# Dataplot Vol 1 Auxillary Chapter 

# PREDICTION LIMITS

Name:
PREDICTION LIMITS Type: Analysis Command Purpose: Generates a prediction inte rval for the mean of one or more new observations given a previous sample. Description: Given a sample of nobservations with mean and standard deviation s , the prediction interval to contain the mean of mnew indpendent, identically distributed observations is

with t denoting the percent poi nt function of the t distribution. In this formula, the only value from the new observat ions is the sample size. That is, it can be applied bef ore the new data is actuallycollected. The number of observations for the new samp le is entered with the command
LET NNEW = <value> If NNEW is not defined, th en a value of 1 is used. This prediction interval is based on t he assumption that the underlying data is approximately normally distri buted. However, this predic tion interval is fairly robust against non-norma lity unless either the original sample size or the new sample is small or the de parture from normality is se vere (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 limi t is returned. If UPPER is specified, a one-sided upper prediction limit is returned. If neither is specified, a two-sid ed limit is returned. This syntax supports matrix argum ents for the response variable. Syntax 2: MULTIPLE <LOWER/UPPER> PREDIC TION 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 fo r each of the response variables. If LOWER is specified, a one-sided lower prediction limi t is returned. If UPPER is specified, a one-sided upper prediction limit is returned. If neither is specified, a two-sid ed limit is returned. This syntax supports matrix argum ents for the response variables. Syntax 3: REPLICATED <LOWER/UPPER> PREDIC TION 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 cro ss-tabulation of the <x1> ... <xk> and generates a prediction interval for each unique combi nation of the cross- tabulated values. For example, if X1 has 3 levels and X2 has 2 levels, six predi ction intervals will be generated. If LOWER is specified, a one-sided lower prediction limi t is returned. If UPPER is specified, a one-sided upper prediction limit is returned. If neither is specified, a two-sid ed 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 PREDIC TION LIMITS command, the followi ng commands can also be used:
LET ALPHA = 0.05 LET NNEW = 3
LET A = LOWER PRED ICTION LIMIT Y LET A = UPPPER PREDICTION LIMIT Y LET A = ONE SIDED LOWE R PREDICTION LIMIT Y LET A = ONE SIDED UPPE R PREDICTION LIMIT Y LET A = SUMMARY LOWER PRED ICTION LIMIT YMEAN YSD N LET A = SUMMARY UPPPER PRED ICTION LIMIT YMEAN YSD N LET A = SUMMARY ONE SIDED LO WER PREDICTION LIMIT YMEAN YSD N LET A = SUMMARY ONE SIDED UPPER PREDICTION LIMIT YMEAN YSD N The first two commands specify the signi ficance level and t he 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 LE T command, built-in stat istics are supported for about 20 differentcommands (enter HELP STATISTICS for details).
Note:
Prediction limits can also be generated for the case where the interval will contain ALL of the new poi nts. 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 sy nonum for PREDICTION LIMITS
Related Commands:
PREDICTION BOUNDS = Generate prediction bounds. SD PREDICTION LIMITS = Generate prediction li mits for the standard deviation. CONFIDENCE LIMITS = Generate a conf idence limit. TOLERANCE LIMITS = Generate a tolerance limit.
Reference: Hahn and Meeker (1991), "Sta tistical 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.htm99.9 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.htmConfidence 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.htmValue (%) 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.htm50.0 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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### http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/predlimi.htm