Notice that the spread of residuals is not constant in width; the residuals are narrower for larger fitted values. This behavior is not unusual for data such as aggregate stability which is expressed as a percentage. An arcsin transformation of the square root of the percent divided by 100 often stabilizes the variance in these cases. You can create a second dependent variable based on this transformation and use it for a second set of results.
Using a formula to transform a variable
SuperANOVA lets you create columns in your dataset that are based on transformations of other columns. For instance, you might want a column that is the product of two columns plus a third column. The formulas that you can use to create your transformations include standard math, trigonometry, logical comparisons, and advanced statistical functions.
• Bring the dataset to the front by clicking on it. You can also double-click in the white area at the top of the model window or select the dataset from the Window (or “∑”) menu.
• Select Formula command from the Manage menu. This opens the Formula dialog:
Formula dialog
You want to create the formula “arcsin(Sqrt(”Aggregate Stability (%)”/100))”. You can type this formula directly in the large box at the top right of the dialog. You can also enter parts of the formula by selecting them from the list of column names, list of functions, or clicking on the keypad. For example, to enter this formula with the mouse you would click the INV button, the sin button, double-click Sqrt from the Functions list, double-click Aggregate Stability (%) from the Columns list, and click the /, 1, 0, and 0 buttons.
• Enter the formula and click Compute. SuperANOVA creates a new column.
• Select the column by clicking on the column name and type Transformed Aggregate to give the column a new name. This column will be a new dependent variable in the model.
Adding another dependent variable
When you add a second dependent variable to a model, SuperANOVA generates a new ANOVA table for that dependent variable and makes duplicates of all the additional tables and charts for that second dependent variable.
• Activate the model window by clicking in it or selecting it from the Window or ∑ menu.
• Select Transformed Aggregate from the variable list. and click the Dependent button. Because the Recalculate button is checked, the model automatically recalculates.
Now you can examine the residual plot for Transformed Aggregate to see how the transformation has changed it.
Model index
You have probably noticed that your model document now has many tables and charts, especially after adding the second dependent variable. To find a specific table or chart, you can use SuperANOVA’s item index.
• Select Show Item Index from the Layout menu.
Item index
This window lists all items in your model by each dependent variable. The Order pop-up menu allows you to view the items by Effect or by Name also. To scroll directly to a particular item in the model window, simply double-click on it in the index. Scroll the item index list down until Scattergram of Residuals versus Fitted Y appears under Dependent: Transformed Aggregate. Double-click on the residual plot for Transformed Aggregate. The item index window moves behind the model window and the model window scrolls to the location of the residual plot.
Residual plot for Transformed Aggregate
The transformation has lessened the problem of unequal variances, but it has not eliminated it. Examination of the ANOVA table for the transformed variable indicates that the conclusions for the transformed variable are similar to those for the untransformed variable.
SuperANOVA also has a feature that rearranges the items in your model window. This is useful if some of your tables fall across page boundaries. The Clean Up Items command in the Layout menu automatically moves your items and places them as close or as far from each other as you specify.
If this were a full working version of SuperANOVA, you could now save this model window for later examination or for use on another set of soil data. Since this demonstration version does not allow you to save datasets or models, close the dataset and model windows and indicate that you do not want to save changes before continuing.
4. Using a Canned Model
This example shows you how to solve a repeated measures ANOVA. In the process, you will create a compact variable and apply a canned model.
The model you are solving involves an experiment where eight music critics are tested to see if consumption of alcohol affects their rating of musical recording. The critics are asked to rate three different recordings on a scale of 1 to 100 after ingesting one, two, and four ounces of alcohol. Their age groups are also recorded. This is a repeated measures model with two within factors, “Recording” and “Alcohol consumption”.
Creating a compact variable
• Choose Open from the File menu. In the Sample Data folder open the file named Music Critics.
The nine columns named r1 through r9 contain the ratings information which represent the Repeated Measurements for this experiment. By making these nine columns a compact variable, you allow SuperANOVA to look at this data as the within factors of a repeated measures model.
Layout of ratings columns
• Select the nine new columns and click the Compact button in the upper left corner of the dataset window. You see the following dialog:
Compact dialog
• Enter Ratings as the compact variable name.
• Click New. The “Create a new category” dialog appears.
New category dialog
• Enter Recording as the category name and add three elements to the category: Record 1, Record 2, Record 3. After you enter each element’s name, click Add. When you have added all three, click Done.
The right-hand scrolling list in the Compact dialog contains the newly created category and indicates that it has three elements. In addition, the Cells in Compact field displays 3. The Columns Selected field displays 9, indicating that you will need to define another category.
• Click New again to create the second category. Enter Drinks as the category name and add three elements to the category: One oz., Two oz., and Four oz. Click Done.
Now the right-hand scrolling list contains both categories. The Cells in Compact field now displays 9 (levels of Recordings x levels of Drinks), as does the Columns Selected field. The smiling face indicates that you have the right number of elements for the compact variable.
• Click OK. The column headings of the nine selected columns have updated to show the structure of the compact variable you just created.
The complete dataset should look like:
Complete dataset
Using a canned model
In the example in Chapter 3, you built the model by selecting the variables from the variables list and using the model building tools. In this example, you will use a canned model to solve the experiment. A canned model is simply a saved model that has been placed in the Canned Models folder. Using a canned model saves you the need to build the model one step at a time; instead, you specify the names of the variables in the model and SuperANOVA uses this information to build the model for you.
We provide canned models for most common linear modeling designs. With the full version of SuperANOVA you are free to create your own models and put them in the Canned Models folder. You might want to do this for your most commonly-used models.
• Choose Canned Model from the Model menu.
• Select the “Repeated - 2 within, 0 between” model from the scrolling list. Click the “Apply to dataset” button. You then see a standard Macintosh dialog allowing you to select the dataset. Use the Drive and folder buttons to find the Music Critics dataset that you opened earlier in this chapter. Click the Open button, and SuperANOVA uses your updated dataset even though you have not saved changes to disk. You see the following dialog:
Variable matching dialog
The scrolling list on the right contains the names of the columns in your dataset. The scrolling list on the left shows the information needed for the model. For this design, you need to specify which variable in the dataset represents the repeated measurement.
• Select “Ratings” in the right list. Drag it across the dialog to the open slot in the left list. This is the method you use to specify which columns in your dataset match variables saved in models.
• Click OK. SuperANOVA opens a model window, solves the model, and displays the results of your experiment:
Model calculated
You can now see the power of saved models (Do-It files). Any model that you create (not just ones in the Canned Models folder) can be applied to any dataset. If you create a model that you like and want to use it with a completely different set of data, simply open the model, ask SuperANOVA to apply it to the new dataset, and specify which columns in the dataset correspond to variables in the model. Remember, these models can contain any additional text and graphics that you need to better present your results.
Try another canned model. To see if the Age group plays a role in ratings, choose the “Repeated - 2 within, 1 between” model. This time make Ratings the within factor and Age the between factor (designated as Factor 1).
Remember, you can apply a Do-It file to any set of data. If you plan to use a particular Do-It file often, add it to your Canned Models folder so that you can quickly access it from the Model menu. Do-It files provide tremendous power and flexibility in working with models. You can use them:
• to save work in progress, as you would a document in a word processing or drawing program
• as a prefabricated model and its dataset (just enter your data into the predefined dataset structure, and compute the associated model)
• to save a model and results display that you have designed, and apply them to different datasets
Creating a selection criterion
The dataset also contains information concerning the age of the music critic. SuperANOVA makes it easy to set up dataset criteria so you can quickly view your model on a subset of the data. Notice how the model recalculates. You create rules for the criteria (such as “all young critics” or “ratings between 65 and 85”) and save those rules with your dataset. This allows you to use these subsets whenever you want.
• Select the Music Critics dataset. Click the pop-up menu next to the word “Criteria:” at the top of the dataset and drag to select New. You see:
Criteria dialog
• Change the name of the criterion to Young.
You enter the formula for the criterion in the choices list below the criterion name. You can type the formula in this box or you can have SuperANOVA help you by clicking in the box under the dotted line. The formula you want to enter is “Age = Young”.
• Double-click on Age in the Select box. The Select box becomes a list of logical operators. Double-click on "? = ?". The Select box becomes a list of the levels of the Age group. Double-click on Young.
• Click Apply. This saves the criterion and applies it to your dataset.
You can see that records 2, 4, 5, and 8 are not included; their record numbers are now gray.
When you click on the model window, you see that the model has been recalculated using only the included rows.
Criteria are automatically saved with the dataset. If you have many criteria in one dataset, you can apply any one simply by pulling down the Criteria pop-up and selecting the criteria name. To select all records, select “No criteria” in the pop-up.
Using the column summary pane
It is often useful to see summary information regarding a dataset. For this example, you may want to know the maximum and minimum ratings for each critic for each recording and drink level. Each dataset has a column summary pane which holds the descriptive summaries for each column. Click on the icon at the top of the vertical scroll bar in the dataset window and drag downwards. The icon is if the column attributes are not shown and if they are. The column summary pane is updated instantly when any data in the column changes.
The column summary pane shows 12 descriptive statistics: mean, standard deviation, standard error, variance, coefficient of variation, minimum, maximum, range, count, number of missing cells, sum, and sum of squares.
5. Additional Information
This document covers only a sample of the variety of features you will find in SuperANOVA. Play around with the demonstration version to see the many capabilities of the program.
Importing to SuperANOVA
SuperANOVA can import data from text files. SuperANOVA’s import mechanism makes intelligent choices about how to place data into columns and how to fill in missing values. This is described in detail in the manual for the full version. One of the ways to try out SuperANOVA’s features is to import data that you have saved in text format.
This demonstration version restricts importing to 100 records and 25 columns of your dataset.
Features disabled in this demonstration
The demonstration version you have does not allow you to save or print your datasets or models and does not let you export your results to other programs. Also, you cannot read StatView files. In the full version of SuperANOVA, you can easily perform all these tasks. It is important to remember that the full SuperANOVA will do these things since they are often vital to your work.
Using Canned Models
The Canned Models folder contains several different model designs. As you saw earlier in this document, you can add your own models to the list of canned models and the the Model menu itself. To explore the power of canned models, apply any of the models shipped with this demonstration to the Lipid Experiment data in the Sample Data folder. Note that in this dataset, Gender and Lipid Type are the factors of interest. You can also try SuperANOVA on your own data after importing your data into this demonstration version.
Looking at Additional Examples
The Example Models folder contains several example models and associated datasets. Please feel free to open these models and examine the results. The SuperANOVA manual contains an in-depth discussion of all these examples. To look at a particular model:
• Choose Open from the File menu. In the dialog, open the Example Models folder, then open the Do-It Files folder within the Example Models folder.
• Select the file with the title for that example. For example, the Do-It file for the one-factor ANOVA is called “One-factor ANOVA.” Click Open.
• When the Do-It file dialog box appears, notice that “Open original dataset” is the default. Click OK to apply the model to the original dataset.
• When the Do-It file opens, click the Recalculate box to calculate the model.
Where to Buy
If you have any questions regarding this demonstration, the complete version of SuperANOVA, or any other software from Abacus Concepts, please call us at (510) 540-1949.
In Australia and New Zealand, please call PICA Software Pty., Ltd. at 61-3-3265255.
In Japan, please call HULINKS INC. +81-3-3590-2311.
