Results from statistical calculations often include display of graphics, and when required, programs from StatToolsalso display graphics as part of the results. Explanations for these graphical outputs are usually included in the explanation of the statistical procedure involved.

There are however stand-alone graphical programs, using the MacroPlot system, and they are explained in their panels within this page.

The MacroPlot Help Page provides detailed explanations on how MacroPlot works, and templates for all MacroPlot commands. Users who wish to use MacroPlot as their graphical utility should familiarize themselves with this help file.

The MacroPlot Program Page is a general purpose graphic editor. It contains a text area for users to enter their own MacroPlot Commands to create whatever graphic within MacroPlot's capabilities. The text box contains random MacroPlot codes as examples for the user.

Data input for the Pie Chart Program Page consists of a single column of values

MacroPlot Code Generation

1. The program converts the number in each row to a percent of the total
2. The percent is converted into wedges in a pie, so that 360 degrees forms the total of 100%
3. The wedges starts at 3 O'clock and proceeds clockwise
4. The fill color for each edge are random numbers generated on the run, so that each run will produce a different set of colors. Users may choose to edit the colors. Color codes to assist in this process is available in the MacroPlot Help Page
5. The MacroPlot codes are placed in a text box, to allow further editing and replotting by the user
6. The bitmap is produced. according to the MacroPlot codes
7. The MacroPlot codes are further translated into VBA codes, which can be imported as macros to a Powerpoint file to create Vector graphic.

Explanation of the example codes : explanations in maroon

Bitmap Initialise 420 300 255 255 255 255 Creates a bitmap 420 pixels wide x 300 pixels high, white background
Line Thick 2 Lines 2 pixels wide
Font Style 1 Text in bold
Fill Color 238 215 40 255 Color of first wedge using red green blue, each a random number 0-255, α=255(opaque)
Bitmap Wedge 125 125 105 0 0 187 A wedge, center(x=125, y=125), radius=105, centrifuged (0 pixels), angles (0-187 degs)
Bitmap Square 5 250 8 A square, radius=5 pixels, center(x=250, y=8)
Bitmap HText 0 1 260 8 52.00% Text="52.00%", Align (horizontal : 0=left, vertical : 1=center), position (x=260 y=8)
The rest of the codes are repeat of other wedges with different color and in different position
Fill Color 172 234 172 255
Bitmap Wedge 125 125 105 0 187 255
Bitmap Square 5 250 24
Bitmap HText 0 1 260 24 18.99%
Fill Color 47 2 67 255
Bitmap Wedge 125 125 105 0 255 270
Bitmap Square 5 250 40
Bitmap HText 0 1 260 40 4.01%
Fill Color 80 143 114 255
Bitmap Wedge 125 125 105 0 270 360
Bitmap Square 5 250 56
Bitmap HText 0 1 260 56 25.00%

Vertical Bar Plots : This is the most common type of bar plots, where the y axis represents percent or values, for different groups identified by the x axis.

• The data input for the Bar Plot Program Page is a table with 2 columns.
  • Column 1 is the x value, representing where the bar will be placed
  • Column 2 the y value, representing how tall the bar will be
• There are two arrangements for vertical bar plots.
  • X axis contains labels : In this arrangement, the groups on the x axis, be they text or numbers are labels, and the bars are evenly spaced. This plot is therefore identical to the one produced by Excel. For example, if the x values for the bars are 1, 1.5, 3, and 4, then the bars are separated with equal distances, the distance between bars for 1 and 1.5 is the same as that for 1.5 and 3, also that between 3 and 4

    Column 1 is process as text. It must be a single word with no gaps. If a gap is required, it should be represented by the underscore _. Column 2 must be a number

  • X axis contains measurements : In this measurement, the x axis is a numerical scale, and the distances between the bars depends on their numerical value. For example, if the x values for the bars are 1, 1.5, 3, and 4, then the distance between the bars for 1 and 1.5 (1.5-1=0.5) is narrower than that between 3 and 4 (4-3=1.0), which is narrower than between 1.5 and 3 (3-1.5=1.5)

    Both columns 1 and 2 must be numbers

Horizontal Bar Plots : This is conceptually the same as the vertical bar plot, except the bars are horizontal

The data is a table with 2 columns.

• Column 1 is the x value, representing how long the bar will be from the left
• Column 2 the y value, representing where the bar will be placed
• Both x and y values must be numbers

MacroPlot Code Generation

1. The program estimates minimum and maximum values for x and y, and creates an inner plotting area
2. Intervals and labels are marked according to minimum and maximum values. These provides some idea of where the values are, but usually not suitable for publication. Users should edit the labels and scaling in the MacroPlot codes, and re-creates the more publishable plot.
3. The bars are painted into the plotting area. Again, users may wish to edit the width and colors of the bars

Explanation of the example codes : explanations in maroon

• Plotting area, scaling and labelling. Please note that the numerical parameters will need editing
  Bitmap Initialise 700 500 255 255 255 255 Creates a bitmap 7000 pixels wide x 500 pixels high, white background
  Line Thick 2 Lines 2 pixels wide
  Font Style 1 Text in bold
  Plot Values 0 5.25 9.5 0.75 Set range of values in the plotting area, x=0 to 9.5, y=0.75 to 5.25
  Plot XAxis 0.75 0 0.5 0 1.0 Place x axis at y=0.75, mark from 0 at 0.5 interval, scale from 0 at 1.0 interval
  Plot YAxis 0 0.75 0.2 0.75 0.4 Place y axis at x=0, mark from 0.75 at 0.2 interval, scale from 0.75 at 0.4 interval
  Plot XLabel x 20 Place the label "x" 20 pixels below the bottom of the plotting area
  Plot YLabel y 30 Place the label "y" 30 pixels to the left of the plotting area
• Vertical Bars
  Plot VBar 15 2 0 213 Place a vertical bar, 31 (2x15+1) pixels wide, at from y=0 to y=213, where x=2
  Plot HText 1 0 3 0 CS 0 2 Text="CS", Align (horizontal : 1=center, vertical : 0=top), position (x=3 y=0), then shift the text 0 pixels horizontally and 2 (+=downwards) pixels vertically. In other words, place "CS" centered the text at x=3 and the top of text 2 pixels below where y=0
• Horizontal Bars
  Plot HBar 15 0 5 1 Place a horizontal bar, 31 (2x15+1) pixels tall, from x=0 to x=5, where y = 1

Forest plots, as in the Forest Plot Program Page are commonly used for the comparison of effect sizes and their confidence intervals, particularly in meta-analysis, where the results of individual studies and their combinations can be displayed in an easily interpretable plot.

Two scaling options are available

• Normal scaling assumes normally distributed values, with a null value of zero 0
• Logarithmic scaling is for the log-normally distributed variables such as ratios, with a null value of one (1). All data in a logarithmically scaled plot must be >0, or the program will crash.

Data Input : The data is a table with 3 columns, separated by spaces or tabs

• Each row is data from a set of effect size
• Column 1 is the central value, usually the mean
• Column 2 and 3 are values for the limits of the confidence interval

MacroPlot Code Generation

1. Program estimates the range of the x axis, and produce the inner plotting area
2. Program then scales the x axis
   • For normal scaling, the markings and scaling are from the central 0 value outwards
   • For logarithmic scaling, the program produces a logarithmic scaling in multiples of 10s
3. Program places each set of effect size, in order from top downwards. The central value represented by a circular dot, and the confidence interval as a line.

Explanation of the example codes : explanations in maroon

• Plotting area, scaling and labelling. Please note that the numerical parameters will need editing
  Bitmap Initialise 300 420 255 255 255 255 Creates a bitmap 300 pixels wide x 420 pixels high, white background
  Plot Pixels 45 21 255 357 Defines the plotting area as 45 and 255 pixels from the left, 21 and 357 pixels from the top
  Line Thick 2 Lines 2 pixels wide
  Font Style 1 Text in bold
  Plot XLabel Forest_Plot 20 Place the label "Forest Plot" 20 pixels below the plotting area. The label can be edited
  Normal Scaling
  Plot Values -0.1875 -1 0.2188 7 Defines the ranges : x from -0.1875 to 0.2188, and y from -1 to 7
  Plot XAxis 7 0 0.03 0 0.06 From zero (0) outwards, at y=7, mark every 0.03 and scale every 0.06. The values require editing
  Plot XAxis 7 0 -0.03 -0.06 -0.06 From zero (0) outwards, at y=7, mark every -0.03 and scale every -0.06. The values require editing
  Plot Line 0 -1 0 7 Draw the line for null, at x=0, from y=-1 to y=7
  Logarithmic scaling
  Plot Values 0.1000 -1 10 7 Defines the ranges : x from 0.1000 to 10, and y from -1 to 7
  Plot XLog Defines the x axis is logarithmically scaled
  Plot XAxisLog 7 Mark and scale the x axis, logarithmically, in multiples of 10
  Plot Line 1 -1 1 7 Draw the line for null, at x=1, from y=-1 to y=7
• Draw the effect size
  Fill Color 0 0 0 255 Set the fill color to black and opaque, for the circular dots
  Line Thick 4 Set the line thickness to 4 pixels, for the confidence intervals
  Plot Line 0.69 1 2.02 1 Draw a line from x=0.69 to x=2.02, where y=1, to mark the confidence interval
  Plot Circle 5 1.18 1 Draw a circular dot with 5 pixels radius, where x=1.18 and y=1, to mark the mean

Scatter plot, as in the Scatter Plot Program Page is a two dimensional plot which displays the relationship between the x and y value of each data point. Although this is a very common plot, it is mainly used as a background to display other statistical results.

Although the Scatter Plot Program Page provides 4 options for scatter plot, they are merely different ways of scaling for the two axis, while data input the main plotting algorithm remains the same. The only thing to remember is that values for any logarithmic calculations must be >0, or the program will crash.

Data Input : The data is a table with 2 columns, separated by spaces or tabs

• Each row is data from a subject to be plotted
• Column 1 is the x value
• Column 2 is the y value

Dot size :

• The size of the dot representing each data point has a diameter of 2 x dotsize + 1. The default radius is 5, making the dot 11 pixels in diameter
• If dotsize is <=0, then a single pixel will be plotted

MacroPlot Code Generation

1. Program estimates the range of the x and y variables, and depending on normal or logarithmic scales, produce the inner plotting area
2. Program then scales the two axis
   • For normal scaling, the markings are approximately 1/10 of the range, and scaling are approximately 1/5 of the range
   • For logarithmic scaling, the program produces a logarithmic scaling in multiples of 10s
3. Program places each data point as a circular dot on the plot. The default is black circular dots, but these can be edited by the user.

Explanation of the example codes : explanations in maroon

• Plotting area, scaling and labelling. Please note that the numerical parameters will need editing
  Bitmap Initialise 700 500 255 255 255 255 Creates a bitmap 700 pixels wide x 500 pixels high, white background
  Plot Values 34.5 3625 41.5 2374 Set the range of values, x from 34.5 to 41.5, y from 2374 to 3625
  Line Thick 2 Lines 2 pixels wide
  Font Style 1 Text in bold
  Plot XLabel X_Values 20 Place the label "X Values" 20 pixels below the plotting area. The label can be edited
  Plot YLabel Y_Values 55 Place the label "Y Values" 50 pixels to the left of the plotting area. The label can be edited
  Normal Scaling
  Plot XAxis 2374 34.5 0.5 34.5 1.0 Place x axis at y=2374, mark from 34.5 at 0.5 intervals, scale from 34.5 at 1.0 intervals. The values require editing
  Plot YAxis 34.5 2374 125 2374 250 Place y axis at x=34.5, mark from 2374 at 125 intervals, scale from 2374 at 250 intervals. The values require editing
  Logarithmic scaling
  Plot Values 10 10000 100 1000 Defines the ranges : x from 10 to 100, and y from 1000 to 10000
  Plot XLog Defines the x axis is logarithmically scaled
  Plot XAxisLog 1000 Placed the x axis where y=1000. Mark and scale the x axis, logarithmically, in multiples of 10
  Plot YLog Defines the y axis is logarithmically scaled
  Plot YAxisLog 10 Placed the y axis where x=10. Mark and scale the y axis, logarithmically, in multiples of 10
• Draw the dot
  Fill Color 0 0 0 255 Set the fill color to black and opaque, for the circular dots
  Plot Circle 5 37 3048 0 0 Draw a circular dot with 5 pixels radius, where x=37 and y=3028, with horizontal shifts of 0 pixels, and vertical shift of 0 pixels.

  Pleas Note : the shift values at the end of the command allows the dot to be moved by a designated number of pixels.

  • The first shift value moves the dot horizontally, a negative value moves it to the left, positive value to the right
  • The second shift value moves the dot vertically, a negative value moves it upwards, positive value downwards
  In most cases the default (0 0 = no move) is used and the values need not be included in the macro. However, in a scatterplot, particularly when there are numerous dots, some dots have same values, so they overlap and cannot be seen. The shift allows dots with same values to be moved slightly so they can be seen. As the program does not check for overlap, all dots have 0 0 shifts, and it is up to the user to edit these values when required

The Count Table Plot was created to produce a plot of a contingency table of counts, to allow an immediate visualisation and precise estimate of the sample size in each of the cells.

The program Count Table Plot Program Page provides the following

• The input is a table of counts, each row must have the same number of columns. Empty cells must have 0 as count
• The size of the dot can be set, usually depending on the size of the table (rows and columns) and the maximum count in any of the cells
• Two styles of output is available

  Style 1 represents each cell as a circle, the size of which depends on the sample size in the cell. The sample size itself will also be displayed.

  • The minimum diameter of the circle is 10 pixels, to accomodate the sample size display
  • The diameter d of the circle is calculated as
    • If the smallest sample size of the table is n_smallest
    • If the radius of the circle for the smallest sample size is d_smallest
    • If the sample size under consideration is n_current
    • The the diameter for the current circle d_current = sqrt(d_smallest² x n_current / n_smallest)
  

  Style 2 represents each count in a cell as a cluster of circles, the number of which is the same as the count in the cell.

  • The diameter of the circles can be set. The default is 5 pixels.
  • Larger circles can be used when there are few cells in the table and the maximum count in any cell are few
  • If a diameter of 0 is set, each circle is represented by a single pixel.

SPSS produce an excellent plot showing 95% confidence interval of the data and 95% confidence interval of the mean. Group data plot from the Group Data Plot Program Page is an attempt to duplicate and perhaps improve upon this. It has the following features.

• It marks out the 95% confidence intervals of data and mean, as produced by SPSS
• It plots all the data points for each group
• Where there are more than one case with the same value in a group, the data points are spread out, so that the density of the data at any level can be visualized.

Data Input : The data is a table with two columns, separated by spaces or tabs

• Each row is data from a case
• Column 1 is the label for the group on the x axis. The label is a single word with no gaps. If a gap is required, it should be represented by an underscore _central value, usually the mean
• Column 2 is the value to be plotted on the y axis

Dot size :

• The size of the dot representing each data point has a diameter of 2 x dotsize + 1. The default radius is 5, making the dot 11 pixels in diameter
• If dotsize is <=0, then a single pixel will be plotted
• if dotsize<0 is used then the number of pixels for a particular value is 1 + log_1.05n, where n is the number of data points for that value. This is introduced to reduce the spread of the plot when there are numerous data points for any value. The down side is that the plot is only approximate

MacroPlot Code Generation

1. Program estimates the range of the x and number of groups, and produce the inner plotting area
2. Program plots data value for each group. Where there are more than one case in a group, the data plot is shifted horizontally so that they can be seen.
3. For each group, program
   • Marks the mean with a horizontal line
   • Marks the 95% confidence interval of measurements with a vertical line
   • Marks the 95% confidence interval of the mean with a box
4. Program produces a table, listing sample size (n), mean, Standard Deviation, Standard Error of the mean, and their 95% confidence intervals, for each group.

Explanation of the example codes : explanations in maroon

• Plotting area, scaling and labelling. Please note that the numerical parameters will need editing
  Bitmap Initialise 700 500 255 255 255 255 Creates a bitmap 700 pixels wide x 500 pixels high, white background
  Line Thick 2 Lines 2 pixels wide
  Font Style 1 Text in bold
  Plot Values -1 4096 2 2047 Set the range of values, x from -1 to 2 ( as the two groups are numerically designated 0 and 1), y from 2047 to 4096
  Plot XAxis 2047 0 1 -2 -1 Place the x axis where y=2047, marks the x axis at 0 and 1. The scales are deliberately given out of range values so they are not produced, as each group is labelled by text
  Plot HText 1 0 0 2047 Boy 0 5 Place the text "Boy", horizontally aligned (1=center), vertically aligned (0=top), where x=0 and y=2047, then shift the text 0 pixels horizontally and 5 pixels downwards. In other words label group 0 as "Boy" 5 pixels below the plotting area.
  Plot HText 1 0 1 2047 Girl 0 5 Place the text "Girl", horizontally aligned (1=center), vertically aligned (0=top), where x=1 and y=2047, then shift the text 0 pixels horizontally and 5 pixels downwards. In other words label group 1 as "Girl" 5 pixels below the plotting area.
  Plot XLabel Groups 25 Place the label "Groups" 25 pixels below the plotting area. The label can be edited
  Plot YLabel Values 55 Place the label "Values" 55 pixels to the left of the plotting area. The label can be edited
• Plotting data points
  Fill Color 255 255 255 0 assign fill color black and opaque for the circular dots
  Plot Circle 5 1 3067 Place a circular dot, 5 pixels in radius, where x = 1 and y = 3067
  Plot Circle 5 1 3067 10 0 Place a circular dot, 5 pixels in radius, where x = 1 and y = 3067,then shift the dot 10 pixels to the right, 0 pixels up and down
  Plot Circle 5 1 3067 -10 0 Place a circular dot, 5 pixels in radius, where x = 1 and y = 3067,then shift the dot 10 pixels to the left, 0 pixels up and down

The normal distribution plot compares a set of data against a theoretical normal distribution plot. It therefore allows a visual inspection of the distribution of the data. The plot was created initially to service the Numerical Transformation Program Page , as it allows a visualisation of the distribution before and after transformation. The algorithm was tidied up to be used more formally in the Normal Distribution Plot Program Page Data and parameters Input :

• The data is a single column of values to be plotted
• Reference Mean and Reference Standard Deviation are nominated value by which the data will be grouped and plotted. If no reference is available, the value of 0 can be used for Standard Deviation, and the program will use the mean and Standard Deviation calculated from the data itself.
• Size of grouping can be the following options
  • By 1 Standard Deviation, one centrally (from -0.5 to 0.5 SD), and 4 (each of 1 SD) on each side, a total of 9 groups
  • By 0.5 Standard Deviation, one centrally (from -0.25 to 0.25 SD), and 8 (each of 0.5 SD) on each side, a total of 17 groups
  • By 0.25 Standard Deviation, one centrally (from -0.125 to 0.125 SD), and 16 (each of 0.25 SD) on each side, a total of 33 groups
  • By 0.125 Standard Deviation, one centrally (from -0.0625 to 0.0625 SD), and 32 (each of 0.125 SD) on each side, a total of 65 groups

MacroPlot Code Generation

1. Program converts values into Standard Deviation units (z = (value-mean) / SD), and place the case in the appropriate group from -4SD to +4SD. Values more extreme than 4 SDs away from the mean are placed in the end group.
2. The number of cases in each group is converted to a percent of the total for plotting.
3. Empty groups are eliminated, the rest are displayed.
4. The groups, numbers, and percent are displayed in a table.
5. The groups and their percentage are displayed in a vertical bar plot.
6. A normal distribution curve, with the designated mean and Standard Deviation, is superimposed upon the bar plot.

Plotting area, scaling and labelling. Please note that the numerical parameters will need editing

All the code except one are the same as those for the vertical bar plot, and will not be explained here.
Plot Normal 0.0 1.0 38.2925 Draws a normal distribution curve from -4SD to +4SD, using the designated mean and Standard Deviation, with a maximum height of 39.2925%
Please Note : the maximum height (central group around mean) of normal distribution curves, in percent(%) are as follows

Size of grouping	Height of central group (%)
1 SD	38.2925
0.5 SD	19.7413
0.25 SD	9.9476
0.125 SD	4.9835