1.
Exploratory Data Analysis
1.4.
EDA Case Studies
1.4.4.

Dataplot Commands for EDA Techniques


This page documents the Dataplot commands that can be used for the
graphical and analytical techniques discussed in this chapter.
This is only meant to guide you to the appropriate commands. The
complete documentation for these commands is available in the
Dataplot
Reference Manual.


Dataplot Commands for 1Factor ANOVA

The Dataplot command for a one way analysis of variance is
where Y is a response variable and X is a group identifier
variable.
Dataplot is currently limited to the balanced case
(i.e., each level has the same number of observations) and
it does not compute interaction effect estimates.


Return to the OneWay Analysis of
Variance Page


Dataplot Commands for MultiFactor ANOVA

The Dataplot commands for generating multifactor analysis of
variance are:
ANOVA Y X1
ANOVA Y X1 X2
ANOVA Y X1 X2 X3
ANOVA Y X1 X2 X3 X4
ANOVA Y X1 X2 X3 X4 X5
where Y is the response variable and X1, X2, X3, X4, and
X5 are factor variables. Dataplot allows up to 10 factor
variables.
Dataplot is currently limited to the balanced case
(i.e., each level has the same number of observations) and
it does not compute interaction effect estimates.


Return to the MultiFactor Analysis
of Variance Page


Dataplot Commands for the AndersonDarling Test

The Dataplot commands for the AndersonDarling test are
ANDERSON DARLING NORMAL TEST Y
ANDERSON DARLING LOGNORMAL TEST Y
ANDERSON DARLING EXPONENTIAL TEST Y
ANDERSON DARLING WEIBULL TEST Y
ANDERSON DARLING EXTREME VALUE TYPE I TEST Y
where Y is the response variable.


Return to the AndersonDarling Test
Page


Dataplot Commands for Autocorrelation

To generate the lag 1 autocorrelation value in Dataplot, enter
LET A = AUTOCORRELATION Y
where Y is the response variable.
In Dataplot, the easiest way to generate the autocorrelations
for lags greater than 1 is:
AUTOCORRELATION PLOT Y
LET AC = YPLOT
LET LAG = XPLOT
RETAIN AC LAG SUBSET TAGPLOT = 1
The AUTOCORRELATION PLOT command generates an autocorrelation
plot for lags 0 to N/4. It also generates 95% and 99%
confidence limits for the autocorrelations. Dataplot stores
the plot coordinates in the internal variables XPLOT, YPLOT,
and TAGPLOT. The 2 LET commands and the RETAIN command
are used to extract the numerical values of the
autocorrelations. The variable LAG identifies the lag
while the corresponding row of AC contains the autocorrelation
value.


Return to the Autocorrelation
Page


Dataplot Commands for Autocorrelation Plots

The command to generate an autocorrelation plot is
The appearance of the autocorrelation plot can be controlled
by appropriate settings of the LINE, CHARACTER, and SPIKE commands.
Dataplot draws the following curves on the autocorrelation plot:
 The auotocorrelations.
 A reference line at zero.
 A reference line at the upper 95% confidence limit.
 A reference line at the lower 95% confidence limit.
 A reference line at the upper 99% confidence limit.
 A reference line at the lower 99% confidence limit.
For example, to draw the autocorrelations as spikes, the zero
reference line as a solid line, the 95% lines as dashed lines, and
the 99% line as dotted lines, enter the command
LINE BLANK SOLID DASH DASH DOT DOT
CHARACTER BLANK ALL
SPIKE ON OFF OFF OFF OFF OFF
SPIKE BASE 0
By default, the confidence bands are fixed width. This is appropriate
for testing for white noise (i.e., randomness). For BoxJenkins
modeling, variablewidth confidence bands are more appropriate. Enter
the following command for variablewidth confidence bands:
SET AUTOCORRELATION BAND BOXJENKINS
To restore fixedwidth confidence bands, enter
SET AUTOCORRELATION BAND WHITENOISE


Return to the Autocorrelation Plot
Page


Dataplot Commands for the Bartlett Test

The Dataplot command for the Bartlett test is
where Y is the response variable and X is the group
id variable.
The above computes the standard form of Bartlett's test.
To compute the DixonMassey form of Bartlett's test, the
Dataplot command is one of the following (these are
synonyms, not distinct commands)
DIXON BARTLETT TEST Y X
DIXON MASSEY BARTLETT TEST Y X
DM BARTLETT TEST Y X


Return to the Bartlett Test Page


Dataplot Commands for Bihistograms

The Dataplot command to generate a bihistogram is
As with the standard histogram, the class width, the lower class
limit, and the upper class limit can be controlled with the commands
CLASS WIDTH <value>
CLASS LOWER <value>
CLASS UPPER <value>
In addition, relative bihistograms, cumulative bihistograms, and
relative cumulative bihistograms can be generated with the
commands
RELATIVE BIHISTOGRAM Y1 Y2
CUMULATIVE BIHISTOGRAM Y1 Y2
RELATIVE CUMULATIVE BIHISTOGRAM Y1 Y2


Return to the Bihistogram Page


Dataplot Commands for the Binomial Probability Functions

Dataplot can compute the probability functions for the binomial
distribution with the following commands.
cdf

LET Y = BINCDF(X,P,N)

pdf

LET Y = BINPDF(X,P,N)

ppf

LET Y = BINPPF(F,P,N)

random numbers

LET N = value
LET P = value
LET Y = BINOMIAL RANDOM NUMBERS FOR I = 1 1 1000

probability plot

LET N = value
LET P = value
BINOMIAL PROBABILITY PLOT Y

where X can be a number, a parameter, or a variable. P and N are the
shape parameters and are required. They can be a number, a parameter,
or a variable. They are typically a number or a parameter.
These functions can be used in the Dataplot PLOT and FIT commands
as well. For example,
PLOT BINPDF(X,0.5,100) FOR X = 0 1 100


Return to the Binomial Distribution
Page


Dataplot Commands for the Block Plot

The Dataplot command for the block plot is
BLOCK PLOT Y X1 X2 X3 etc. XP
where
 Y is the response variable,
 X1, X2, X3, etc. are the one or more nuisance (= secondary)
factors, and
 XP is the primary factor of interest.
The following commands typically precede the block plot.
CHARACTER 1 2
LINE BLANK BLANK
These commands set the plot character for the primary factor.
Although 1 and 2 are useful indicators, the choice of plot
character is at the discretion of the user.


Return to the Block Plot Page


Dataplot Commands for the Bootstrap Plot

The Dataplot command for the bootstrap plot is
where <STAT> is one of the following:
MEAN
MIDMEAN
MIDRANGE
MEDIAN
TRIMMED MEAN
WINSORIZED MEAN
GEOMETRIC MEAN
HARMONIC MEAN
SUM
PRODUCT
MINIMUM
MAXIMUM
STANDARD DEVIATION
VARIANCE
STANDARD DEVIATION OF MEAN
VARIANCE OF MEAN
RELATIVE STANDARD DEVIATION
RELATIVE VARIANCE
AVERAGE ABSOLUTE DEVIATION
MEDIAN ABSOLUTE DEVIATION
LOWER QUARTILE
LOWER HINGE
UPPER QUARTILE
UPPER HINGE
FIRST DECILE
SECOND DECILE
THIRD DECILE
FOURTH DECILE
FIFTH DECILE
SIXTH DECILE
SEVENTH DECILE
EIGHTH DECILE
NINTH DECILE
PERCENTILE
SKEWNESS
KURTOSIS
AUTOCORRELATION
AUTOCOVARIANCE
SINE FREQUENCY
COSINE FREQUENCY
TAGUCHI SN0
TAGUCHI SN+
TAGUCHI SN
TAGUCHI SN00
The BOOTSTRAP PLOT command is almost always followed by
a histogram or some other
distributional plot.
Dataplot automatically stores the following internal parameters
after a BOOTSTRAP PLOT command:
BMEAN  mean of the plotted bootstrap values
BSD  standard deviation of the plotted bootstrap values
B001  the 0.1 percentile of the plotted bootstrap values
B005  the 0.5 percentile of the plotted bootstrap values
B01  the 1.0 percentile of the plotted bootstrap values
B025  the 2.5 percentile of the plotted bootstrap values
B05  the 5.0 percentile of the plotted bootstrap values
B10  the 10 percentile of the plotted bootstrap values
B20  the 20 percentile of the plotted bootstrap values
B80  the 80 percentile of the plotted bootstrap values
B90  the 90 percentile of the plotted bootstrap values
B95  the 95 percentile of the plotted bootstrap values
B975  the 97.5 percentile of the plotted bootstrap values
B99  the 99 percentile of the plotted bootstrap values
B995  the 99.5 percentile of the plotted bootstrap values
B999  the 99.9 percentile of the plotted bootstrap values
These internal parameters are useful for generating confidence
intervals and can be printed (PRINT BMEAN) or used as any
userdefined parameter could (e.g., LET UCL = B95).
To specify the number of bootstrap subsamples to use, enter
the command
where <N> is the number of samples you want. The
default is 500 (it may be 100 in older implementations).
Dataplot can also generate bootstrap estimates for statistics
that are not directly supported. The following example
shows a bootstrap calculation for the mean of 500 normal
random numbers. Although we can do this directly in
Dataplot, this demonstrates the steps necessary for an
unsupported statistic. The subsamples are generated
with a loop. The BOOTSTRAP INDEX and BOOTSTRAP SAMPLE commands
generate a single subsample which is stored in Y2. The
desired statistic is then calculated for Y2 and the result
stored in an array. After the loop, the array XMEAN contains
the 100 mean values.
LET Y = NORMAL RANDOM NUMBERS FOR I = 1 1 500
LET N = SIZE Y
LOOP FOR K = 1 1 500
LET IND = BOOTSTRAP INDEX FOR I = 1 1 N
LET Y2 = BOOTSTRAP SAMPLE Y IND
LET A = MEAN Y2
LET XMEAN(K) = A
END OF LOOP
HISTOGRAM XMEAN


Return to the Bootstrap Page


Dataplot Command for the BoxCox Linearity Plot

The Dataplot command to generate a BoxCox linearity plot is
BOXCOX LINEARITY PLOT Y X
where Y and X are the response variables.


Return to the BoxCox Linearity Plot Page


Dataplot Command for the BoxCox Normality Plot

The Dataplot command to generate a BoxCox normality plot is
where Y is the response variable.


Return to the BoxCox Normality Plot Page


Dataplot Commands for the Boxplot

The Dataplot command to generate a boxplot is
The BOX PLOT command is usually preceded by the commands
CHARACTER BOX PLOT
LINE BOX PLOT
These commands set the default line and character settings for
the box plot. You can use the CHARACTER and LINE commands to choose
your own line and character settings if you prefer.
To show the outliers as circles, enter the command


Return to the Boxplot Page


Dataplot Commands for the Cauchy Probability Functions

Dataplot can compute the probability functions for the Cauchy
distribution with the following commands.
cdf

LET Y = CAUCDF(X,A,B)

pdf

LET Y = CAUPDF(X,A,B)

ppf

LET Y = CAUPPF(X,A,B)

hazard

LET Y = CAUHAZ(X,A,B)

cumulative hazard

LET Y = CAUCHAZ(X,A,B)

survival

LET Y = 1  CAUCDF(X,A,B)

inverse survival

LET Y = CAUPPF(1X,A,B)

random numbers

LET Y = CAUCHY RANDOM NUMBERS FOR I = 1 1 1000

probability plot

CAUCHY PROBABILITY PLOT Y

where X can be a number, a parameter, or a variable. A and B
are the location and scale parameters and they are optional
(a location of 0 and scale of 1 are used if they are omitted).
If given, A and B can be a number, a parameter, or a variable.
However, they are typically either a number or a parameter.
These functions can be used in the Dataplot PLOT and FIT commands
as well. For example,
PLOT CAUPDF(X) FOR X = 5 0.01 5


Return to the Cauchy Distribution Page


Dataplot Commands for the ChiSquare Probability Functions

Dataplot can compute the probability functions for the chisquare
distribution with the following commands.
cdf

LET Y = CHSCDF(X,NU,NU2,A,B)

pdf

LET Y = CHSPDF(X,NU,A,B)

ppf

LET Y = CHSPPF(X,NU,A,B)

random numbers

LET NU = value
LET Y = CHISQUARE RANDOM NUMBERS FOR I = 1 1 1000

probability plot

LET NU = value
CHISQUARE PROBABILITY PLOT Y

ppcc plot

LET NU = value
CHISQUARE PPCC PLOT Y

where X can be a number, a parameter, or a variable. NU is
the shape parameter (number of degrees of freedom). NU
can be a number, a parameter, or a variable. However, it is
typically either a number or a parameter. A and B
are the location and scale parameters and they are optional
(a location of 0 and scale of 1 are used if they are omitted).
If given, A and B can be a number, a parameter, or a variable.
However, they are typically either a number or a parameter.
These functions can be used in the Dataplot PLOT and FIT commands
as well. For example,
PLOT CHSPDF(X,5) FOR X = 0 0.01 5


Return to the ChiSquare Distribution Page


Dataplot Commands for the ChiSquare Goodness of Fit Test

The Dataplot commands for the chisquare goodness of fit
test are
<dist> CHISQUARE GOODNESS OF FIT TEST Y
<dist> CHISQUARE GOODNESS OF FIT TEST Y X
<dist> CHISQUARE GOODNESS OF FIT TEST Y XL XU
where <dist> is one of 70+ builtin distributions.
Dataplot supports the chisquare goodnessoffit test for
all distributions that support the cumulative distribution
function. To see a list of supported distributions, enter
the command LIST DISTRIBUTIONS. Some specific examples are
NORMAL CHISQUARE GOODNESS OF FIT TEST Y
LOGISTIC CHISQUARE GOODNESS OF FIT TEST Y
DOUBLE EXPONENTIAL CHISQUARE GOODNESS OF FIT TEST Y
You can specify the location and scale parameters (for any
of the supported distributions) by entering
LET CHSLOC = value
LET CHSSCAL = value
You may need to enter the values for 1 or more shape parameters
for distributions that require them. For example, to specify
the shape parameter gamma for the gamma distribution, enter
the commands
LET GAMMA = value
GAMMA CHISQUARE GOODNESS OF FIT TEST Y
Dataplot also allows you to control the class width, the
lower limit (i.e., start of the first bin), and the
upper limit (i.e., the end value for the last bin).
These commands are
CLASS WIDTH value
CLASS LOWER value
CLASS UPPER value
In most cases, the default Dataplot class intervals will be
adequate.
If your data are already binned, you can enter the commands
NORMAL CHISQUARE GOODNESS OF FIT TEST Y X
NORMAL CHISQUARE GOODNESS OF FIT TEST Y XL XU
In both commands above, Y is the frequency variable. If one
X variable is given, Dataplot assumes that it is the bin
mid point and that bins have equal width. If two X variables
are given, Dataplot assumes that these are the bin end points
and that the bin widths are not necessarily of equal width.
Unequal bin widths are typically used to combine classes
with small frequencies since the chisquare approximation
for the test may not be accurate if there are frequency classes
with less than five observations.


Return to the ChiSquare Goodness of Fit Page


Dataplot Command for the ChiSquare Test for the
Standard Deviation

The Dataplot command for the chisquare test for the standard
deviation is
where Y is the response variable and A is the value being
tested.


Return to the ChiSquare Test for the
Standard Deviation Page


Dataplot Command for Complex Demodulation Amplitude Plot

The Dataplot command for a complex demodulation amplitude plot is
COMPLEX DEMODULATION AMPLITUDE PLOT Y
where Y is the response variable.


Return to the Complex Demodulation Amplitude
Plot Page


Dataplot Commands for Complex Demodulation Phase Plot

The Dataplot commands for a complex demodulation phase plot are
DEMODULATION FREQUENCY <VALUE>
COMPLEX DEMODULATION PHASE PLOT Y
where Y is the response variable.
The DEMODULATION FREQUENCY is used to specify the desired
frequency for the COMPLEX DEMODULATION PLOT. The value of
the demodulation frequency is usually obtained from a spectral
plot.


Return to the Complex Demodulation Phase
Plot Page


Dataplot Commands for Conditioning Plot

The Dataplot command to generate a conditioning plot is
Y is the response variable, X is the independent variable, and
COND is the conditioning variable. Dataplot expects COND to
contain a discrete number of distinct values. Dataplot provides
a number of commands for creating a discrete variable from a
continuous variable. For example, suppose X2 is a continuous
variable that we want to split into 4 regions. We could enter
the following sequence of commands to create a discrete variable
from X2.
LET COND = X2
LET COND = 1 SUBSET X2 = 0 TO 99.99
LET COND = 2 SUBSET X2 = 100 TO 199.99
LET COND = 3 SUBSET X2 = 200 TO 299.99
LET COND = 4 SUBSET X2 = 300 TO 400
The SUBSET feature can be used as above to create whatever ranges we
want. A simpler, more automatic way is to use the CODE
command in Dataplot. For example,
splits the data into quartiles and assigns a value of 1 to 4
to COND based on what quartile the corresponding value of X2 is in.
The appearance of the plot can be controlled by appropriate
settings of the CHARACTER and LINE commands and their various
attribute setting commands.
In addition, Dataplot provides a number of SET commands to control
the appearance of the conditioning plot. In Dataplot, enter
HELP CONDITION PLOT for details.


Return to the Condition Plot
Page


Dataplot Commands for Confidence Limits and
One Sample ttest

The following commands can be used in Dataplot to generate a
confidence interval for the mean or to generate a one sample
ttest, respectively.
CONFIDENCE LIMITS Y
T TEST Y U0
where Y is the response variable and U0 is a parameter or
scalar value that defines the hypothesized value.


Return to the Confidence Limits for the
Mean Page


Dataplot Commands for Contour Plots

The Dataplot command for generating a contour plot is
The variables X and Y define the grid, the Z variable is the
response variable, and Z0 defines the desired contour levels.
Currently, Dataplot only supports contour plots over regular
grids. Dataplot does provide 2D interpolation capabilities to
form regular grids from irregular data. Dataplot also does not
support labels for the contour lines or solid fills between
contour lines.


Return to the Contour Plot Page


Dataplot Commands for Control Charts

The Dataplot commands for generating control charts are
XBAR CONTROL CHART Y X
R CONTROL CHART Y X
S CONTROL CHART Y X
C CONTROL CHART Y X
U CONTROL CHART Y X
P CONTROL CHART Y X
NP CONTROL CHART Y X
CUSUM CONTROL CHART Y X
EWMA CONTROL CHART Y X
MOVING AVERAGE CONTROL CHART Y
MOVING AVERAGE CONTROL CHART Y X
MOVING RANGE CONTROL CHART Y
MOVING RANGE CONTROL CHART Y X
MOVING SD CONTROL CHART Y
MOVING SD CONTROL CHART Y X
where Y is the response variable and X is the group
identifier variable.
Dataplot computes the control limits. In some cases, you
may have pre determined values to put in as control limits
(e.g., based on historical data). Dataplot allows you to
specify these limits by entering the following commands
before the control chart command.


Return to the Control Chart
Page


Dataplot Commands for DEX Contour Plots

The Dataplot command for generating a linear dex contour plot is
DEX CONTOUR PLOT Y X1 X2 Y0
The variables X1 and X2 are the two factor variables, Y
is the response variable, and Y0 defines the desired
contour levels.
Dataplot does not have a builtin quadratic dex contour
plot. However, the macro DEXCONTQ.DP will generate a
quadratic dex contour plot. Enter LIST DEXCONTQ.DP for
more information.


Return to the DEX Contour Plot
Page


Dataplot Commands for DEX Interaction Effects Plots

The Dataplot command to generate a dex mean interaction effects
plot is
DEX MEAN INTERACTION EFFECTS PLOT Y X1 X2 X3 X4 X5
where Y is the response variable and X1, X2, X3, X4, and X5
are the factor variables. The number of factor variables
can vary, and is at least one.
Dataplot supports the following additional plots for other
location statistics
DEX MEDIAN INTERACTION EFFECTS PLOT Y X1 X2 X3 X4 X5
DEX MIDMEAN INTERACTION EFFECTS PLOT Y X1 X2 X3 X4 X5
DEX TRIMMED MEAN INTERACTION EFFECTS PLOT Y X1 X2 X3 X4 X5
DEX WINSORIZED MEAN INTERACTION EFFECTS PLOT Y X1 X2 X3 X4 X5
If you want the raw data plotted rather than a statistic,
enter
DEX INTERACTION EFFECTS PLOT Y X1 X2 X3 X4 X5
The LINE and CHARACTER commands can be used to control
the appearance of the plot. For example, a typical
sequence of commands might be
LINE SOLID SOLID
CHARACTER CIRCLE BLANK
CHARACTER FILL ON
This draws the connecting line between the levels of a factor
and the overall mean reference line as solid lines. In
addition, the level means are drawn with a solid fill circle.
This command is a variant of the SCATTER PLOT MATRIX
command. There are a number of options to control the
appearance of these plots. In Dataplot, you can enter
HELP SCATTER PLOT MATRIX for details.


Return to the Dex Mean Plot Page


Dataplot Commands for DEX Mean Plots

The Dataplot command to generate a dex mean plot is
DEX MEAN PLOT Y X1 X2 X3 X4 X5
where Y is the response variable and X1, X2, X3, X4, and X5
are the factor variables. The number of factor variables
can vary, and is at least one.
Dataplot supports the following additional plots for other
location statistics
DEX MEDIAN PLOT Y X1 X2 X3 X4 X5
DEX MIDMEAN PLOT Y X1 X2 X3 X4 X5
DEX TRIMMED MEAN PLOT Y X1 X2 X3 X4 X5
DEX WINSORIZED MEAN PLOT Y X1 X2 X3 X4 X5
The LINE and CHARACTER commands can be used to control
the appearance of the plot. For example, a typical
sequence of commands might be
LINE SOLID SOLID
CHARACTER CIRCLE BLANK
CHARACTER FILL ON
This draws the connecting line between the levels of a factor
and the overall mean reference line as solid lines. In addition,
the level means are drawn with a solid fill circle.
It is often desirable to provide alphabetic labels for
the factors. For example, if there are 2 factors,
time and temperature, the following commands could be used
to define alphabetic labels:
XLIMITS 1 2
XTIC OFFSET 0.5 0.5
MAJOR XTIC MARK NUMBER 2
MINOR XTIC MARK NUMBER 0
XTIC MARK LABEL FORMAT ALPHA
XTIC MARK LABEL CONTENT TIME TEMPERATURE


Return to the Dex Mean Plot Page


Dataplot Commands for a DEX Scatter Plot

The Dataplot command for generating a dex scatter plot is
DEX SCATTER PLOT Y X1 X2 X3 X4 X5
where Y is the response variable and X1, X2, X3, X4, and X5
are the factor variables. The number of factor variables
can vary, and is at least one.
The DEX SCATTER PLOT is typically preceded by the commands
CHARACTER X BLANK
LINE BLANK SOLID
However, you can set the plot character and line settings
to whatever seems appropriate.
It is often desirable to provide alphabetic labels for
the factors. For example, if there are 2 factors,
time and temperature, the following commands could be used
to define alphabetic labels:
XLIMITS 1 2
XTIC OFFSET 0.5 0.5
MAJOR XTIC MARK NUMBER 2
MINOR XTIC MARK NUMBER 0
XTIC MARK LABEL FORMAT ALPHA
XTIC MARK LABEL CONTENT TIME TEMPERATURE


Return to the Dex Scatter Plot Page


Dataplot Commands for a DEX Standard Deviation Plot

The Dataplot command to generate a dex standard deviation
plot is
DEX STANDARD DEVIATION PLOT Y X1 X2 X3 X4 X5
where Y is the response variable and X1, X2, X3, X4, and X5
are the factor variables. The number of factor variables
can vary, and is at least one.
Dataplot supports the following additional plots for other
scale statistics.
DEX VARIANCE PLOT Y X1 X2 X3 X4 X5
DEX MEDIAN ABSOLUTE VALUE PLOT Y X1 X2 X3 X4 X5
DEX AVERAGE ABSOLUTE VALUE PLOT Y X1 X2 X3 X4 X5
DEX RANGE VALUE PLOT Y X1 X2 X3 X4 X5
DEX MIDRANGE VALUE PLOT Y X1 X2 X3 X4 X5
DEX MINIMUM PLOT Y X1 X2 X3 X4 X5
DEX MAXIMUM PLOT Y X1 X2 X3 X4 X5
The LINE and CHARACTER commands can be used to control
the appearance of the plot. For example, a typical
sequence of commands might be
LINE SOLID SOLID
CHARACTER CIRCLE BLANK
CHARACTER FILL ON
This draws the connecting line between the levels of a factor
and the overall mean reference line as solid lines. In addition,
the level means are drawn with a solid fill circle.
It is often desirable to provide alphabetic labels for
the factors. For example, if there are 2 factors,
time and temperature, the following commands could be used
to define alphabetic labels:
XLIMITS 1 2
XTIC OFFSET 0.5 0.5
MAJOR XTIC MARK NUMBER 2
MINOR XTIC MARK NUMBER 0
XTIC MARK LABEL FORMAT ALPHA
XTIC MARK LABEL CONTENT TIME TEMPERATURE


Return to the Dex Standard Deviation Plot Page


Dataplot Commands for the Double Exponential Probability Functions

Dataplot can compute the probability functions for the double
exponential distribution with the following commands.
cdf

LET Y = DEXCDF(X,A,B)

pdf

LET Y = DEXPDF(X,A,B)

ppf

LET Y = DEXPPF(X,A,B)

hazard

LET Y = DEXHAZ(X,A,B)/(1  DEXCDF(X,A,B))

cumulative hazard

LET Y = LOG(1  DEXCHAZ(X,A,B))

survival

LET Y = 1  DEXCDF(X,A,B)

inverse survival

LET Y = DEXPPF(1X,A,B)

random numbers

LET Y = DOUBLE EXPONENTIAL RANDOM NUMBERS FOR I = 1 1 1000

probability plot

DOUBLE EXPONENTIAL PROBABILITY PLOT Y

maximum likelihood

LET MU = MEDIAN Y
LET BETA = MEDIAN ABSOLUTE DEVIATION Y

where X can be a number, a parameter, or a variable. A and B
are the location and scale parameters and they are optional
(a location of 0 and scale of 1 are used if they are omitted).
If given, A and B can be a number, a parameter, or a variable.
However, they are typically either a number or a parameter.
These functions can be used in the Dataplot PLOT and FIT commands
as well. For example,
PLOT DEXPDF(X) FOR X = 5 0.01 5


Return to the Double Exponential Distribution
Page


Dataplot Command for Confidence Interval for the
Difference Between Two Proportions

The Dataplot command for a confidence interval for the
difference of two proportions is
DIFFERENCE OF PROPORTIONS CONFIDENCE INTERVAL Y1 Y2
where Y1 contains the data for sample 1 and Y2 contains the
data for sample 2. For large samples, Dataplot uses the
binomial computation, not the normal approximation.
The following command sets the lower and upper bounds that
define a success in the response variable
ANOP LIMITS <lower bound> <upper bound>


Return to the Difference of
Two Proportions Page


Dataplot Command for Duane Plot

The Dataplot command for a Duane plot is
where Y is a response variable containing failure times.


Return to the Duane Plot
Page


Dataplot Command for Starting Values for Rational
Function Models

Starting values for a rational function model can be obtained
by fitting an exact rational function to a subset of the
original data. The number of points in the subset should
equal the number of parameters to be estimated in the
rational function model. The EXACT RATIONAL FIT can be
used to fit this subset model and thus to provide starting
values for the rational function model. For example, to
fit a quadratic/quadratic rational function model to data
in X and Y, you might do something like the following.
LET X2 = DATA 12 17 22 34 56
LET Y2 = DATA 7 9 6 19 23
EXACT 2/2 FIT Y2 X2 Y X
FIT Y = (A0 + A1*X + A2*X**2)/(1 + B1*X + B2*X**2)
The DATA command is used to define the subset variables
and EXACT 2/2 FIT is used to fit the exact rational function.
The "2/2" identifies the degree of the numerator as 2 and the
degree of the denominator as 2. It provides values for
A0, A1, A2, B1, and B2, which are used to fit the
rational function model for the full data set.


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Dataplot Commands for the Exponential Probability Functions

Dataplot can compute the probability functions for the exponential
distribution with the following commands.
cdf

LET Y = EXPCDF(X,A,B)

pdf

LET Y = EXPPDF(X,A,B)

ppf

LET Y = EXPPPF(X,A,B)

hazard

LET Y = EXPHAZ(X,A,B)

cumulative hazard

LET Y = EXPCHAZ(X,A,B)

survival

LET Y = 1  EXPCDF(X,A,B)

inverse survival

LET Y = EXPPPF(1X,A,B)

random numbers

LET Y = EXPONENTIAL RANDOM NUMBERS FOR I = 1 1 1000

probability plot

EXPONENTIAL PROBABILITY PLOT Y

parameter estimation

If your data are not censored, enter the commands
SET CENSORING TYPE NONE
EXPONENTIAL MLE Y
If your data have type 1 censoring at fixed time t_{0},
enter the commands
LET TEND = censoring time
SET CENSORING TYPE 1
EXPONENTIAL MLE Y X
If your data have type 2 censoring, enter the commands
SET CENSORING TYPE 2
EXPONENTIAL MLE Y X
Y is the response variable and X is the censoring variable
where a value of 1 indicates a failure time and a value of
0 indicates a censoring time. In addition to the
point estimates, confidence intervals for the parameters
are generated.

In the above, X can be a number, a parameter, or a variable. A and B
are the location and scale parameters and they are optional
(a location of 0 and scale of 1 are used if they are omitted).
If given, A and B can be a number, a parameter, or a variable.
However, they are typically either a number or parameter.
These functions can be used in the Dataplot PLOT and FIT commands
as well. For example,
PLOT EXPPDF(X) FOR X = 0 0.01 4


Return to the Exponential Distribution Page


Dataplot Command for Generalized ESD Test

The Dataplot command for the generalized ESD (Extreme
Studentized Deviate) test is
LET NOUTLIER = <value>
EXTREME STUDENTIZED DEVIATE TEST Y
where Y is the response variable and NOUTLIER specifies the
upper bound on the number of outliers to test.


Return to the Generalized ESD Page


Dataplot Commands for the Extreme Value Type I (Gumbel) Distribution

To specify the form of the Gumbel distribution based on the
smallest value, enter the command
To specify the form of the Gumbel distribution based on the
largest value, enter the command
One of these commands must be entered before using the commands
below.
Dataplot can compute the probability functions for the extreme value
type I distribution with the following commands.
cdf

LET Y = EV1CDF(X,A,B)

pdf

LET Y = EV1PDF(X,A,B)

ppf

LET Y = EV1PPF(X,A,B)

hazard

LET Y = EV1HAZ(X,A,B)

cumulative hazard

LET Y = EV1CHAZ(X,A,B)

survival

LET Y = 1  EV1CDF(X,A,B)

inverse survival

LET Y = EV1PPF(1X,A,B)

random numbers

LET Y = EXTREME VALUE TYPE 1 RANDOM NUMBERS FOR I = 1 1 1000

probability plot

EXTREME VALUE TYPE 1 PROBABILITY PLOT Y

maximum likelihood

EV1 MLE Y
This returns a point estimate for the full sample
case. It does not provide confidence intervals for
the parameters and it does not handle censored data.

In the above, X can be a number, a parameter, or a variable. A and B
are the location and scale parameters and they are optional
(a location of 0 and scale of 1 are used if they are omitted).
If given, A and B can be a number, a parameter, or a variable.
However, they are typically either a number or a parameter.
These functions can be used in the Dataplot PLOT and FIT commands
as well. For example,
SET MINMAX 1
PLOT EV1PDF(X) FOR X = 4 0.01 4


Return to the Extreme Value Type I
Distribution Page


Dataplot Commands for the F Distribution Probability Functions

Dataplot can compute the probability functions for the F distribution
with the following commands.
cdf

LET Y = FCDF(X,NU1,NU2,A,B)

pdf

LET Y = FPDF(X,NU1,NU2,A,B)

ppf

LET Y = FPPF(X,NU1,NU2,A,B)

random numbers

LET NU1 = value
LET NU2 = value
LET Y = F RANDOM NUMBERS FOR I = 1 1 1000

probability plot

LET NU1 = value
LET NU2 = value
F PROBABILITY PLOT Y

where X can be a number, a parameter, or a variable. NU1 and NU2 are
the shape parameters (= number of degrees of freedom). NU1 and NU2
can be a number, a parameter, or a variable. However, they are
typically either a number or a parameter. A and B
are the location and scale parameters and they are optional
(a location of 0 and scale of 1 are used if they are omitted).
If given, A and B can be a number, a parameter, or a variable.
However, they are typically either a number or a parameter.
These functions can be used in the Dataplot PLOT and FIT commands
as well. For example,
PLOT FPDF(X,10,10) FOR X = 0 0.01 5


Return to the F Distribution Page


Dataplot Command for F Test for Equality of Two Standard
Deviations

The Datpalot command for the F test for the equality of
two standard deviations is
where Y1 is the data for sample one and Y2 is the data for
sample two.


Return to the F Test for Equality of Two Standard
Deviations Page


Dataplot Commands for the Histogram

The Dataplot command to generate a histogram is
where Y is the response variable.
The different variants of the histogram can be generated
with the commands
RELATIVE HISTOGRAM Y
CUMULATIVE HISTOGRAM Y
RELATIVE CUMULATIVE HISTOGRAM Y
The class width, the start of the first class, and the end
of the last class can be specified with the commands
CLASS WIDTH <value>
CLASS LOWER <value>
CLASS UPPER <value>
By default, Dataplot uses a class width of 0.3*SD where SD is the
standard deviation of the data. The lower class limit is
the sample mean minus 6 times the sample standard deviation.
Similarly, the upper class limit is the sample mean plus
6 times the sample standard deviation.
By default, Dataplot uses the probability normalization for
relative histograms. If you want the relative counts to
sum to one instead, enter the command
SET RELATIVE HISTOGRAM PERCENT
To reset the probability interpretation, enter
SET RELATIVE HISTOGRAM AREA


Return to the Histogram Page


Dataplot Commands for a Lag Plot

The Dataplot command to generate a lag plot is
The appearance of the lag plot can be controlled with
appropriate settings for the LINE and CHARACTER commands.
Typical settings for these commands would be
To generate a linear fit of the points on the lag plot
when an autoregressive fit is suggested, enter the following
commands
LAG PLOT Y
LINEAR FIT YPLOT XPLOT
The variables YPLOT and XPLOT are internal variables that
store the coordinates of the most recent plot.


Return to the Lag Plot Page


Dataplot Commands for the Fatigue Life Probability Functions

Dataplot can compute the probability functions for the fatigue life
distribution with the following commands.
cdf

LET Y = FLCDF(X,GAMMA,A,B)

pdf

LET Y = FLPDF(X,GAMMA,A,B)

ppf

LET Y = FLPPF(X,GAMMA,A,B)

hazard

LET Y = FLHAZ(X,GAMMA,A,B)

cumulative hazard

LET Y = FLCHAZ(X,GAMMA,A,B)

survival

LET Y = 1  FLCDF(X,GAMMA,A,B)

inverse survival

LET Y = FLPPF(1X,GAMMA,A,B)

random numbers

LET GAMMA = value
LET Y = FATIGUE LIFE RANDOM NUMBERS FOR I = 1 1 1000

probability plot

LET GAMMA = value
FATIGUE LIFE PROBABILITY PLOT Y

ppcc plot

LET GAMMA = value
FATIGUE LIFE PPCC PLOT Y

where X can be a number, a parameter, or a variable. FLMA is the
shape parameter and is required. It can be a number, a parameter, or
a variable. It is typically a number or a parameter. A and B
are the location and scale parameters and they are optional
(a location of 0 and scale of 1 are used if they are omitted).
If given, A and B can be a number, a parameter, or a variable.
However, they are typically either a number or a parameter.
These functions can be used in the Dataplot PLOT and FIT commands
as well. For example,
PLOT FLPDF(X,2) FOR X = 0.01 0.01 10


Return to the Fatigue Life Distribution Page


Dataplot Command for Fitting

Dataplot can generate both linear and nonlinear fit commands.
For example, to generate a linear fit of Y versus X1, X2, and
X3, the command is:
To generate quadratic and cubic fits of Y versus X, the
commands are:
QUADRATIC FIT Y X
CUBIC FIT Y X
Nonlinear fits are generated by entering an equation. For
example,
FIT Y = A*(EXP(B*X/10)  EXP(X/10))
FIT Y = C/(1+C*A*X**B)
FIT Y = A  B*X  ATAN(C/(XD))/3.14159
In the above equations, there are variables (X and Y),
parameters (A, B, C, and D), and constants (10 and 3.14159).
The FIT command estimates values for the parameters.
If you have a parameter that you do not want
estimated, enter it as a constant or with the "^" (e.g.,
FIT Y = ^C/(1+^C*A*X**B). The "^" substitutes the value
of a parameter into a command.
You can also define a function and then fit the function.
For example,
LET FUNCTION F = C/(1+C*A*X**B)
FIT Y = F


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location.


Dataplot Commands for the Gamma Probability Functions

Dataplot can compute the probability functions for the gamma
distribution with the following commands.
cdf

LET Y = GAMCDF(X,GAMMA,A,B)

pdf

LET Y = GAMPDF(X,GAMMA,A,B)

ppf

LET Y = GAMPPF(X,GAMMA,A,B)

hazard

LET Y = GAMHAZ(X,GAMMA,A,B)

cumulative hazard

LET Y = GAMCHAZ(X,GAMMA,A,B)

survival

LET Y = 1  GAMCDF(X,GAMMA,A,B)

inverse survival

LET Y = GAMPPF(1X,GAMMA,A,B)

random numbers

LET GAMMA = value
LET Y = Gamma RANDOM NUMBERS FOR I = 1 1 1000

probability plot

LET GAMMA = value
Gamma PROBABILITY PLOT Y

ppcc plot

LET GAMMA = value
Gamma PPCC PLOT Y

maximum likelihood

GAMMA MLE Y
This returns a point estimate for the fullsample
case. It does not provide confidence intervals for
the parameters and it does not handle censored data.

where X can be a number, a parameter, or a variable. GAMMA is the
shape parameter and is required. It can be a number, a parameter, or
a variable. It is typically a number or a parameter. A and B
are the location and scale parameters and they are optional
(a location of 0 and scale of 1 are used if they are omitted).
If given, A and B can be a number, a parameter, or a variable.
However, they are typically either a number or a parameter.
These functions can be used in the Dataplot PLOT and FIT commands
as well. For example,
PLOT GAMPDF(X,2) FOR X = 0.01 0.01 10


Return to the Gamma Distribution Page


Dataplot Command for Grubbs' Test

The Dataplot command for Grubbs' test is
GRUBBS <MINIMUM/MAXIMUM> TEST Y
where Y is the response variable. Dataplot identifies one
outlier at a time. The MINIMUM or MAXIMUM keyword is optional.
If omitted, the most extreme value will be checked (regardless
of whether it is in the minimum or maximum direction).


Return to the Grubbs Test Page


Dataplot Commands for Hazard Plots

The Dataplot commands for hazard plots are
EXPONENTIAL HAZARD PLOT Y X
NORMAL HAZARD PLOT Y X
LOGNORMAL HAZARD PLOT Y X
WEIBULL HAZARD PLOT Y X
where Y is a response variable containing failure times
and X is a censoring variable (0 means failure time, 1
means censoring time).


Return to the Hazard Plot
Page


Dataplot Command for KruskalWallis Test

The Dataplot command for a KruskalWallis test is
where Y is the response variable and X is the group
identifier variable.


Return to the KruskalWallis
Test Page


Dataplot Commands for the Kolmogorov Smirnov
GoodnessofFit Test

The Dataplot command for the KolmogorovSmirnov
goodnessoffit test is
<dist> KOLMOGOROVSMIRNOV GOODNESS OF FIT TEST Y
where <dist> is one of 60+ builtin distributions. The
KS goodness of fit test is supported for all Dataplot internal
continuous distributions that support the CDF (cumulative
distribution function). The command LIST DISTRIBUTIONS shows
the currently supported distributions in Dataplot. Some
specific examples are
NORMAL KOLMSMIR GOODNESS OF FIT Y
LOGISTIC KOLMSMIR GOODNESS OF FIT Y
DOUBLE EXPONENTIAL KOLMSMIR GOODNESS OF FIT Y
You can specify the location and scale parameters by
entering
LET KSLOC = value
LET KSSCALE = value
You may need to enter the values for 1 or more shape parameters
for distributions that require them. For example, to specify
the shape parameter gamma for the gamma distribution, enter
the commands
LET GAMMA = value
GAMMA KOLMOGOROVSMIRNOV GOODNESS OF FIT TEST Y
Be aware that you should not use the same data to
estimate these distributional parameters as you use to
calculate the KS test as the critical values of the KS
test assume the distribution is fully specified.
The empirical cdf function can be plotted with the
following command


Return to the KolmogorovSmirnov Goodness of
Fit Test Page


Dataplot Commands for Least Squares Estimation of Distributional
Parameters

The following example shows how to use Dataplot to obtain
least squares estimates for data generated from a Weibull
distribution.
. Generate some Weibull data
SET MINMAX MIN
LET GAMMA = 5
LET Y = WEIBULL RAND NUMB FOR I = 1 1 1000
. Bin the data
SET RELATIVE HISTOGRAM AREA
RELATIVE HISTOGRAM Y
LET ZY = YPLOT
LET ZX = XPLOT
RETAIN ZY ZX SUBSET YPLOT > 0
. Specify some starting values
LET SHAPE = 3
LET LOC = MINIMUM Y
LET SCALE = 1
. Now perform the least squares fit
FIT ZY = WEIPDF(ZX,SHAPE,LOC,SCALE)
The RELATIVE HISTOGRAM generates a relative
histogram. The command SET RELATIVE HISTOGRAM specifies that the
relative histogram is created so that the area under the histogram is
1 (i.e., the integral is 1) rather than the sum of the bars
equaling 1. This effectively makes the relative histogram an
estimator of the underlying density function. Dataplot saves
the coordinates of the histogram in the internal variables
XPLOT and YPLOT. The SUBSET command eliminates zero frequency
classes. The FIT command then performs the least squares fit.
The same general approach can be used to compute least squares
estimates for any distribution for which Dataplot has a pdf
function. The primary difficulty with the least squares fitting
is that it can be quite sensitive to starting values. For
distributions with no shape parameters, the
probability plot can be used to
determine starting values for the location and scale parameters.
For distributions with a single shape parameter, the
ppcc plot can be used to determine a
starting value for the shape parameter and the probability plot used
to determine starting values for the location and scale parameters.
The approach above can be used in any statistical software package
that provides nonlinear least squares fitting and a method for
defining the probability density function (either builtin or
user definable).


Return to the Least Squares Estimation Page


Dataplot Command for Levene's Test

The Dataplot command for the Levene test is
where Y is the response variable and X is the group
id variable.


Return to the Levene Test Page


Dataplot Command for the Linear Correlation Plot

The Dataplot command to generate a linear correlation plot is
LINEAR CORRELATION PLOT Y X TAG
where Y is the response variable, X is the independent variable,
and TAG is the group id variable.
The appearance of the plot can be controlled with appropriate
settings for the LINE and CHARACTER commands. Typical settings
would be
CHARACTER X BLANK
LINE BLANK SOLID


Return to the Linear Correlation Plot Page


Dataplot Command for the Linear Intercept Plot

The Dataplot command to generate a linear intercept plot is
LINEAR INTERCEPT PLOT Y X TAG
where Y is the response variable, X is the independent variable,
and TAG is the group id variable.
The appearance of the plot can be controlled with appropriate
settings for the LINE and CHARACTER commands. Typical settings
would be
CHARACTER X BLANK
LINE BLANK SOLID


Return to the Linear Intercept Plot Page


Dataplot Command for the Linear Slope Plot

The Dataplot command to generate a linear slope plot is
LINEAR SLOPE PLOT Y X TAG
where Y is the response variable, X is the independent variable,
and TAG is the group id variable.
The appearance of the plot can be controlled with appropriate
settings for the LINE and CHARACTER commands. Typical settings
would be
CHARACTER X BLANK
LINE BLANK SOLID


Return to the Linear Slope Plot Page


Dataplot Command for the Linear Residual Standard
Deviation Plot

The Dataplot command to generate a linear residual standard
deviation plot is
LINEAR RESSD PLOT Y X TAG
where Y is the response variable, X is the independent variable,
and TAG is the group id variable.
The appearance of the plot can be controlled with appropriate
settings for the LINE and CHARACTER commands. Typical settings
would be
CHARACTER X BLANK
LINE BLANK SOLID


Return to the Linear Residual Standard Deviation
Plot Page


Dataplot Commands for Measures of Location

Various measures of location can be computed in Dataplot as follows:
LET A = MEAN Y
LET A = MEDIAN Y
LET A = MIDMEAN Y
LET P1 = 10
LET P2 = 10
LET A = TRIMMED MEAN Y
LET P1 = 10
LET P2 = 10
LET A = WINSORIZED Y
In the above, P1 and P2 are used to set the percentage of values
that are trimmed or Winsorized. Use P1 to set the percentage for
the lower tail and P2 the percentage for the upper tail.


Return to the Measures of Location Page


Dataplot Commands for the Lognormal Probability Functions

Dataplot can compute the probability functions for the lognormal
distribution with the following commands.
cdf

LET Y = LGNCDF(X,SD,A,B)

pdf

LET Y = LGNPDF(X,SD,A,B)

ppf

LET Y = LGNPPF(X,SD,A,B)

hazard

LET Y = LGNHAZ(X,SD,A,B)

cumulative hazard

LET Y = LGNCHAZ(X,SD,A,B)

survival

LET Y = 1  LGNCDF(X,SD,A,B)

inverse survival

LET Y = LGNPPF(1X,SD,A,B)

random numbers

LET SD = value
LET Y = LOGNORMAL RANDOM NUMBERS FOR I = 1 1 1000

probability plot

LET SD = value
LOGNORMAL PROBABILITY PLOT Y

ppcc plot

LET SD = value
LOGNORMAL PPCC PLOT Y

parameter estimation

LOGNORMAL MLE Y
This returns point estimates for the shape and scale
parameters. It does not handle censored data and
it does not generate confidence intervals for the
parameters.

where X can be a number, a parameter, or a variable. SD is the
shape parameter and is optional. It can be a number, a parameter, or
a variable. It is typically a number or a parameter. A and B
are the location and scale parameters and they are optional
(a location of 0 and scale of 1 are used if they are omitted).
If given, A and B can be a number, a parameter, or a variable.
However, they are typically either a number or a parameter.
These functions can be used in the Dataplot PLOT and FIT commands
as well. For example,
PLOT LGNPDF(X,5) FOR X = 0.01 0.01 5


Return to the Lognormal Distribution Page


Dataplot Commands for Maximum Likelihood Estimation for Distributions

Dataplot performs maximum likelihood estimation for a few specific
distributions as documented in the table below. Unless specified
otherwise, censored data are not supported and only point estimates
are generated (i.e., no confidence intervals for the parameters).
For censored data, create an id variable that is equal to 1 for
a failure time and equal to 0 for a censoring time. Type I
censoring is censoring at a fixed time t_{0}. Type II
censoring is censoring after a predetermined number of units
have failed.
Normal

NORMAL MAXIMUM LIKELIHOOD Y

Exponential

EXPONENTIAL MAXIMUM LIKELIHOOD Y
Confidence intervals are generated for the parameters and
both type I and type II censoring are supported.
For type I censoring, enter the following commands
SET CENSORING TYPE 1
LET TEND = censoring time
EXPONENTIAL MAXIMUM LIKELIHOOD Y ID
For type II censoring, enter the following commands
SET CENSORING TYPE 2
EXPONENTIAL MAXIMUM LIKELIHOOD Y ID

Weibull

WEIBULL MAXIMUM LIKELIHOOD Y
Confidence intervals are generated for the parameters and
both type I and type II censoring are supported.
For type I censoring, enter the following commands
SET CENSORING TYPE 1
LET TEND = censoring time
WEIBULL MAXIMUM LIKELIHOOD Y ID
For type II censoring, enter the following commands
SET CENSORING TYPE 2
WEIBULL MAXIMUM LIKELIHOOD Y ID

Lognormal

LOGNORMAL MAXIMUM LIKELIHOOD Y

Double
Exponential

DOUBLE EXPONENTIAL MAXIMUM LIKELIHOOD Y

Pareto

PARETO MAXIMUM LIKELIHOOD Y

Gamma

GAMMA MAXIMUM LIKELIHOOD Y

Inverse
Gaussian

INVERSE GAUSSIAN MAXIMUM LIKELIHOOD Y

Gumbel

GUMBEL MAXIMUM LIKELIHOOD Y

Binomial

BINOMIAL MAXIMUM LIKELIHOOD Y

Poisson

POISSON MAXIMUM LIKELIHOOD Y



Return to the Maximum Likelihood
Estimation Page


Dataplot Command for the Mean Plot

The Dataplot command to generate a mean plot is
where Y is a response variable and X is a group id variable.
Dataplot supports this command for a number of other
common location statistics. For example, MEDIAN PLOT Y X and
MIDRANGE PLOT Y X compute the median and midrange instead of
the mean for each group.


Return to the Mean Plot Page


Dataplot Commands for Normal Probability Functions

Dataplot can compute the various probability functions for the
normal distribution with the following commands.
cdf

LET Y = NORCDF(X,A,B)

pdf

LET Y = NORPDF(X,A,B)

ppf

LET Y = NORPPF(X,A,B)

hazard

LET Y = NORHAZ(X,A,B)

cumulative hazard

LET Y = NORCHAZ(X,A,B)

survival

LET Y = 1  NORCDF(X,A,B)

inverse survival

LET Y = NORPPF(1X,A,B)

random numbers

LET Y = NORMAL RANDOM NUMBERS FOR I = 1 1 1000

probability plot

NORMAL PROBABILITY PLOT Y

parameter estimates

LET YMEAN = MEAN Y
LET YSD = STANDARD DEVIATION Y

where X can be a number, a parameter, or a variable. A and B
are the location and scale parameters and they are optional
(a location of 0 and scale of 1 are used if they are omitted).
If given, A and B can be a number, a parameter, or a variable.
However, they are typically either a number or parameter.
These functions can be used in the Dataplot PLOT and FIT commands
as well. For example,
PLOT NORPDF(X) FOR X = 4 0.01 4


Return to the Normal Distribution Page


Dataplot Commands for a Normal Probability Plot

The Dataplot command to generate a normal probability plot is
NORMAL PROBABILITY PLOT Y
where Y is the response variable.
If your data are already grouped (i.e., Y contains counts for
the groups identified by X), the Dataplot command is
NORMAL PROBABILITY PLOT Y X
Dataplot returns the following internal parameters when it
generates a probability plot.
 PPCC  the correlation coefficient of the fitted line
on the probability plot. This is a measure of how
well the straight line fits the probability plot.
 PPA0  the intercept term for the fitted line on the
probability plot. This is an estimate of the location
parameter.
 PPA1  the slope term for the fitted line on the
probability plot. This is an estimate of the scale
parameter.
 SDPPA0  the standard deviation of the intercept term for
the fitted line on the probability plot.
 SDPPA1  the standard deviation of the slope term for
the fitted line on the probability plot.
 PPRESSD  the residual standard deviation of the fitted
line on the probability plot. This is a measure of the
adequacy of the fitted line.
 PPRESDF  the residual degrees of freedom of the fitted
line on the probability plot.


Return to the Normal Probability Plot Page


Dataplot Commands for the Generation of Normal Random Numbers

The Dataplot commands to generate 1,000 normal random numbers with
a location of 50 and a scale of 20 are
LET LOC = 50
LET SCALE = 20
LET Y = NORM RAND NUMBERS FOR I = 1 1 1000
LET Y = LOC + SCALE*Y
Programs that automatically generate random numbers are typically
controlled by a seed, which is usually an integer value. The
importance of the seed is that it allows the random numbers to be
replicated. That is, giving the program the same seed should generate
the same sequence of random numbers. If the ability to replicate the
set of random numbers is not important, you can give any valid value
for the seed.
In Dataplot, the seed is an odd integer with a minimum (and default)
value of 305. Seeds less than 305 generate the same sequence as 305
and even numbers generate the same sequence as the preceding odd
number. To change the seed value to 401 in Dataplot, enter the
command:


Return to the Normal Random Numbers Case
Study (Background and Data) Page


Dataplot Commands for Partial Autocorrelation Plots

The command to generate a partial autocorrelation plot is
PARTIAL AUTOCORRELATION PLOT Y
The appearance of the partial autocorrelation plot can be controlled
by appropriate settings of the LINE, CHARACTER, and SPIKE commands.
Dataplot draws the following curves on the autocorrelation plot:
 The autocorrelations.
 A reference line at zero.
 A reference line at the upper 95% confidence limit.
 A reference line at the lower 95% confidence limit.
 A reference line at the upper 99% confidence limit.
 A reference line at the lower 99% confidence limit.
For example, to draw the partial autocorrelations as spikes, the zero
reference line as a solid line, the 95% lines as dashed lines, and
the 99% line as dotted lines, enter the command
LINE BLANK SOLID DASH DASH DOT DOT
CHARACTER BLANK ALL
SPIKE ON OFF OFF OFF OFF OFF
SPIKE BASE 0


Return to the Partial
Autocorrelation Plot Page


Dataplot Commands for the Poisson Probability Functions

Dataplot can compute the probability functions for the Poisson
distribution with the following commands.
cdf

LET Y = POICDF(X,LAMBDA)

pdf

LET Y = POIPDF(X,LAMBDA)

ppf

LET Y = POIPPF(X,LAMBDA)

random numbers

LET LAMBDA = value
LET Y = POISSON RANDOM NUMBERS FOR I = 1 1 1000

probability plot

LET LAMBDA = value
POISSON PROBABILITY PLOT Y

ppcc plot

POISSON PPCC PLOT Y

where X can be a number, a parameter, or a variable. LAMBDA is the
shape parameter and is required. It can be a number, a parameter,
or a variable. It is typically a number or a parameter.
These functions can be used in the Dataplot PLOT and FIT commands
as well. For example,
PLOT POIPDF(X,15) FOR X = 0 1 50


Return to the Poisson Distribution Page


Dataplot Commands for the Power Lognormal Distribution

Dataplot can compute the probability functions for the power lognormal
distribution with the following commands.
cdf

LET Y = PLNCDF(X,P,SD,MU)

pdf

LET Y = PLNPDF(X,P,SD,MU)

ppf

LET Y = PLNPPF(X,P,SD,MU)

hazard

LET Y = PLNHAZ(X,P,SD,MU)

cumulative hazard

LET Y = PLNCHAZ(X,P,SD,MU)

survival

LET Y = 1  PLNCDF(X,P,SD,MU)

inverse survival

LET Y = PLNPPF(1X,P,SD,MU)

probability plot

LET P = value
LET SD = value (defaults to 1)
POWER LOGNORMAL PROBABILITY PLOT Y

ppcc plot

LET SD = value
POWER LOGNORMAL PPCC PLOT Y

In the above, X can be a number, a parameter, or a variable. SD and MU
are the scale and location parameters, respectively, and they are
optional (a location of 0 and scale of 1 are used if they are omitted).
If given, SD and MU can be a number, a parameter, or a variable.
However, they are typically either a number or a parameter.
These functions can be used in the Dataplot PLOT and FIT commands
as well. For example,
the command
PLOT PLNPDF(X,5,1) FOR X = 0.01 0.01 5


Return to the Power Lognormal Distribution
Page


Dataplot Commands for the Power Normal Probability Functions

Dataplot can compute the probability functions for the power
normal distribution with the following commands.
cdf

LET Y = PNRCDF(X,P,SD,MU)

pdf

LET Y = PNRPDF(X,P,SD,MU)

ppf

LET Y = PNRPPF(X,P,SD,MU)

hazard

LET Y = PNRHAZ(X,P,SD,MU)

cumulative hazard

LET Y = PNRCHAZ(X,P,SD,MU)

survival

LET Y = 1  PNRCDF(X,P,SD,MU)

inverse survival

LET Y = PNRPPF(1X,P,SD,MU)

probability plot

LET P = value
LET SD = value (defaults to 1)
POWER NORMAL PROBABILITY PLOT Y

ppcc plot

POWER NORMAL PPCC PLOT Y

In the above, X can be a number, a parameter, or a variable. SD and MU
are the scale and location parameters, respectively, and they are
optional (a location of 0 and scale of 1 are used if they are omitted).
If given, SD and MU can be a number, a parameter, or a variable.
However, they are typically either a number or a parameter.
These functions can be used in the Dataplot PLOT and FIT commands
as well. For example,
PLOT PNRPDF(X,10,1) FOR X = 5 0.01 5


Return to the Power Normal Distribution Page


Dataplot Commands for Probability Plots

The Dataplot command for a probability plot is
<dist> PROBABILITY PLOT Y
where <dist> is the name of the specific distribution.
Dataplot currently supports probability plots for over 70
distributions. For example,
NORMAL PROBABILITY PLOT Y
EXPONENTIAL PROBABILITY PLOT Y
DOUBLE EXPONENTIAL PROBABILITY PLOT Y
CAUCHY PROBABILITY PLOT Y
For some distributions, you may need to specify one or more
shape parameters. For
example, to specify the shape parameter for the gamma
distribution, you might enter the following commands:
LET GAMMA = 2
GAMMA PROBABILITY PLOT Y
Enter the command LIST DISTRIBUTIONS to see a list of
distributions for which Dataplot supports probability
plots (and to see what parameters need to be specified).
Dataplot returns the following internal parameters when it
generates a probability plot.
 PPCC  the correlation coefficient of the fitted line
on the probability plot. This is a measure of how
well the straight line fits the probability plot.
 PPA0  the intercept term for the fitted line on the
probability plot. This is an estimate of the location
parameter.
 PPA1  the slope term for the fitted line on the
probability plot. This is an estimate of the scale
parameter.
 SDPPA0  the standard deviation of the intercept term for
the fitted line on the probability plot.
 SDPPA1  the standard deviation of the slope term for
the fitted line on the probability plot.
 PPRESSD  the residual standard deviation of the fitted
line on the probability plot. This is a measure of the
adequacy of the fitted line.
 PPRESDF  the residual degrees of freedom of the fitted
line on the probability plot.


Return to the Probability Plot Page


Dataplot Commands for the PPCC Plot

The Dataplot command to generate a PPCC plot for unbinned
data is:
where <dist> identifies the distributional family and
Y is the response variable.
The Dataplot command to generate a PPCC plot for binned
data is:
where <dist> identifies the distributional family, Y is
the counts variable, and X is the bin identifier variable.
Dataplot supports the PPCC plot for over 25 distributions.
Some of the most common are WEIBULL, TUKEY LAMBDA, GAMMA, PARETO,
and INVERSE GAUSSIAN. Enter the command LIST DISTRIBUTIONS
for a list of supported distributions.
Dataplot allows you to specify the range of the shape parameter.
Dataplot generates 50 probability plots in equally spaced
intervals from the smallest value of the shape parameter to
the largest value of the shape parameter. For example, to
generate a Weibull PPCC plot for values of the shape parameter
gamma from 2 to 4, enter the commands:
LET GAMMA1 = 2
LET GAMMA2 = 4
WEIBULL PPCC PLOT Y
The command LIST DISTRIBUTIONS gives the name of the
shape parameter for the supported distributions. The
"1" and "2" suffixes imply the minimum and maximum value
for the shape parameter, respectively.
Whenever Dataplot generates a PPCC plot, it saves the
following internal parameters:
 MAXPPCC  the maximum correlation coefficient from
the PPCC plot.
 SHAPE  the value of the shape parameter that generated
the maximum correlation coefficient.


Return to the PPCC Plot Page


Dataplot Command for Proportion Defective Confidence
Interval

The Dataplot command for a confidence interval for the
proportion defective is
PROPORTION CONFIDENCE LIMITS Y
where Y is a response variable. Note that for large samples,
Dataplot generates the interval based on the exact binomial
probability, not the normal approximation.
The following command sets the lower and upper bounds that
define a success in the response variable:
ANOP LIMITS <lower bound> <upper bound>


Return to the Proportion
Defective Page


Dataplot Command for QQ Plot

The Dataplot command to generate a qq plot is
QUANTILEQUANTILE PLOT Y1 Y2
The CHARACTER and LINE commands can be used to control
the appearance of the qq plot. For example, to draw
the quantile points as circles and the reference line as
a solid line, enter the commands
LINE BLANK SOLID
CHARACTER CIRCLE BLANK


Return to the QuantileQuantile Plot Page


Dataplot Commands for the Generation of Random Walk Numbers

To generate a random walk with 1,000 points requires the
following Dataplot commands:
LET Y = UNIFORM RANDOM NUMBERS FOR I = 1 1 1000
LET Y2 = Y  0.5
LET RW = CUMULATIVE SUM Y2


Return to the Random Walk Case
Study (Background and Data) Page


Dataplot Commands for Rank Sum Test

The Dataplot commands for a rank sum (Wilcoxon rank
sum, MannWhitney) test are
RANK SUM TEST Y1 Y2
RANK SUM TEST Y1 Y2 A
where Y1 contains the data for sample 1, Y2 contains the
data for sample 2, and A is a scalar value (either a number
or a parameter). Y1 and Y2 need not have the same
number of observations.
The first syntax is used to test the hypothesis that
two sample means are equal. The second syntax is used to
test that the difference between two means is equal to a
specified constant.


Return to the Sign Test
Page


Dataplot Commands for the Run Sequence Plot

The Dataplot command to generate a run sequence plot is
Equivalently, you can enter
The appearance of the plot can be controlled with appropriate
settings of the LINE, CHARACTER, SPIKE, and BAR commands
and their associated attributesetting commands.


Return to the Run Sequence Plot Page


Dataplot Command for the Runs Test

The Dataplot command for a runs test is
where Y is a response variable.


Return to the Runs Test Page


Dataplot Commands for Measures of Scale

The various scale measures can be computed in Dataplot as follows:
LET A = VARIANCE Y
LET A = STANDARD DEVIATION Y
LET A = AVERAGE ABSOLUTE DEVIATION Y
LET A = MEDIAN ABSOLUTE DEVIATION Y
LET A = RANGE Y
LET A1 = LOWER QUARTILE Y
LET A2 = UPPER QUARTILE Y
LET IQRANGE = A2  A1


Return to the Measures of Scale Page


Dataplot Commands for Scatter Plots

The Dataplot command to generate a scatter plot is
The appearance of the plot can be controlled by appropriate
settings of the CHARACTER and LINE commands and their various
attributesetting commands.


Return to the Scatter Plot Page


Dataplot Commands for Scatterplot Matrix

The Dataplot command to generate a scatterplot matrix is
SCATTER PLOT MATRIX X1 X2 ... XK
The appearance of the plot can be controlled by appropriate
settings of the CHARACTER and LINE commands and their various
attributesetting commands.
In addition, Dataplot provides a number of SET commands to control
the appearance of the scatterplot matrix. The most common
commands are:
 SET MATRIX PLOT LOWER DIAGONAL <ON/OFF>
This command controls whether or not the plots below the
diagonal are plotted.
 SET MATRIX PLOT TAG <ON/OFF>
If ON, the last variable on the SCATTER PLOT MATRIX command
is not plotted directly. Instead, it is used as a groupid
variable. You can use the CHARACTER and LINE commands to
set the plot attributes for each group.
 SET MATRIX PLOT FRAME <DEFAULT/USER/CONNECTED>
If DEFAULT, the plot frames are connected (that is, it
does a FRAME CORNER COORDINATES 0 0 100 100). The axis tic
marks and labels are controlled automatically. If
CONNECTED, then it is similar to DEFAULT except the current
value of FRAME CORNER COORDINATES is used. This is useful
for putting a small gap between the plots (e.g., enter
FRAME CORNER COORDINATES 3 3 97 97 before generating
the scatterplot matrix). If USER, Dataplot does not
connect the plot frames. The tic marks and labels
are as the user set them.
 SET MATRIX PLOT FIT <NONE/LOWESS/LINEAR/QUADRATIC>
This controls whether a lowess fit, a linear fit, a
quadratic fit line, or no fit is superimposed on the plot
points. If lowess, a rather high value of the lowess
fraction is recommended (e.g., LOWESS FRACTION 0.6).
In Dataplot, enter HELP SCATTER PLOT MATRIX for additional
options for this plot.


Return to the Scatterplot
Matrix Page


Dataplot Commands for Seasonal Subseries Plot

The Dataplot commands to generate a seasonal subseries plot are
LET PERIOD = <value>
LET START = <value>
SEASONAL SUBSERIES PLOT Y
The value of PERIOD defines the length of the seasonal period
(e.g., 12 for monthly data) and START identifies which group the
series starts with (e.g., if you have monthly data that starts in
March, set START to 3).
The appearance of the plot can be controlled by appropriate
settings of the CHARACTER and LINE commands and their various
attributesetting commands.


Return to the Seasonal
Subseries Plot Page


Dataplot Commands for Sign Test

The Dataplot commands for a sign test are
SIGN TEST Y1 A
SIGN TEST Y1 Y2
SIGN TEST Y1 Y2 A
where Y1 contains the data for sample 1, Y2 contains the
data for sample 2, and A is a scalar value (either a number
or a parameter). Y1 and Y2 should have the same
number of observations.
The first syntax is used to test the hypothesis that
the mean for one sample equals a specified constant.
The second syntax is used to test the hypothesis that
two sample means are equal. The third syntax is used to
test that the difference between two means is equal to a
specified constant.


Return to the Sign Test
Page


Dataplot Commands for Signed Rank Test

The Dataplot commands for a signed rank (or Wilcoxon
signedrank) test are
SIGNED RANK TEST Y1 A
SIGNED RANK TEST Y1 Y2
SIGNED RANK TEST Y1 Y2 A
where Y1 contains the data for sample 1, Y2 contains the
data for sample 2, and A is a scalar value (either a number
or a parameter). Y1 and Y2 should have the same
number of observations.
The first syntax is used to test the hypothesis that
the mean for one sample equals a specified constant.
The second syntax is used to test the hypothesis that
two sample means are equal. The third syntax is used to
test that the difference between two means is equal to a
specified constant.


Return to the Signed RANK
Test Page


Dataplot Commands for Skewness and Kurtosis

The Dataplot commands for skewness and kurtosis are
LET A = SKEWNESS Y
LET A = KURTOSIS Y
where Y is the response variable.
Dataplot can also generate plots of the skewness and kurtosis for
grouped data or onefactor data with the following commands:
SKEWNESS PLOT Y X
KURTOSIS PLOT Y X
where Y is the response variable and X is the group id variable.


Return to the Measures of Skewness and
Kurtosis Page


Dataplot Command for the Spectral Plot

The Dataplot command to generate a spectral plot is


Return to the Spectral Plot Page


Dataplot Command for the Standard Deviation Plot

The Dataplot command to generate a standard deviation plot is
STANDARD DEVIATION PLOT Y X
where Y is a response variable and X is a group id variable.
Dataplot supports this command for a number of other common
scale statistics. For example, AAD PLOT Y X and MAD PLOT Y X
compute the average absolute deviation and median absolute
deviation, respectively, instead of the standard deviation
for each group.


Return to the Standard Deviation Plot Page


Dataplot Command for the Star Plot

The Dataplot command to generate a star plot is
STAR PLOT X1 TO XP FOR I = 10 1 10
where there are p response variables called X1, X2, ... ,
XP. Note that this syntax prints one star, specifically the
tenth row of the X1, X2, ..., XP variables.
Typically, multiple star plots will be displayed on the
same page. For example, to plot the first 25 rows on
the same page, enter the following sequence of commands
MULTIPLOT CORNER COORDINATES 0 0 100 100
MULTIPLOT 5 5
LOOP FOR K = 1 1 25
STAR PLOT X1 TO XP FOR I = K 1 K
END OF LOOP


Return to the Star Plot Page


Dataplot Command to Generate a Table of Summary Statistics

The Dataplot command to generate a table of summary statistics is
where Y is the response variable.


Return to the Normal Random Numbers Case
Study (Quantitative Output) Page


Dataplot Commands for the t Probability Functions

Dataplot can compute the probability functions for the t
distribution with the following commands.
cdf

LET Y = TCDF(X,NU,A,B)

pdf

LET Y = TPDF(X,NU,A,B)

ppf

LET Y = TPPF(X,NU,A,B)

random numbers

LET NU = value
LET Y = T RANDOM NUMBERS FOR I = 1 1 1000

probability plot

LET NU = value
T PROBABILITY PLOT Y

ppcc plot

LET NU = value
T PPCC PLOT Y

In the above, X can be a number, a parameter, or a variable. NU is the
shape parameter (= number of degrees of freedom). NU can be a number, a
parameter, or a variable. However, it is typically either a
number or a parameter. A and B are the location and scale parameters,
respectively, and they are optional
(a location of 0 and scale of 1 are used if they are omitted).
If given, A and B can be a number, a parameter, or a variable.
However, they are typically either a number or a parameter.
These functions can be used in the Dataplot PLOT and FIT commands
as well. For example,
PLOT TPDF(X) FOR X = 4 0.01 4


Return to the T Distribution Page


Dataplot Command for TietjenMoore Test

The Dataplot command for the TietjenMoore test is
LET NOUTLIER = <value>
TIETJENMOORE <MINIMUM/MAXIMUM> TEST Y
where Y is the response variable and NOUTLIER specifies the number
of outliers to test. The MINIMUM or MAXIMUM keyword is optional.
If it is omitted, outliers will be checked in both the minimum
and the maximum direction.


Return to the TietjenMoore Page


Dataplot Command for Tolerance Intervals

The Dataplot command for tolerance intervals is
where Y is the response variable. Both normal and
nonparametric tolerance intervals are printed.


Return to the Tolerance
Interval Page


Dataplot Command for TwoSample tTest

The Dataplot command to generate a twosample ttest is
where Y1 contains the data for sample 1 and Y2 contains the
data for sample 2. Y1 and Y2 do not need to have the same
number of observations.


Return to the TwoSample tTest
Page



Dataplot Commands for the TukeyLambda Probability Functions

Dataplot can compute the probability functions for the TukeyLambda
distribution with the following commands.
cdf

LET Y = LAMCDF(X,LAMBDA,A,B)

pdf

LET Y = LAMPDF(X,LAMBDA,A,B)

ppf

LET Y = LAMPPF(X,LAMBDA,A,B)

random numbers

LET LAMBDA = value
LET Y = TUKEYLAMBDA RANDOM NUMBERS FOR I = 1 1 1000

probability plot

LET LAMBDA = value
TUKEYLAMBDA PROBABILITY PLOT Y

ppcc plot

TUKEYLAMBDA PPCC PLOT Y

In the above, X can be a number, a parameter, or a variable. LAMBDA is
the shape parameter and is required. It can be a number, a parameter,
or a variable. It is typically a number or a parameter. A and B
are the location and scale parameters, respectively, and they are
optional (a location of 0 and scale of 1 are used if they are omitted).
If given, A and B can be a number, a parameter, or a variable.
However, they are typically either a number or a parameter.
These functions can be used in the Dataplot PLOT and FIT commands
as well. For example,
PLOT LAMPDF(X,0.14) FOR X = 5 0.01 5


Return to the TukeyLambda Distribution Page


Dataplot Commands for the Uniform Probability Functions

Dataplot can compute the probability functions for the uniform
distribution with the following commands.
cdf

LET Y = UNICDF(X,A,B)

pdf

LET Y = UNIPDF(X,A,B)

ppf

LET Y = UNIPPF(X,A,B)

hazard

LET Y = UNIHAZ(X,A,B)

cumulative hazard

LET Y = UNICHAZ(X,A,B)

survival

LET Y = 1  UNICDF(X,A,B)

inverse survival

LET Y = UNIPPF(1X,A,B)

random numbers

LET Y = UNIFORM RANDOM NUMBERS FOR I = 1 1 1000

probability plot

UNIFORM PROBABILITY PLOT Y

parameter estimation

The method of moment estimators can be computed
with the commands
LET YMEAN = MEAN Y
LET YSD = STANDARD DEVIATION Y
LET A = YMEAN  SQRT(3)*YSD
LET B = YMEAN + SQRT(3)*YSD
The maximum likelihood estimators can be computed with the
commands
LET YRANGE = RANGE Y
LET YMIDRANG = MIDRANGE Y
LET A = YMIDRANG  0.5*YRANGE
LET B = YMIDRANG + 0.5*YRANGE

In the above, X can be a number, a parameter, or a variable. A and B
are the lower and upper limits of the uniform distribution
and they are optional (A is 0 and B is 1 if they are omitted).
The location parameter is A and the scale parameter is (B  A).
If given, A and B can be a number, a parameter, or a variable.
However, they are typically either a number or a parameter.
These functions can be used in the Dataplot PLOT and FIT commands
as well. For example,
PLOT UNIPDF(X) FOR X = 0 0.1 1


Return to the Uniform Distribution Page


Dataplot Commands for the Generation of Uniform Random Numbers

The Dataplot commands to generate 1,000 uniform random numbers
in the interval (100,100) are
LET A = 100
LET B = 100
LET Y = UNIFORM RANDOM NUMBERS FOR I = 1 1 1000
LET Y = A + (BA)*Y
A similar technique can be used for any package that can
generate standard uniform random numbers. Simply multiply
by the scale value (equals upper limit minus lower limit)
and add the location value.
Programs that automatically generate random numbers are typically
controlled by a seed, which is usually an integer value. The
importance of the seed is that it allows the random numbers to be
replicated. That is, giving the program the same seed should generate
the same sequence of random numbers. If the ability to replicate the
set of random numbers is not important, you can give any valid value
for the seed.
In Dataplot, the seed is an odd integer with a minimum (and default)
value of 305. Seeds less than 305 generate the same sequence as 305
and even numbers generate the same sequence as the preceeding odd
number. To change the seed value to 401 in Dataplot, enter the
command:


Return to the Uniform Random Numbers Case
Study (Background and Data) Page


Dataplot Commands for the Weibull Probability Functions

Dataplot can compute the probability functions for the Weibull
distribution with the following commands.
cdf

LET Y = WEICDF(X,GAMMA,A,B)

pdf

LET Y = WEIPDF(X,GAMMA,A,B)

ppf

LET Y = WEIPPF(X,GAMMA,A,B)

hazard

LET Y = WEIHAZ(X,GAMMA,A,B)

cumulative hazard

LET Y = WEICHAZ(X,GAMMA,A,B)

survival

LET Y = 1  WEICDF(X,GAMMA,A,B)

inverse survival

LET Y = WEIPPF(1X,GAMMA,A,B)

random numbers

LET GAMMA = value
LET Y = WEIBULL RANDOM NUMBERS FOR I = 1 1 1000

probability plot

LET GAMMA = value
WEIBULL PROBABILITY PLOT Y

ppcc plot

LET GAMMA = value
WEIBULL PPCC PLOT Y

parameter estimation

If your data are not censored, enter the commands
SET CENSORING TYPE NONE
WEIBULL MLE Y
If your data have type 1 censoring at fixed time t_{0},
enter the commands
LET TEND = censoring time
SET CENSORING TYPE 1
WEIBULL MLE Y X
If your data have type 2 censoring, enter the commands
SET CENSORING TYPE 2
WEIBULL MLE Y X
Y is the response variable and X is the censoring variable
where a value of 1 indicates a failure time and a value of
0 indicates a censoring time. In addition to the
point estimates, confidence intervals for the parameters
are generated.

In the above, X can be a number, a parameter, or a variable. GAMMA is
the shape parameter and is required. It can be a number, a parameter,
or a variable. It is typically a number or a parameter. A and B
are the location and scale parameters, respectively, and they are
optional (a location of 0 and scale of 1 are used if they are omitted).
If given, A and B can be a number, a parameter, or a variable.
However, they are typically either a number or a parameter.
These functions can be used in the Dataplot PLOT and FIT commands
as well. For example,
PLOT WEIPDF(X,2) FOR X = 0.01 0.01 5


Return to the Weibull Distribution
Page


Dataplot Commands for the Weibull Plot

The Dataplot commands to generate a Weibull plot are
WEIBULL PLOT Y
WEIBULL PLOT Y X
where Y is the response variable containing failure times
and X is an optional censoring variable. A value of 1 indicates
the item failed by the failure mode of interest while a value of
0 indicates that the item failed by a failure mode that is not
of interest.
The appearance of the plot can be controlled with appropriate
settings for the LINE and CHARACTER commands. For example,
to draw the raw data with the "X" character and the 2 reference
lines as dashed lines, enter the commands
LINE BLANK DASH DASH
CHARACTER X BLANK BLANK
WEIBULL PLOT Y X
Dataplot saves the following internal parameters after the
Weibull plot.
ETA  the estimated characterstic life
BETA  the estimated shape parameter
SDETA  the estimated standard deviation of ETA
SDBETA  the estimated standard deviation of BETA
BPT1  the estimated 0.1% point of failure times
BPT5  the estimated 0.5% point of failure times
B1  the estimated 1% point of failure times
B5  the estimated 5% point of failure times
B10  the estimated 10% point of failure times
B20  the estimated 20% point of failure times
B50  the estimated 50% point of failure times
B80  the estimated 80% point of failure times
B90  the estimated 90% point of failure times
B95  the estimated 95% point of failure times
B99  the estimated 99% point of failure times
B995  the estimated 99.5% point of failure times
B999  the estimated 99.9% point of failure times


Return to the Weibull Plot Page


Dataplot Command for the WilkShapiro Normality Test

The Dataplot command for a WilkShapiro normality test is
where Y is the response variable.
The significance value is only valid if there is less than
5,000 points.


Return to the Wilk Shapiro
Page


Dataplot Commands for Yates Analysis

The Dataplot command for a Yates analysis is
where Y is a response variable in Yates order.


Return to the Yates Analysis
Page


Dataplot Commands for the Youden Plot

The Dataplot command to generate a Youden plot is
where Y1 and Y2 are the response variables and LAB is
a laboratory (or run number) identifier. The LINE and
CHARACTER commands can be used to control the appearance
of the Youden plot. For example, if there are 5 labs,
a typical sequence would be
LINE BLANK ALL
CHARACTER 1 2 3 4 5
YOUDEN PLOT Y X LAB


Return to the Youden Plot Page


Dataplot Commands for the 4plot

The Dataplot command to generate the 4plot is
where Y is the response variable.


Return to the 4Plot Page


Dataplot Commands for the 6Plot

The Dataplot commands to generate a 6plot are
where Y is the response variable and X is the independent
variable.


Return to the 6Plot Page
