Welcome to your SuperANOVA™ demonstration. After you use this program, we are sure that you will find that SuperANOVA is by far the most versatile and easy-to-use, comprehensive general linear modeling package available on any computer.
This document explains how to use SuperANOVA demonstration software. Its purpose is to show how quickly and easily you can create datasets, construct models, analyze results and create presentations. The disk you received contains a fully functional version of SuperANOVA with the following limitations:
• You cannot save a document
• You cannot print a document
• You cannot paste from the Clipboard into either the Scrapbook or another application
• You cannot open StatView files
• Imported text files are limited to 100 rows and 25 columns
If you have any questions, please feel free to call Abacus Concepts Technical Support at (510) 540-1949.
If you decide to purchase SuperANOVA, please use the order form enclosed with this package or call your order in over the telephone between 8:30 am and 4:00 pm Pacific Standard Time. You can also send us orders by FAX at (510) 540-0260. Orders can be paid using purchase orders, MasterCard/Visa, or check. Site licenses and educational discounts are also available.
If you know of other people who would like to see first-hand how our software performs, you may copy your demonstration diskette and this document for them. The SuperANOVA demonstration program and this document are not in the public domain. However, we allow you to copy them for non-commercial use.
System requirements
SuperANOVA runs on the Macintosh Plus and later Macintoshes that meet the following requirements:
• a hard disk
• Macintosh Operating System Version 6.0.2 or later
• a minimum of 1 megabyte of main memory (RAM)
There are two versions of SuperANOVA. The difference between the two is related to the kind of Macintosh you use. Make sure you order the correct version.
The FPU version of SuperANOVA requires a floating-point math coprocessor (or FPU) and consequently will operate only on the following Macintosh systems:
• a Macintosh II, IIx, IIcx, IIci, IIfx, SE/30 or IIsi. The IIsi must contain the optional FPU available from Apple.
• a Macintosh SE, Macintosh Plus, Macintosh Portable, or any Macintosh with a 3rd party accelerator board containing a 68020 (or later) CPU and 68881 (or later) floating-point math coprocessor.
The non-FPU version of SuperANOVA does not require a floating-point math coprocessor. It is designed for the following Macintosh systems:
• a Macintosh Classic, Plus, SE, Portable or LC. It will also run on the IIsi if you have not purchased the optional FPU
• a Macintosh 512k enhanced with 1 or more megabyte of RAM
Installing SuperANOVA
To install the software:
• Write-protect the SuperANOVA demonstration disk by exposing the hole in the upper right corner of the disk.
• Insert the disk in your disk drive. You will see a single icon. This application contains the compacted SuperANOVA demonstration and all related documents.
• Double-click on the SuperANOVA Installer application or select it and choose Open from the File menu. Click the Continue button in the dialog box that appears.
• The program puts up the following standard Macintosh “save” dialog:
Installation dialog
• Click on the Drive button to select the drive and folder where you want to put the demonstration files. When you have selected the target folder, click the Install button. A folder titled “SuperANOVA v1.11 Folder” will appear at this location on your hard disk. It will contain the SuperANOVA demonstration application and all related files.
2. SuperANOVA Features
SuperANOVA is a complete solution for general linear modeling. It has been carefully designed for ease of use, with an intuitive approach to model-building. It minimizes unnecessary or repetitive steps in building models, and provides great flexibility in analyzing and managing data. With SuperANOVA you can easily produce attractive and informative presentations.
By streamlining the process of solving ANOVA models, SuperANOVA lets you concentrate on producing results, exploring their significance, and presenting your tables and graphs. SuperANOVA accomplishes all this by means of its complete graphic interface, an array of canned models, access to powerful tools such as contrasts, extensive drawing capabilities, and other features described in the rest of this chapter.
SuperANOVA’s graphic interface focuses on your ANOVA table as the one format for both input and output. This makes the entire model-building process intuitive and visually easy to follow. There is no need to master complex syntax or esoteric notation in order to create a model, and you are certain of what model you are studying as you proceed with your analysis.
Datasets and models
There are two basic SuperANOVA document types: datasets and models.
A dataset holds your data in a standard row-and-column format, similar to a spreadsheet. A dataset can contain up to 32,765 variables with 500 million cases. You can import data from other programs or enter it yourself. You can specify variable types (integer, long integer, real, category, string, currency, or date/time), source of data (user entered or formula), class (nominal, continuous, or informative), display format, and number of decimal places to show. You can also specify selection criteria in the dataset. Specifying the characteristics of a SuperANOVA dataset, like entering and editing data, is extremely easy.
A model is where you create your ANOVA tables, means tables, post-hoc tests, contrasts, and all output from the program; it is also where you view your graphs. SuperANOVA models are like documents in drawing programs; you can move and modify the tables and graphs (as well as any graphics and text you add) by clicking and dragging. Your model begins with an empty ANOVA table. You build your model by building the ANOVA table, specifying the factors, dependent variables, and regressors. You can add graphics and text at any time.
Unlike other programs, SuperANOVA does not limit you to a single model for a dataset. You can have many different models (in separate documents) associated with a single dataset, and these models can all be open at the same time. You can also have many different datasets associated with a model. For example, if you have a set of tables and graphs that you generate for every dataset you construct, you can use a single SuperANOVA model. When you open the model, you choose the dataset to apply it to.
Your datasets and models are kept in separate windows. A typical dataset window looks like:
Typical dataset window
You type data in the rows and columns or use the Paste command to enter data from the Clipboard. In addition, you can import text files created by other applications and read datasets created by any member of the StatView family. The Criteria pop-up menu lets you define a subset of the records for use in a model. A typical model window looks like:
Typical model window
The list at the lower left of the window displays the variables (or columns) in your dataset. The buttons above the variable list move selected variables into your ANOVA table. The effect display buttons along the top of the window allow you to display further information about your model.
SuperANOVA’s highlights
The best way to understand the power of SuperANOVA’s features is to explore the demonstration program. Since SuperANOVA is an interactive, graphics-based program, using it is the easiest way to get a feel for its power. The rest of this manual shows you step-by-step how to explore SuperANOVA’s main features which include:
Models
SuperANOVA can solve models containing an unlimited number of factors, each with up to 32,765 levels. Models supported include ANOVA, MANOVA, ANCOVA, MANCOVA, and regression. You can solve any design including various split-plot designs, nested designs, block and incomplete block designs, confounded factorial designs and latin and greco-latin squares. It handles unbalanced designs, missing cells, and repeated measures designs with up to twelve within factors. Repeated measures designs can be solved using multivariate or univariate methods. SuperANOVA also displays type I, type II, type III and type IV sums of squares. Models can either include or exclude the intercept.
Contrasts
A contrast is a specialized type of hypothesis test which compares the means of selected levels of a factor or combination of factors. SuperANOVA gives you quick access to contrasts, one of the most powerful tools in ANOVA, and makes it easy to both define and verify them. Choose from orthogonal polynomials, Helmhert, and any means/regression coefficient comparison.
Means tables
SuperANOVA can generate means tables for any nominal effect, providing counts, means, standard deviations, and standard errors, as well as confidence intervals.
Post-hoc tests
Available post-hoc tests include Fisher Protected LSD, Duncan New Multiple Range, Student-Newman-Keuls, Tukey Compromise, Tukey-Kramer, Spjotvoll-Stoline, Scheffé’s S, Bonferroni/Dunn (All Means and Control), Dunnett (One-tailed and Two-tailed) and Games-Howell. All come with multiple-display formats.
Graphs
SuperANOVA gives you interaction plots; scattergrams of cell means; Y versus fitted Y, residuals versus fitted Y; residuals versus Y; residuals vs. covariates; Y versus covariates and fitted Y versus covariates plots.
Least squares means tables
You can generate least squares (adjusted) means tables for any nominal effect, providing cell names, counts, adjusted means, standard deviations, and standard errors.
Table formatting
You can easily format your table to match the style used in professional publications. You can also change the fonts and sizes, add a border, change the background colors, and so on.
Large array of canned models
SuperANOVA comes with many canned models which solve most experimental designs. These are called Do-It™ files. Simply choose the appropriate model for a given experimental design from the “Canned Models” dialog. The canned models shipped with the full working version of SuperANOVA include one-factor and two-factor ANOVA, randomized complete block, Latin square, split plot, repeated measures (with multiple “between” and “within” factors), ANCOVA, and regression models. You are not limited to just these models; with SuperANOVA, you can easily create and add your own canned models, even custom designs, for yourself or for your co-workers. Any model you design can be saved for later use with different sets of data.
Informational tables
In addition to the above, you can display model summary tables, model coefficients, coefficient correlations, residual summaries, eigenvalues and eigenvectors. You can also save residuals, fitted values, and predicted values to a dataset, and display summary descriptive statistics for any column in a dataset.
Model validity checking
SuperANOVA checks each model for validity before recalculating results. This helps prevent making mistakes that would yield misleading results.
Dataset handling
Data can be entered by hand or imported from other programs. You can specify exactly how data appears in dataset windows and describe the format for each variable. All format and structure changes are made in the single dataset window and your view is updated instantly. You can recode data, create columns with distributions of random numbers, do multi-key sorts, and use the standard Cut/Copy/Paste functions. In addition, you can use compact variables to organize your data. Using criteria, you can partition data into groups for inclusion or exclusion from analysis.
Data formulae
With SuperANOVA’s powerful formula generator, you can create new columns using simple or complex expressions. If your original data columns change, the formula columns change or not, according to your choice.
Selection criteria
You can change the selection criteria for the records in your data that are used in a model easily. You can create complex criteria (such as “all males over 65 who weigh less than 130 pounds”) and save those criteria with the dataset. You can also specify random criteria.
Interactivity
Like all Abacus Concepts software, SuperANOVA is fully interactive. Any changes to your data are automatically reflected in the results. This feature makes it easy to perform “what-if’s” on data. It also means that once you’ve defined your model, there is no need to repeat the whole process if you find a data error. Simply correct it, and SuperANOVA automatically recalculates your model. If it is more convenient, you can turn off the recalculation function while you make changes, then easily cause a complete recalculation at any time.
Presentation graphics
SuperANOVA combines powerful statistical capabilities with sophisticated presentation graphics. After generating your analysis output, you can customize it using SuperANOVA’s extensive drawing and presentation capabilities, which include complete control of color and the ability to insert and manipulate text and graphics anywhere on the screen. Your output can be customized for slide shows, posters, reports or on-line presentations. You can add lines, arrows, circles, squares, arcs, and polygons; control line width; insert text anywhere on the screen; add rulers to control alignment; and fill drawn objects.
Color
You can control the color of any selected object on the screen. On a color system, 16.8 million colors are available. With a black-and-white system, you can assign any of eight colors for display at printing time. There is no need to customize your system because SuperANOVA automatically adjusts to either environment.
Documentation
As you would expect, the manual that comes with SuperANOVA has a complete description of all of SuperANOVA’s features. In addition, the documentation covers in detail statistical topics such as hypothesis testing and the uses for all of the multivariate tests found in SuperANOVA. It also gives the formulae on which SuperANOVA’s tests are based.
Using SuperANOVA
The following chapters detail step-by-step hypothetical analyses to solve with SuperANOVA. By following the steps, you can see how easy it is to start a new dataset and produce a complete model including ANOVA tables, charts, and so on. The examples are:
• Generate an advanced analysis of a soil dataset, including the use of SuperANOVA’s presentation tools to produce a high-quality report
• Modify a sample dataset and apply a canned repeated measures model to it
These examples cover many of the features listed above. If you want to see how to use a particular feature, use the following table to find the page on which the feature is shown.
Feature Page
ANOVA table 10
Canned models 24
Column summary pane 28
Compact variables 24
Contrasts 19
Dependent variable (additional) 21
Error terms (changing) 13
Example models 29
Formulae 21
Importing data 29
Index to model items 22
Interaction effect 13
Interaction plot 16
Means comparison 19
Means table 15
Nested effect 12
Post-hoc tests 15
Presentation graphics 17
Recalculation 14
Repeated measures 24
Residuals plot 20
Selection criteria 27
Table style 11
Text 18
3. Building a Model
This example shows you how to perform an ANOVA on your data by actually building an ANOVA table, which SuperANOVA will then solve. The dataset in this example, “Soil Data,” contains information about the aggregate stability of soil in an experimental corn field exposed to two levels of nitrogen fertilizer and two winter cover crops. In addition, the dataset contains information about the aggregate stability at two depths in the soil. For each treatment/depth combination, two repetitions of the measurement were taken to reduce errors. You want to analyze the data to find out if any of the four management practices in the experiment significantly affect aggregate stability. Stable soil aggregates allow air, water, and plant shoots and roots to move through the soil.
Starting a new model
• Choose Open from the File menu. In the Sample Data folder, select the Soil Data file and open it. You will see:
Soil Data dataset
You can scroll around the dataset using the scroll bars.
• Choose New Model from the Model menu. This creates a new, empty model:
New model window
Every new model window contains an empty ANOVA table. You will fill in the first column of this table, the Source column, with names of the effects you want to explore. The window has five areas:
Area Description
Drawing Your tables, text, charts, and graphics. This area is much like a document in a drawing program like MacDraw.
Variables list The names of each column in your dataset. The controls to the left of the name indicate the class of the variable
Nominal
Continuous
Compact
You use these controls to change a variable from one class to another
Model tools Buttons for adding and changing effects in your ANOVA table
Effect tools Buttons to add tables that provide information on particular effects in your model
Recalculate button Control for whether or not SuperANOVA will automatically recalculate results
For this experiment, make Aggregate Stability (%) the dependent variable.
• Click on Aggregate Stability (%) in the variables list by clicking directly on it in the variable list. You should not click on the indicators to the left of the names.
Aggregate Stability (%) selected
• Click on the Dependent button in the model tools. This makes Aggregate Stability (%) a dependent variable as indicated at the bottom of the table:
Aggregate Stability (%) as the dependent variable
The first desired effect to be tested is Treatment.
• Click on Treatment in the variables list, then click Add in the model tools. The Add button adds the selected variable to the selected effect in the ANOVA table. You have just made Treatment a main effect.
Treatment as a main effect
That’s all there is to creating an effect!
Changing the table style
SuperANOVA lets you display your ANOVA tables in five different styles. You can also change the formatting of the text in the table with the commands in the Text menu. The default style has boxes around each effect and result.
• Double-click anywhere on the table. Alternatively, click once on the table to select it and choose Open Item in the Layout menu. This opens the following dialog:
Open Item dialog for ANOVA table
• Choose one of the table styles from the choices on the right and click OK. For instance, if you choose the item with just vertical lines, your table would look like:
ANOVA table with only vertical lines
The rest of this manual uses the default table style (both horizontal and vertical lines).
Extending the ANOVA table
So far, your table only tests for Treatment. In this experimental design, you also want to test Rep nested within Treatment, Depth, and the interaction between Depth and Treatment. Adding these effects to your ANOVA table are as easy as creating the first effect.
The New button opens up a space in the ANOVA table for an effect. If you have a variable selected in the variable list, the New/Add button opens up a space and adds the selected variable to the new effect.
• Select Rep in the variables list and click the New/Add button.
Rep added to table
To create a nested effect, you select the effect in the table, select the variable in the variables list within which the effect is nested, and click the Nest button.
• Rep is already selected in the ANOVA table. Select Treatment in the variables list and click the Nest button.
Rep nested within Treatment
• To add the Depth main effect, select Depth in the variables list and click the New/Add button.
Depth effect added to table
To create an interaction, select the variables you want to cross with the selected effect and click Add.
• To create an interaction between Depth and Treatment, select Depth in the variables list and click the New/Add button.
• Select Treatment in the variables list and click the Add button. SuperANOVA creates an interaction between Depth and Treatment.
Table with Depth * Treatment interaction effect
Error terms
By default, SuperANOVA uses the residual error as the denominators of F tests for calculating the significance of the effects in your model. This is appropriate for a wide range of models. If you are studying a model where a different error term is appropriate, you can change the error term of any of effect in your ANOVA table from “Residual” to any other effect in the table.
• Double-click anywhere in the table to bring up the Open Item dialog again. In the Columns section, select Error Terms. This adds a new column to your table:
Error terms added
The default error term is the Residual. You can change the error term for any effect. For this model, you want the error term for Treatment to be Rep(Treatment).
• Select the table so that there is a dotted border around it:
Table selected
• Move the cursor over the error term for the Treatment effect. The cursor becomes a picture of a pop-up menu. This indicates that clicking here will bring up a pop-up list.
Pop-up cursor
• Click the mouse button to bring up the list of choices for the error term:
List of choices for error term
• While holding down the mouse button, drag down to Rep(Treatment) and release the mouse button. This changes the error term:
New error term
Calculating the model
Notice that this table does not contain any values for the Sum of Squares, Mean Square, F-Value, or P-Value. This is because recalculation is turned off (the Recalculate box in the upper left corner of the model window is not checked). SuperANOVA models normally start with recalculation turned off so that you can build your models without waiting for SuperANOVA to give you results at each step. In this case, however, you want to turn recalculation on so that you can see the results of your ANOVA table.
SuperANOVA will not recalculate your table if you have made an obvious mistake in setting it up. For example, if you have not specified a dependent variable, SuperANOVA will alert you when you try to recalculate.
• Click the Recalculate button so that it is checked.
Recalculate button checked
The cursor changes to a rotating yin-yang symbol while SuperANOVA performs the calculation. The table’s values are then filled in:
The table with results
Notice how little time it took to build your model and how easy it would be to change the model to handle different designs.
Means table
To examine the means of the different treatment levels, you can request a means table for this effect.
• Select the Treatment effect by clicking on the first cell in the first line of the ANOVA table.
• Click the Means Table effect tool at the top of the window. The following table appears:
Means table for Treatment
This table shows the means for each level of the treatment. You can see that the means for four of the treatments are quite close (ranging from 74.2 for 150 lb/ac to 76.8 for oats), while one treatment (Vetch) stands out from the others with a mean of 81.0.
You can expand the means table to also display confidence intervals.
• Double-click on the means table or select the table and choose Open Item from the Layout menu. In the dialog, specify a 99% confidence interval. The table changes to:
Means table with 99% confidence interval
Post-hoc tests
To determine which differences among the treatment means are significant, you may want to examine the post-hoc tests using the Post-Hocs button at the top of the model window.
• Select Treatment in the ANOVA table.
• Click the Post-Hocs button at the top of the window. You see the following dialog:
Post-hocs dialog
• Click on the Display Format pop-up menu and drag to Group Letters.
• Select Fisher’s Protected LSD from the scrolling list.
• Click the Select button to select it, then click Done. The table is shown in the model:
Fisher’s Protected LSD post-hoc
You can see that the four similar means form one group (denoted by the letter “a”), while the higher value for Vetch is in a separate group (letter “b”). Thus, at the 0.05 significance level, the treatment mean for Vetch is significantly different from the other four treatments, but there was no significant difference detected among the other four treatment means.
Interaction plot
You can create an interaction plot to compare the means of the cells formed by the Depth*Treatment interaction. The plot gives you a visual sense of which treatments differ for various depths.
• Select the Depth*Treatment effect in the ANOVA table.
• Click the Graph Effect button at the top of the model window. Choose Interaction Plot from the dialog. SuperANOVA displays the plot.
Interaction plot for Depth*Treatment
You can see that the means for 150 lb/ac at the two different levels of depth differ widely and may be a candidate for further analysis. You might want to contrast the two depths for that treatment. First, however, it would be useful to highlight that difference in the graph.
Presentation graphics
If you want to show these results to someone else, you may want to add notes to your model about your assumptions and conclusions. These notes, in the form of graphics, arrows, and text, are saved with your model. For example, you can highlight the wide difference between the means illustrated by the interaction plot.
• Click on the Draw menu to see the tools. These are just like the tools you see in a regular drawing program. You can “tear off” this menu by holding down the mouse button and moving the cursor down and away from the menu. This leaves the drawing tools on the screen so that you don’t have to keep going back to the Draw menu.
Draw menu
• Click on the ellipse tool, the first tool in the third row. The cursor becomes a cross-hair.
• Click above and to the left of the “150 lb/ac” label on the horizontal axis and drag up so that both points are surrounded:
Ellipse drawn around points
• Click on the line tool, the third tool in the first row.
• Click near the bottom of the ellipse and drag left and below the table.
Line drawn
• Click on the line to the right of the word “arrow” and drag down to the second choice, an arrow at the right end of the line. When you release the mouse, this becomes the selected arrow type and an arrow is added to the end of the line.
Arrow type chosen
• Click on the text tool, the second tool in the first row.
• Click the cursor below the arrow that you drew. A text box appears:
Text entry box
• Type in “Means are very different”. Click the arrow tool, the first tool in the first row, click on the new text, and drag it so that it aligns well with the arrow.
Text moved over arrow
You can change the font, size, or style of the selected text with the commands in the Text menu. You can also use the other tools in the Draw menu to add highlighting and/or other effects to your model.
Means comparison
To create a contrast table, select an effect you want to examine and click the Contrasts button at the top of the model window. SuperANOVA gives you a dialog which helps you to easily specify the type of contrast to create. In this case, you want to create a means comparison that tests whether there is a significant difference between the “surface, 150 lb/ac” cell and the “subsurface, 150 lb/ac” cell in order to determine whether the application of 150 lb/ac nitrogen fertilizer produces a significant difference between surface and subsurface aggregate stability as suggested by the interaction plot.
• Scroll up to the ANOVA table and be sure that the Depth*Treatment effect is selected.
• Click the Contrasts button. SuperANOVA shows you the following dialog:
Contrasts dialog
• Select Means comparisons and click OK. SuperANOVA displays the “pie” dialog:
Pie dialog
• Change the contrast name to “Contrast of 150 lb/ac”.
• Select “surface, 150 lb/ac” and click Add Plus. Select “subsurface, 150 lb/ac” and click Add Minus. Click Done. Your table appears in the model window.
Means comparison
Contrasts such as these, which are suggested by examining the data, must be interpreted with caution. In practice, the probability levels of these contrasts are only accurate when the contrast is specified before viewing the data. In the current example, the very low P-value of 0.008 strongly suggests that there is a significant difference between the two means.
Residuals plot
To help you examine the model results, you can display a plot of residuals versus fitted values. Residual plots help point out whether there are any violations of the assumptions upon which your model is based. If the assumptions of the general linear model are met, a Residual versus Fitted Y plot should show a band of constant width independent of the fitted value.
• Choose Residuals versus Fitted Y from the Display menu. The following graph appears.
