Dataplot Vol 1 Auxillary 

Chapter 

PREDICTION LIMITS 

Name: 

PREDICTION LIMITS 

Type: 

Analysis Command 

Purpose: 

Generates a prediction interval for the mean of one or more new observations 

given a previous sample. 

Description: 

Given a sample of n observations with mean and standard deviation s, the 

prediction interval to contain the mean of m new indpendent, identically 

distributed observations is 

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 

LET NNEW = <value> 

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 non-normality unless either the original sample size or the new 

sample is small or the departure from normality is severe (in particular, the 

http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/predlimi.htm
data is not too skewed). Note that this includes the case of a prediction interval 

for a single future observation. 

Syntax 1: 

<LOWER/UPPER> PREDICTION LIMITS <y>

 <SUBSET/EXCEPT/FOR qualification>

where <y> is the response variable;

and where the <SUBSET/EXCEPT/FOR qualification> is optional. 

If LOWER is specified, a one-sided lower prediction limit is returned. If UPPER 

is specified, a one-sided upper prediction limit is returned. If neither is 

specified, a two-sided limit is returned. 

This syntax supports matrix arguments for the response variable. 

Syntax 2: 

MULTIPLE <LOWER/UPPER> 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 one-sided lower prediction limit is returned. If UPPER 

is specified, a one-sided upper prediction limit is returned. If neither is 

specified, a two-sided limit is returned. 

This syntax supports matrix arguments for the response variables. 

Syntax 3: 

REPLICATED <LOWER/UPPER> PREDICTION LIMITS <y> <x1> ... <xk>

 <SUBSET/EXCEPT/FOR qualification>

where <y> is the response variable;

 <x1> .... <xk> is a list of 1 to 6 group-id variables;

and where the <SUBSET/EXCEPT/FOR qualification> is optional. 

This syntax performs a cross-tabulation of the <x1> ... <xk> and generates a 

prediction interval for each unique combination of the cross-tabulated values. 

For example, if X1 has 3 levels and X2 has 2 levels, six prediction intervals will 

be generated. 

If LOWER is specified, a one-sided lower prediction limit is returned. If UPPER 

is specified, a one-sided upper prediction limit is returned. If neither is 

specified, a two-sided limit is returned. 

This syntax does not support matrix arguments. 

http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/predlimi.htm
Examples: 

PREDICTION LIMITS Y1 

PREDICTION LIMITS Y1 SUBSET TAG > 2 

MULTIPLE PREDICTION LIMITS Y1 TO Y5 

REPLICATED PREDICTION LIMITS Y X 

Note: 

A table of prediction limits is printed for alpha levels of 50.0, 80.0, 90.0, 95.0, 

99.0, and 99.9. 

Note: 

In addition to the PREDICTION LIMITS command, the following commands 

can also be used: 

LET ALPHA = 0.05

LET NNEW = 3

LET A = LOWER PREDICTION LIMIT Y

LET A = UPPPER PREDICTION LIMIT Y

LET A = ONE SIDED LOWER PREDICTION LIMIT Y

LET A = ONE SIDED UPPER PREDICTION LIMIT Y

LET A = SUMMARY LOWER PREDICTION LIMIT YMEAN YSD N

LET A = SUMMARY UPPPER PREDICTION LIMIT YMEAN YSD N

LET A = SUMMARY ONE SIDED LOWER PREDICTION LIMIT YMEAN 

YSD N

LET A = SUMMARY ONE SIDED UPPER 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, built-in statistics are supported for 

about 20 different commands (enter HELP STATISTICS for details). 

Note: 

Prediction limits can also be generated for the case where the interval will 

contain ALL of the new points. Enter HELP PREDICTION BOUNDS for details. 

Default: 

None 

Synonyms: 

http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/predlimi.htm
PREDICTION INTERVALS is a synonum for PREDICTION LIMITS 

Related Commands: 

PREDICTION BOUNDS = Generate prediction bounds. 

SD PREDICTION 

LIMITS

= Generate prediction limits for the standard 

deviation. 

CONFIDENCE LIMITS = Generate a confidence limit. 

TOLERANCE LIMITS = Generate a tolerance limit. 

Reference: 

Hahn and Meeker (1991), "Statistical Intervals: A Guide for Practitioners", 

Wiley, pp. 61-62. 

Applications: 

Confirmatory Data Analysis 

Implementation Date: 

2013/04 

Program 1: 

SKIP 25 

READ ZARR13.DAT Y 

SET WRITE DECIMALS 5 

LET NNEW = 5 

. 

PREDICTION LIMITS Y 

LOWER PREDICTION LIMITS Y 

UPPER PREDICTION LIMITS Y 

The following output is generated 

 Two-Sided 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 

Two-Sided 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 

http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/predlimi.htm
 99.9 9.22697 9.29594 

 One-Sided 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 

One-Sided 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 

 One-Sided 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 

One-Sided 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 9.29379 

Program 2: 

SKIP 25 

READ GEAR.DAT Y X 

SET WRITE DECIMALS 5 

LET NNEW = 3 

REPLICATED PREDICTION LIMITS Y X 

The following output is generated 

 Two-Sided 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 

Two-Sided Prediction Limits for the Mean 

------------------------------------------ 

http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/predlimi.htm
 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 

 Two-Sided 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 

Two-Sided 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 

 Two-Sided 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 

Two-Sided 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 

 Two-Sided 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 

Two-Sided Prediction Limits for the Mean 

------------------------------------------ 

 Confidence Lower Upper 

http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/predlimi.htm
 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 

 Two-Sided 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 

Two-Sided 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 

 Two-Sided 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 

Two-Sided 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 

 Two-Sided 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 

Two-Sided Prediction Limits for the Mean 

------------------------------------------ 

 Confidence Lower Upper 

 Value (%) Limit Limit 

http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/predlimi.htm
------------------------------------------ 

 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 

 Two-Sided 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 

Two-Sided 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 

 Two-Sided 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 

Two-Sided 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 

 Two-Sided 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 

Two-Sided Prediction Limits for the Mean 

------------------------------------------ 

 Confidence Lower Upper 

 Value (%) Limit Limit 

------------------------------------------ 

http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/predlimi.htm
 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 1.01156 

Program 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 supp2 

The 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: 04/15/2013

Please email comments on this WWW page to alan.heckert@nist.gov. 

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