1.00132 99.0 0.98689 1.00390 99.9 0.98288 1.00791 TwoSided Prediction Limits for the Mean Response Variable: Y Factor Variable 1: X 4.00000 Summary Statistics: Number of Observations: 10 Sample Mean: 0.99820 Sample Standard Deviation: 0.00385 Number of New Observations: 3 TwoSided Prediction Limits for the Mean  Confidence Lower Upper Value (%) Limit Limit  50.0 0.99641 0.99998 80.0 0.99469 1.00170 90.0 0.99355 1.00284 95.0 0.99246 1.00393 99.0 0.98995 1.00644 99.9 0.98607 1.01032 TwoSided Prediction Limits for the Mean Response Variable: Y Factor Variable 1: X 5.00000 Summary Statistics: Number of Observations: 10 Sample Mean: 0.99190 Sample Standard Deviation: 0.00757 Number of New Observations: 3 TwoSided Prediction Limits for the Mean  Confidence Lower Upper Value (%) Limit Limit  50.0 0.98839 0.99540 80.0 0.98500 0.99879 90.0 0.98275 1.00104 95.0 0.98061 1.00318 99.0 0.97568 1.00811 99.9 0.96805 1.01574 TwoSided Prediction Limits for the Mean Response Variable: Y Factor Variable 1: X 6.00000 Summary Statistics: Number of Observations: 10 Sample Mean: 0.99879 Sample Standard Deviation: 0.00988 Number of New Observations: 3 TwoSided Prediction Limits for the Mean  Confidence Lower Upper Value (%) Limit Limit  50.0 0.99422 1.00337 80.0 0.98979 1.00780 90.0 0.98687 1.01072 95.0 0.98407 1.01352 99.0 0.97765 1.01994 99.9 0.96769 1.02990 TwoSided Prediction Limits for the Mean Response Variable: Y Factor Variable 1: X 7.00000 Summary Statistics: Number of Observations: 10 Sample Mean: 1.00150 Sample Standard Deviation: 0.00787 Number of New Observations: 3 TwoSided Prediction Limits for the Mean  Confidence Lower Upper Value (%) Limit Limit  50.0 0.99785 1.00514 80.0 0.99432 1.00867 90.0 0.99199 1.01100 95.0 0.98976 1.01323 99.0 0.98464 1.01835 99.9 0.97671 1.02628 TwoSided Prediction Limits for the Mean Response Variable: Y Factor Variable 1: X 8.00000 Summary Statistics: Number of Observations: 10 Sample Mean: 1.00039 Sample Standard Deviation: 0.00362 Number of New Observations: 3 TwoSided Prediction Limits for the Mean  Confidence Lower Upper Value (%) Limit Limit  50.0 0.99872 1.00207 80.0 0.99709 1.00370 90.0 0.99602 1.00477 95.0 0.99499 1.00580 99.0 0.99264 1.00815 99.9 0.98898 1.01181 TwoSided Prediction Limits for the Mean Response Variable: Y Factor Variable 1: X 9.00000 Summary Statistics: Number of Observations: 10 Sample Mean: 0.99829 Sample Standard Deviation: 0.00413 Number of New Observations: 3 TwoSided Prediction Limits for the Mean  Confidence Lower Upper Value (%) Limit Limit  50.0 0.99638 1.00021 80.0 0.99453 1.00206 90.0 0.99330 1.00329 95.0 0.99213 1.00446 99.0 0.98944 1.00715 99.9 0.98528 1.01131 TwoSided Prediction Limits for the Mean Response Variable: Y Factor Variable 1: X 10.00000 Summary Statistics: Number of Observations: 10 Sample Mean: 0.99479 Sample Standard Deviation: 0.00532 Number of New Observations: 3 TwoSided Prediction Limits for the Mean  Confidence Lower Upper Value (%) Limit Limit  50.0 0.99233 0.99726 80.0 0.98994 0.99965 90.0 0.98836 1.00123 95.0 0.98686 1.00273 99.0 0.98339 1.00620 99.9 0.97803 1.01156Program 3: . Following example from Hahn and Meeker's book. . let ymean = 50.10 let ysd = 1.31 let n1 = 5 let nnew = 3 . set write decimals 5 let slow1 = summary lower prediction limits ymean ysd n1 let supp1 = summary upper prediction limits ymean ysd n1 let slow2 = summary one sided lower prediction limits ymean ysd n1 let supp2 = summary one sided upper prediction limits ymean ysd n1 print slow1 supp1 slow2 supp2The following output is generated PARAMETERS AND CONSTANTS SLOW1  47.44381 SUPP1  52.75619 SLOW2  48.06049 SUPP2  52.13951  
Date created: 04/15/2013 Last updated: 12/11/2023 Please email comments on this WWW page to alan.heckert@nist.gov. 