
QUANTILE QUANTILE PLOTName:
The "quantiles" of a distribution are the distribution's "percent points" (e.g., .5 quantile = 50% point = median). The advantage of the quantilequantile plot is 2fold:
The quantilequantile plot has 3 components:
If the two data sets come from similar distributions, then the points of the qq plot should lie along the 45 degree reference line. Like usual, the appearance of these 2 components is controlled by the first 2 settings of the CHARACTERS and LINES commands. It is typical for the quantile points to be represented as, say, X's with no connecting line, and the reference line to have no plot characters but to be solid. This is demonstrated in the sample programs below.
<SUBSET/EXCEPT/FOR qualification> where <y1> is the first response variable; <y2> is the second response variable; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
<SUBSET/EXCEPT/FOR qualification> where <y1> is the first response variable; <y2> is the second response variable; <tag> is a groupid variable that defines the highlighting; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax can be used to plot different plot points with different attributes. For example, it can used to highlight groups in the data or to emphasize the extremes.
QUANTILEQUANTILE PLOT RUN1 RUN2 QUANTILEQUANTILE PLOT BATCH1 BATCH2 QUANTILEQUANTILE PLOT Y1 Y2 SUBSET AUTO 4 QUANTILEQUANTILE PLOT Y1 Y2 SUBSET STATE 25
LET X = SEQUENCE .01 .01 .99 LET Y2 = NORPPF(X) QUANTILEQUANTILE PLOT Y1 Y2 This same technique can be used other distributions (use the proper PPF function). This is also fairly close to what a probability plot does (DATAPLOT has a PROBABILITY PLOT command for over 25 distributions).
<value> where <value> specifies the desired number of quantiles. This is demonstrated in the Program 2 example below.
The parameters containing the intercept, slope, and correlation coefficient are automatically saved in the parameters PPA0, PPA1, and PPCC, respectively. This can be useful in labeling qq plots.
2011/02: Support for highlight option 2016/06: Support for SET QUANTILE QUANTILE PLOT NUMBER OF PERCENTILES 2016/06: Generate a fitted line to the quantile points 2016/06: Automatically save PPA0, PPA1, and PPCC SKIP 25 READ AUTO83B.DAT Y1 Y2 DELETE Y2 SUBSET Y2 < 0 . LINE BLANK SOLID DASHED CHARACTER CIRCLE BLANK BLANK CHARACTER FILL ON OFF OFF CHARACTER HW 0.5 0.375 TITLE AUTOMATIC TITLE OFFSET 2 LABEL CASE ASIS Y1LABEL MPG for US Cars X1LABEL MPG for Japanese Cars . QUANTILEQUANTILE PLOT Y1 Y2 . LET PPA0 = ROUND(PPA0,3) LET PPA1 = ROUND(PPA1,3) LET PPCC = ROUND(PPCC,3) JUSTIFICATION LEFT MOVE 20 87; TEXT A0: ^PPA0 MOVE 20 85; TEXT A1: ^PPA1 MOVE 20 83; TEXT PPCC: ^PPCCProgram 2: LET Y1 = NORMAL RANDOM NUMBER FOR I = 1 1 1000000 LET Y2 = DOUBLE EXPONENTIAL RANDOM NUMBER FOR I = 1 1 1000000 . LINE BLANK SOLID DASH CHARACTER CIRCLE BLANK BLANK CHARACTER FILL ON OFF CHARACTER HW 0.5 0.375 TITLE AUTOMATIC TITLE OFFSET 2 LABEL CASE ASIS Y1LABEL Normal Random Numbers X1LABEL Double Exponential Random Numbers . SET QUANTILE QUANTILE PLOT NUMBER OF PERCENTILES 1000 QUANTILEQUANTILE PLOT Y1 Y2 . LET PPA0 = ROUND(PPA),3) LET PPA1 = ROUND(PPA1,3) LET PPCC = ROUND(PPCC,3) JUSTIFICATION LEFT MOVE 20 87; TEXT A0: ^PPA0 MOVE 20 85; TEXT A1: ^PPA1 MOVE 20 83; TEXT PPCC: ^PPCCProgram 3: SKIP 25 READ AUTO83B.DAT Y1 Y2 DELETE Y2 SUBSET Y2 < 0 . LINE BLANK BLANK SOLID DASH CHARACTER CIRCLE CIRCLE BLANK BLANK CHARACTER FILL ON ON CHARACTER HW 0.5 0.375 ALL CHARACTER COLOR BLACK RED TITLE AUTOMATIC TITLE OFFSET 2 . LET N2 = SIZE Y2 LET TAG = 1 FOR I = 1 1 N2 LET TAG = 2 SUBSET Y2 > 32 . HIGHLIGHT QUANTILE QUANTILE PLOT Y2 Y1 TAGProgram 4: . Step 1: Read the data . skip 25 read exp.dat y1 read weibbury.dat y2 read gamma.dat y3 read frechet.dat y4 skip 0 . variable label y1 exp.dat variable label y2 weibbury.dat variable label y3 gamma.dat variable label y4 frechet.dat . . Step 2: Set some plot control features . case asis label case asis title case asis title offset 2 tic mark offset units screen tic mark offset 5 5 multiplot scale factor 4 multiplot corner coordinates 10 10 90 90 . line blank solid blank blank character circle blank blank blank character fill on character hw 0.5 0.375 all . . Step 3: Scatter plot matrix of quantilequantile plot . label displacement 18 set scatter plot matrix type quantile quantile scatter plot matrix y1 y2 y3 y4 . justification center move 50 97 text QuantileQuantile Plots of Four Data Sets  
Date created: 07/07/2016 Last updated: 12/04/2023 Please email comments on this WWW page to alan.heckert@nist.gov. 