BLOCK PLOT

Name:

BLOCK PLOT Type:

Graphics Command Purpose:

Generates a block plot. Description:

It replaces the analysis of variance test with a less assumption-dependent binomial test and should be routinely used whenever we are trying to robustly decide whether a primary factor has an effect.

Block plots are formed as follows:

Vertical axis:	the response variable
Horizontal axis:	all combinations of all levels of all nuisance (secondary) factors
Plot Character:	levels of the primary factor

For example, if we have 2 nuisance factors and n1=2 and n2=2, the blocks will be set up on the X axis as follows:

 
          |                |          |               |
        =====================       =====================
        x2(1)            x2(2)      X2(1)           X2(2)
                 |                           |
               x1(1)                       x1(2)

Syntax 1:

Syntax 2:

Enter HELP STATISTICS for a list of Dataplot's supported statistics.

Note that only statistics requiring a single response variable are supported (e.g., MEAN BLOCK PLOT is supported, but CORRELATION BLOCK PLOT is not).

This syntax can be used when there is replication at each of the combinations of factor levels. The requested statistic is calculated for all the response values with the same levels of the factor variables. The variable is plotted at the computed statistic on the vertical axis. MEAN BLOCK PLOT is the most commonly used.

Examples:

Note:

HEADS:	the number of times the heads setting is the maximum value
TRIALS:	the total number of blocks
FACES:	the number of settings for the primary factor
TAILPROB:	the binomial CDF based on the number of heads and the number of trials
AVEDEL:	the mean difference between the minimum setting and the maximum setting of the primary factor
SDAVED:	the standard error of AVEDEL

Note:

When the BLOCK PLOT FILTER option is ON, when a specific block only has one value for the combination of factor levels, that block will be suppressed. This option is OFF by default.

The other two commands are most frequently used when the FILTER option is ON. The BLOCK PLOT LABEL will label the level of the last nuisance factor of the block. When the FILTER option results in many missing blocks, this can be helpful. The BLOCK PLOT WIDTH option allows you to manually set the width of the blocks. In most cases, this is not needed. However, it may occassionally be helpful to be able to do this. The value is set in 0 to 100 screen units. A typical value would be on the order of 0.05.

Note:

SET BLOCK PLOT BACKGROUND <ON/OFF>

If this option is ON, you can use the REGION commands to provide a background color for the blocks. The first block uses the first arguments of the REGION commands, the second block uses the second argumemts of the REGION commands, and so on. This is demonstrated in the Program 2 example below.

In some cases, you may want to give all blocks the same background. You can do this with the command

In other cases, you may want to highlight specific blocks with different colors. For example, if the blocks have two levels (say 1 and 2), you may want to color those blocks where 1 is higher than 2 with one color and those blocks where 2 is higher than 1 with another color. In this case, you need to list the specific color for each block as is demonstrated in the Program 2 example.

Note:

SET BLOCK PLOT JITTER <value>

where <value> is a value between 0 and 1 (values less than 0 are set to 0 and values greater than 1 are set to 1). Typically this value should be less than 0.5. A value of 0 means that no jittering is applied (this is the default).

This option can be useful if the plot characters within a block have significant overlap so that some of the characters are not readable. With this option, you can add some "jitter" so that the characters are offset horizontally.

Specifically, a uniform random number between -<value> and +<value> will be generated and that will be added to the x-coordinate value of the character position.

Default:

None Synonyms:

None Related Commands:

LINES	=	Sets the type for plot lines.
CHARACTER	=	Sets the type for plot characters
BOX PLOT	=	Generates a box plot
YOUDEN PLOT	=	Generates a Youden plot.
ANOVA	=	Performs a fixed effects analysis of variance for balanced data.
PLOT	=	Generates a data or function plot.

Applications:

Analysis of Variance Reference:

Quality Through Engineering Design

Implementation Date:

Program 1:

 
READ Y PROC PLANT SPEED SHIFT
28.4    1     1    1    1
21.9    2     1    1    1
36.8    1     1    1    2
19.2    2     1    1    2
28.2    1     1    1    3
26.6    2     1    1    3
30.4    1     1    2    1
25.1    2     1    2    1
25.5    1     1    2    2
21.5    2     1    2    2
26.0    1     1    2    3
21.9    2     1    2    3
20.2    1     2    1    1
14.3    2     2    1    1
19.9    1     2    1    2
22.5    2     2    1    2
23.4    1     2    1    3
18.5    2     2    1    3
38.2    1     2    2    1
12.8    2     2    2    1
22.0    1     2    2    2
22.5    2     2    2    2
30.3    1     2    2    3
17.7    2     2    2    3
END OF DATA
.
XLIMITS 1 2
MAJOR X1TIC MARK NUMBER 2
MINOR X1TIC MARK NUMBER 0
TIC MARK OFFSET UNITS DATA
X1TIC MARK OFFSET 0.6 0.6
X1TIC MARK LABEL FORMAT ALPHA
X1TIC MARK LABEL CASE ASIS
X1TIC MARK LABEL CONTENT PlantSP()1CR()Speed(2)-Shift(3) ...
                         PlantSP()2CR()Speed(2)-Shift(3)
.
CHARACTERS 1 2
LINE BLANK BLANK
BLOCK PLOT Y PLANT SPEED SHIFT PROC
.
LET CDF = ROUND(TAILPROB,3)
CASE ASIS
JUST CENTER
MOVE 50 5
TEXT Heads: ^heads, Trials: ^trials, CDF: ^cdf

Program 2:

 
LET Y = DATA  55 61 57 58 62 54
LET X = DATA   1  1  2  2  3  3
LET TAG = DATA 1  2  1  2  1  2
.
CHARACTER 1 2
REGION FILL ON ON ON
REGION FILL COLOR BLUE BLUE RED
.
SET BLOCK PLOT BACKGROUND ON
BLOCK PLOT Y X TAG