SED navigation bar go to SED home page go to Dataplot home page go to NIST home page SED Home Page SED Staff SED Projects SED Products and Publications Search SED Pages
Dataplot Vol 1 Vol 2

I PLOT

Name:
    I PLOT
Type:
    Graphics Command
Purpose:
    Generates an I plot.
Description:
    Given a response variable and a group-id variable, the I plot is used to plot a location value, a lower extreme value, and an upper extreme value for each group. The default is to use the median for the location and the minimum and maximum values as the extreme points (alternatives will be discussed below).

    An I plot is used in two ways:

    1. As a graphical data analysis technique (similar to the box plot, but simpler) for determining if differences exist between the various levels of a 1-factor model. It is a graphical alternative to 1-factor ANOVA.

    2. As an uncertainty chart in which the analyst wishes to plot estimated values of a certain quantity and to also illustrate the uncertainty bars associated with each estimate. In such case, a given value of the horizontal axis variable is typically accompanied by exactly 3 values for the vertical axis variable:

      1. the estimate - the uncertainty;
      2. the estimate;
      3. the estimate + the uncertainty.

    For both applications, the resulting plot is similar in appearance. Namely, a target value which typically appears as an X, a vertical bar with small horizontal bars at the extremes (hence the name "I plot").

    The I plot has five components (characters and lines) which can be individually controlled. These components are:

    1. the maximum (or upper extreme value)
    2. the median (or other location value)
    3. the minimum (or lower extreme value)
    4. the line between the median (location value) and the maximum (upper extreme)
    5. the line between the median (location value) and the minimum (lower extreme)

    For the default I plot, the I PLOT command can be preceded by the following two commands:

      CHARACTERS I PLOT
      LINES I PLOT

    With these commands, the first three lines are set to blank and lines four and five are set blank. The second character is set to "X", characters one and three are set to "-", and characters four and five are set to blank. After the I plot is formed, the analyst should redefine plot characters and lines via the usual CHARACTERS and LINES commands.

    As mentioned above, the I plot can use location statistics other than the median. Specifically, you can use the MEAN I PLOT, MIDMEAN I PLOT, MIDRANGE I PLOT, TRIMMED MEAN I PLOT, and BIWEIGHT I PLOT to specify the mean, midmean, midrange, trimmed mean, and biweight location, respectively.

    This plot is also useful for displaying confidence intervals as well as other types of intervals. The following are currently supported:

    1. mean confidence limits
    2. trimmed mean confidence limits
    3. median confidence limits
    4. quantile confidence limits
    5. biweight confidence limits
    6. one standard error (mean ± \(s/\sqrt{n}\))
    7. two standard error (mean ± \(2s/\sqrt{n}i\))
    8. one standard deviation (mean ± s)
    9. two standard deviation (mean ± 2s)
    10. normal tolerance limits
    11. normal prediction limits
    12. Agresti Coull limits (for binomial proportions)
Syntax 1:
    <stat> I PLOT <y> <x>             <SUBSET/EXCEPT/FOR qualification>
    where <stat> is MEDIAN, MEAN, MIDMEAN, MIDRANGE, BIWEIGHT,
                           or TRIMMED MEAN;
                <y> is the response (= dependent) variable;
                <x> is the horizontal axis (= independent) variable;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.

    For this syntax, the extreme values will be the minimum and maximum values. If <stat> is omitted, the location statistic will be the median.

Syntax 2:
    <stat> PLOT <y> <x>             <SUBSET/EXCEPT/FOR qualification>
    where <stat> is one of:
                           MEAN CONFIDENCE LIMIT
                           TRIMMED MEAN CONFIDENCE LIMIT
                           MEDIAN CONFIDENCE LIMIT
                           QUANTILE CONFIDENCE LIMIT
                           BIWEIGHT CONFIDENCE LIMIT
                           STANDARD DEVIATION CONFIDENCE LIMIT
                           NORMAL TOLERANCE LIMIT
                           NORMAL PREDICTION LIMIT
                           AGRESTI COULL LIMIT
                           ONE STANDARD ERROR
                           TWO STANDARD ERROR
                           ONE STANDARD DEVIATION
                           TWO STANDARD DEVIATIONS
                <y> is the response (= dependent) variable;
                <x> is the horizontal axis (= independent) variable;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.

    For this syntax, the extreme values will be the lower and upper bounds of the appropriate limits.

Syntax 3:
    MULTIPLE <stat> PLOT <y1> ... <yk>
                            <SUBSET/EXCEPT/FOR qualification>
    where <stat> is one of:
                            MEDIAN I
                            MEAN I
                            MIDMEAN I
                            MIDRANGE I
                            BIWEIGHT I
                            TRIMMED MEAN I
                            MEAN CONFIDENCE LIMIT
                            TRIMMED MEAN CONFIDENCE LIMIT
                            MEDIAN CONFIDENCE LIMIT
                            QUANTILE CONFIDENCE LIMIT
                            BIWEIGHT CONFIDENCE LIMIT
                            STANDARD DEVIATION CONFIDENCE LIMIT
                            NORMAL TOLERANCE LIMIT
                            NORMAL PREDICTION LIMIT
                            ONE STANDARD ERROR
                            TWO STANDARD ERROR
                            ONE STANDARD DEVIATION
                            TWO STANDARD DEVIATION
                <y1> ... <yk> is a list of up to k response variables;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.

    This syntax is useful when the data for each group is stored in separate response variables. Up to 30 response variables may be specified.

    Note that the syntax

      MULTIPLE I PLOT Y1 TO Y4

    is supported. This is equivalent to

      MULTIPLE I PLOT Y1 Y2 Y3 Y4
Syntax 4:
    REPLICATED <stat> PLOT <y> <x1> ... <xk>
                            <SUBSET/EXCEPT/FOR qualification>
    where <stat> is one of the variants listed for Syntax 3;
                <y> is the response variable;
                <x1> ... <xk> is a list of up to k group-id variables;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.

    This syntax performs a cross-tabulation of <x1> ... <xk> and generates an i plot (on the same graph) for each unique combination of cross-tabulated values. For example, if X1 has 3 levels and X2 has 2 levels, there will be a total of 6 i plots generated. Up to six group-id variables can be specified.

    Note that the syntax

    REPLICATED I PLOT Y X1 TO X4

    is supported. This is equivalent to

    REPLICATED I PLOT Y X1 X2 X3 X4

    In this syntax, all i plots are drawn with the sampe plot attributes.

    As an example of how the x-coordinates are determined, assume we have 3 levels for X1 and 2 levels for X2. The x-coordinates will be

      X1 X2 X-COORDINATE
      1 1 1
      1 2 2
      2 1 3
      2 2 4
      3 1 5
      3 2 6
Syntax 5:
    <stat> PLOT <y> <x1> <x2>
                            <SUBSET/EXCEPT/FOR qualification>
    where <stat> is one of the variants listed for Syntax 3;
                <y> is the response variable;
                <x1> is the first group-id variable;
                <x2> is the second group-id variable;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.

    This syntax is similar to syntax 4. However, it has the following distinctions:

    1. There must be exactly two group-id variables and the word REPLICATION is omitted from the command.

    2. The groups in the second group-id variable are drawn with different attributes.

    3. The x-coordinates are generated to emphasize the comparisons between the groups for each level of the group. Using the same example as Syntax 4, we have
        X1 X2 X-COORDINATE
        1 1 0.8
        1 2 1.2
        2 1 1.8
        2 2 2.2
        3 1 2.8
        3 2 3.2

    Program 2 demonstrates the difference between Syntax 4 and Syntax 5.

Examples:
    I PLOT Y X
    I PLOT Y X SUBSET X > 2
    ONE STANDARD ERROR PLOT Y X
    MEAN CONFIDENCE LIMIT PLOT Y X
Note:
    The ERROR BAR PLOT provides a more general method for error bars in that it can support asymmetric limits and errors in both the horizontal and vertical directions. However, the I PLOT syntax can be easier for some basic cases (i.e., for confidence limits or for one or two standard errors from the mean).
Note:
    For some cases, you can specify optional parameters.

    To specify the alpha level for the confidence limit cases, enter the command (0.05 will be used if this command is not given)

      LET ALPHA = <value>

    For the QUANTILE CONFIDENCE LIMIT case, specify the desired quantile with the command (0.50 will be used if this command is not given)

      LET XQ = <value>

    For the TRIMMED MEAN CONFIDENCE LIMIT case, specify the trimming parameters with the commands (0.25 and 0.75 will be used if these commands are not given)

      LET P1 = <value>
      LET P2 = <value>
Default:
    None
Synonyms:
    None
Related Commands: Applications:
    One Factor Analysis, Data Analysis
Implementation Date:
    Pre-1987
    2011/02: Support for MULTIPLE and REPLICATION options
    2013/10: Support for MEAN, MIDMEAN, MIDRANGE I plots
    2013/10: Support for various confidence interval cases (Syntax 2)
    2013/10: Support for special 3 variable case (Syntax 5)
Program 1:
     
    . Step 1:   Read the data
    .
    skip 25
    read gear.dat y x
    .
    . Step 2:   Basic i-plot
    .
    title case asis
    title offset 2
    label case asis
    character case asis
    line i plot
    character blank circle blank blank blank
    character fill off on
    character hw 0.5 0.375 all
    xlimits 1 10
    major xtic mark number 10
    minor xtic mark number 0
    x1tic mark offset 0.5 0.5
    title automatic
    .
    multiplot corner coordinates 5 5 95 95
    multiplot scale factor 2
    multiplot 2 2
    i plot y x
    mean i plot y x
    midrange i plot y x
    midmean i plot y x
    end of multiplot
        
    plot generated by sample program
    .
    multiplot 2 2
    one standard error plot y x
    two standard error plot y x
    mean confidence limit plot y x
    median confidence limit plot y x
    end of multiplot
    .
        
    plot generated by sample program
    multiplot 2 2
    mean confidence limit plot y x
    median confidence limit plot y x
    biweight confidence limit plot y x
    trimmed mean confidence limit plot y x
    end of multiplot
        
    plot generated by sample program
Program 2:
     
    . Step 1:   Read the data
    .
    .           y = voltage drop
    .           x1  = elapsed days (1, 8, 15, 29, 43, 57, 71, 107)
    .           x2  = type of connector
    .                 1 = brass
    .                 2 = steel
    .                 3 = innovative
    skip 25
    read clark0.dat  y days x2
    let days = 8 subset days = 9
    let days = 15 subset days = 16
    let days = 29 subset days = 30
    let days = 43 subset days = 44
    let days = 57 subset days = 58
    let days = 71 subset days = 72
    let days = 107 subset days = 108
    let x1 = coded days
    let nx1 = unique x1
    let nx2 = unique x2
    let ntot = nx1*nx2
    .
    . Step 2:   I Plot with standard replication option
    .
    title case asis
    title offset 2
    label case asis
    character case asis
    line i plot
    character blank circle blank blank blank
    character fill off on
    character hw 0.5 0.375 all
    .
    y1label Voltage Drop
    x3label Elapsed Days/Connector Type
    xlimits 1 ntot
    major xtic mark number ntot
    minor xtic mark number 0
    x1tic mark offset 0.5 0.5
    x1tic mark label format alpha
    x1tic mark label content 1 8 15 29 43 57 71 107 1 8 15 29 43 57 71 107 ...
          1 8 15 29 43 57 71 107 
    x1tic mark label size 1.6
    title automatic
    replicated i plot y x2 x1
    .
    justification center
    let xcoor = (nx1/2) + 0.5
    let ycoor = 10
    moveds xcoor ycoor
    text Brass
    let xcoor = xcoor + nx1
    moveds xcoor ycoor
    text Steel
    let xcoor = xcoor + nx1
    moveds xcoor ycoor
    text Innovative
        
    plot generated by sample program
    .
    . Step 3:   I Plot with alternative replication option
    .
    line i plot bl bl bl so so bl bl bl so so bl bl bl so so
    character bl circ bl bl bl bl circ bl bl bl bl circ bl bl bl
    character fill on all
    character hw 0.5 0.375 all
    character color blue blue blue blue blue red red red red red ...
                    green green green green green
    line color blue blue blue blue blue red red red red red ...
               green green green green green
    .
    x1label Elapsed Days/Connector Type
    x3label
    xlimits 1 nx1
    major xtic mark number nx1
    minor xtic mark number 0
    x1tic mark offset 0.5 0.5
    x1tic mark label format alpha
    x1tic mark label content 1 8 15 29 43 57 71 107
    title automatic
    i plot y x1 x2
        
    plot generated by sample program

Privacy Policy/Security Notice
Disclaimer | FOIA

NIST is an agency of the U.S. Commerce Department.

Date created: 11/05/2013
Last updated: 11/05/2013

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