SigmaPlot
Crie gráficos precisos com rapidez
Software
Sigmaplot
Produtor: Systat Systems
Última versão: SigmaPlot 14.5 (November 2020)
Sistema operativo: Windows
Versão teste: Sim (https://systatsoftware.com/downloads/downloadsigmaplot)
Áreas: Gráficos, Estatística, Análise de Dados
Informação: Visão Geral  What’s New in Version 14.5  SigmaPlot Features  Informações Adicionais
visão geral
O SigmaPlot permite a criação de gráficos precisos com rapidez
Com a nova interface Graph Properties, pode selecionar a categoria da propriedade na árvore à esquerda e depois alterar as propriedades à direita. A mudança é imediatamente representada graficamente e, se tirar o cursor do painel, ficará transparente e poderá ver o efeito das suas alterações sem sair do painel.
O procedimento “selecionar à esquerda e alterar à direita” facilita a edição dos seus gráficos de maneira rápida e fácil. O SigmaPlot permite ao utilizador ir além de simples folhas de cálculo e ajudálo a mostrar o seu trabalho com clareza e precisão. Com o SigmaPlot, pode produzir gráficos de alta qualidade sem gastar horas em frente de um computador. O SigmaPlot oferece uma integração perfeita do Microsoft Office®, para que possa aceder facilmente aos dados das folhas de cálculo do Microsoft Excel® e apresentar os seus resultados em apresentações do Microsoft PowerPoint®
O que o SigmaPlot poderá fazer para si?
• O SigmaPlot software ajuda a criar gráficos precisos e de uma forma rápida e simples
• Software gráfico que facilita a visualização de dados
• Mais de 100 models de gráficos técnicos em 2D e 3D
• Personaliza cada detalhes dos seus gráficos e tabelas
• Cria graficamente os seus dados a partir dos templates de gráficos existentes em gráficos numa galeria de estilos próprios
• Publica as suas tabelas e gráficos em qualquer lado
• Partilha com alta qualidade os seus dados e gráficos na Web
Mais informação: https://systatsoftware.com/downloads/downloadsigmaplot/
What’s New in Version 14.5
Graph Enhancements
New graph styles and options have been added to the Create Graph Wizard for Statistical Graphs.
 QuantileQuantile Plots
QuantileQuantile Plots for comparing the empirical distributions of two data sets.

Confidence and Prediction ellipses
Confidence and Prediction ellipses for a bivariate data sample.
 Jitter Plots
Jitter Plots are a variation of the Point and Column Means graph where options are given to jitter the symbols of the vertical point plot to reduce overlap and improve the identification of observations. To obtains this graph, select Point and Column Means from the Statistics Graph type in the Create Graph Wizard. Set the jitter multiplier and a random number starting seed, Random, say. Select the column to plot and then Finish to obtain jitter as shown below.
Improvements have been made to use column titles as tick labels.

Tick labels improved for Point and Column Means graph
Tick labels improved for Point and Column Means graph to have the xaxis tick labels show as worksheet column titles to indicate the source of each tuple pair that appears in the two plots created for the graph, a vertical point plot and an error bar plot. This graph is a style for the Statistics Graph type created from the Create Graph Wizard. The example below shows the column titles “Iron” and “plasti” as xaxis tick labels on the graph.
User Interface Improvements

Value symbols easily added to symbol and bar graphs
Value symbols easily added to symbol and bar graphs. Click the Plot Labels icon in the Manage Plots group of the Create Graph ribbon to select options for placing labels for symbols and bars.

Plots can be deleted from Graph Properties.
Plots can be deleted from Graph Properties. Now you can delete plots directly from the Graph Properties dialog. Select the particular plot from the Plot panel in Graph Properties (Plot 2 below). Then click the Delete plot button with the results shown below.

Changed the Add Axis default to be Y Axis.
Changed the Add Axis default to be Y Axis. We’ve changed the Default of Add Axis to the Y Axis from the X Axis since this is almost always the desired option.

Align Objects now available from the right mouse menu. You can select multiple items and use right click “Align Objects” to align them. For example, select two objects as shown in the upper left in the page below. Right click and select Align Objects as shown in upper right. Then select the alignment you want and click OK.

New option to use the Y column title only as the default for legend items.
New option to use the Y column title only as the default for legend items. The Y column title is commonly used in the legend. In previous versions the default has been “X column title vs Y column title”. We’ve improved legends so that you can use the “Y column title” only as the default for the legend items. This option is available on the Legend panel of Graph Properties.
 Quick access to change font.
Quick access to change font. Now you can quickly get to a font in the long list from the ribbon. For example, to change the font of a graph title from Arial to Times New Roman use the following steps: Left click on the text of interest.
 Move your cursor to the font list box and click the font list box down arrow to show two or more fonts.
 Type the letter “t”, the first letter of Times New Roman.
 Now scroll the short distance to select the font Times New Roman.

Mini toolbars have been improved when drawing arrows.
Mini toolbars have been improved when drawing arrows. The graphs below show the minitoolbar covering most of the arrow before the improvement (left) and after the improvement (right).

Improved access to the ribbon controls from a statistics report or result graph
Access from a statistics report or a result graph to the SigmaStat panel on the ribbon has been improved to make it easier to continue with further analysis. From a report or graph page, you will now be able to access the Test Options dialog, the Advisor, and make a new selection from the Test Combo Box. The worksheet will automatically appear when needed for these commands.
Worksheet Import

Import multiple sheets from Excel files.
Import multiple sheets from Excel files. Use Import File in the Worksheet ribbon and select the sheets to import. Sheets are imported to separate SigmaPlot worksheets.
Analysis Features

Additional numerical and graph results for contingency tables
The ChiSquare test for contingency tables has been enhanced to include more options for the content of tables, to improve the formatting of tables, to add more statistics, and to create a grouped bar chart for the two categorical variables being tested. The updated Options dialog box with these new options is shown below with program defaults selected.
The report below shows the improved table formatting.
Below is an example of a grouped bar chart of the categories.

Assumption checking and table formatting added to correlation tests
The Pearson Product Moment and Spearman Rank Order correlation tests have been modified to add bivariate normality testing for each pair of the selected columns that are tested and measured for correlation. A new table display format for the report results has been added as an option together with our previous matrix display format. The table format is especially useful when more than seven columns are selected in the worksheet for the correlation tests.
Below are the panels of the Options dialog box showing the new options for assumption checking and formatting.
The two reports below show the Pearson correlation and Spearman Rank correlation results, respectively, with bivariate normality testing and table formatting.

Expanded model selection criteria in Polynomial Regression
The Polynomial Regression feature has been modified to add more goodness of fit criteria for selecting the best model for your data, based on order. More explanations have been included in the report to interpret the criteria and to show the user how to use and complete a polynomial regression analysis.
The new model selection criteria are displayed on the Criterion panel of the Options dialog box. The program defaults are shown below.
Below is the section of the report showing the best fit models for each order below the threshold set in the Options dialog box.
Below is the section of the report showing the computed values of the selected criteria to assess for each order below the threshold set in the Options dialog box.
Below is the section of the report explaining each model selection criterion so all models can be properly assessed in the tables above for goodness of fit.

Easier access for setting population mean and median for onesample tests.
The setting for the population value of the mean and median for the OneSample TTest and the OneSample Signed Rank Test, respectively, has been moved from the test options dialog to the Test Wizard for user convenience. Below are shown the old positions of the controls in the options dialog for the hypothesized values.
The panels of the Test Wizard for navigating to the new controls are shown below for each test.

Option to generate reports for 2D and 3D Smoothers
An optional report can be generated when using the Smoothers 2D and Smoothers 3D features to save the settings used to create a smoother’s plot for future reference. The new Create Report option is shown in the Smoother Wizard below. The option is checked by default.
The report shows the worksheet location of the input data, the smoother specification detailing the properties of the selected smoother method, the grid locations of the xvalues for the smoothed values, the columns in the worksheet for the smoothed values and their locations (this is the graph data), and the name of the graph and the graph page containing the smoother results. If the user requested that smoothed values and/or residuals of those values be computed at the input data locations, then a new section will be added to the end of the report for the locations of these values. Examples of 2D and 3D Smoother reports are shown below.

Histogram improvements from the Histogram Wizard
Options have been added to the Histogram Wizard to include scaling options for histogram counts and options for either leftedge or rightedge binning. The algorithm for automatic binning has been improved. There are three options to scale or normalize histogram counts so that the yaxis is measured as count, fraction of the total count, or percent of the total count. The Bin Options panel of the Test Wizard is shown below with the new normalization and bin edge options.
The histograms below generated by the Histogram Wizard have percent scaling and represent the same data, but have different edge binning.

Histogram improvements to result graphs created for statistical procedures
A new Histogram Options dialog has been added for the histogram result graphs that are available as part of ANOVA and regression testing. The options include a userdefined number of bins, automatic binning, bin count normalization, and bin type for choosing which edge of the bin to include when partitioning the data. The xaxis scaling has been changed in terms of the data (usually in the form of residuals) being binned rather than just representing the bin number as before.
The new options dialog box for histogram result graphs is shown below.
The graph below is a histogram of the residuals from a 2way repeated measures ANOVA.

Enhancements to polar plots from the Polar and Parametric Equations macro
The Plotting Polar and Parametric Equations macro in our macro library has been modified to correctly plot polar equations whose sample values contain negative values of the radial coordinate. The macro dialog has been modified to include options for both radians and degrees for the angular units, which assumed only radians before.
Examples of polar plots created by the macro after adjustment for negative radial values.
 New transform language functions for matrix computations
Added four transform language functions for performing matrix operations and solving matrix equations:
 trp – Generates the transpose of a matrix
 prod – Computes the product of two matrices using the standard definition of matrix multiplication.
 eigen – Computes the eigenvalues and corresponding eigenvectors of a real symmetric matrix.
 linsys – Solves a system of linear equations and multilinear regression problems. In addition to a solution vector, an optional distance measure and an estimate of numerical rank are given. The optional values indicate whether the problem has a solution or not, and whether the solution, if it exists, is unique.
In the transform language, a matrix is realized by using the block function. The above transforms can greatly strengthen the computational capabilities of userdefined transforms and macros.
The transform library or samples file (xfms.jnb) has been modified to change its structure by reorganizing the transform sections into subsections under twelve different sections (categories) which are titled by the general application or the field of study that the transforms under it apply to. These categories are not rigidly defined but are meant to serve as a guide for locating transforms.
The twelve categories of transforms are shown below on the left with Regression selected. Example transforms under the Regression category are shown on the right.
 New transforms added to the transform library
1. Multilinear Orthogonal Regression and Regression w/ Equality Constraints
The Multilinear Orthogonal Regression transform computes the coefficients of a plane in ndimensions that minimizes the sum of squares of orthogonal distances from a given set of points to the plane.
The Regression w/ Equality Constraints transform computes the solution to a multilinear least squares problem where the parameters satisfy a system of linear equality constraints. Also, it tests the hypothesis that the constraints hold for the true parameter values.
The new transforms have been added to the Regression section of the transform library. The coding for both transforms illustrates the use of the new transform functions trp, prod, eigen, and linsys.
2. PassingBablok Regression
The transform performs PassingBablok regression for method comparison which is a nonparametric procedure for fitting a straight line to twodimensional data where both variables, X and Y, are measured with error. It complements Deming Regression. As part of the results, the transform generates graph data that can be used to produce the following graph types:
3. ChiSquare Goodness of Fit Test for category data
This transform uses a column of data sampled from a finite number of categories that partition the members of a population. The test determines if the user’s data supports the hypothesis that each category in the population occurs with a specified probability or that the categories occur with specified ratios that are supplied by the user. This transform is a supplement to the transform for OneWay Frequency Analysis.
The output of the transform can be used to construct a grouped bar chart of the data and expected frequencies of the categories in the problem:

Improvements in the random number generators when using a random seed
The random number generator functions in the Transform Language, gaussian and random, have been improved when selecting a random seed that results when the user specifies 0/0 for the seed argument. The advantage is to make larger variations in the seed value so that the random number sequence varies more often and, in particular, won’t repeat values when you restart the program. This makes the behavior of these functions consistent with their counterparts in the statistical transforms.
Miscellaneous Features

A notebook section can now contain one or more subsections.
Subsections in a notebook can be used to better categorize and locate items in the notebook. These items could be worksheets, graph pages, reports, transforms, equations and macros. Here is an example using multiple subsections in a notebook.

The Histogram Plus Kernel Density macro has been added to the toolbox.

Added a system memory indicator
A system memory indicator has been added to the status bar showing the amount left.

Improved search in Help
Search results in Help take you right to the topic you are looking for. For example, click Help, click the Search tab, enter the topic (“Excel” in this case), click List Topics, double click the specific topic, and then select the item of interest.

Unicode Support
The Unicode support in SigmaPlot 14.5 is described in the file “SPW 14 Unicode Support.pdf” that is located in the product’s application folder SigmaPlot/SPW14_5 under Program Files.

Licensing Features
License search mode settings on the license information tab page. Based on the settings (Local, Network, Auto) appropriate license will be loaded.
Local Mode: Search for valid license (Standalone/Network) only from local machine
Network Mode: Search for network license from the server machine (s). Only network license is searched, local license files are ignored.
Auto: Search for valid license either local machine or network license from other servers.
Added license transfer mechanism for rehostable licenses (between sender and recipient machines) in license transfer tab. Added support to apply H2H (Host to Host) license file to transfer license from one machine to other.
New tab added to transfer license from current machine to another machine. With SigmaPlot 14, user need to follow with Systat sales to install SigmaPlot in another machine, since the license is locked to that machine.
Added additional option to handle license manager in different subnet in network tab, where user can provide sever name or IP address of the license manager and save the settings. On successful settings, hasp_107466.ini file will be created/updated in local user appdata folder (sample location C:\Users\user1\AppData\Local\SafeNet Sentinel \Sentinel LDK).
New UI to support creation of INI, this feature is required for network license with server and client is in different subnet. With SigmaPlot 14, it is a manual process without UI.
Additional support information in the log file.
Log file details are improved. With SigmaPlot 14, there was limited details on the log file, now we collect detailed information to trace back the problem or give more details to the user.
Additional validation to handle remote desktop / remote session / remote terminal
No specific UI. SigmaPlot display messages when the license is applied thru remote session or application is invoked thru remote session.

Installer Features
– Added a check box at the end of installation to open Readme file.New check box has been added to open ‘Readme.txt’ file after installation. By default, this is disabled and will not open the file.
– Added a check box “Always check patch updates on application start up” at the end installation.
Check box has been added to enable or disable checking patch updates at the beginning of the application startup. If this check box is not enabled then user can update the patch manually using the license utility.
– If the Excel running, we are NOT forcing the user to close the Excel. Instead we are giving the user option to Ignore and continue.
No UI for this feature. SigmaPlot gives out a warning message and let the user continue with the installation. In earlier versions, we don’t allow the user to continue until they close Excel.
– Improved Silent installation tool.
No UI for this feature. MSI based silent installation has been improved with a Silent installation tool, which validates all conditions before starting the MSI installation.
SigmaPlot Features
New Graph Features Include:
• Forest Plots
• Kernel Density Plots
• 10 New Color Schemes
• Dot Density Graph with mean and standard error bars
• Legend Improvements
• Horizontal, Vertical and Rectangular Legend Shapes
• Cursor over side or upper or lower handle
• allows for multicolumn legends
• User interface to set number of legend item columns in the Properties dialog. The permissible column numbers are displayed in the combo list
• Change the number of legend item columns by selecting and dragging the middle handle in the bounding box
• Reorder legend items
• Through properties dialog – move one or multiple legend items up or down using the up/down control on top of the list box
• Through cursor movement – move one or multiple legend items up or down. Select the legend item(s) and use keyboard up and down arrow key for movement within the bounding box
• Through mouse select and cursor movement for items in the bounding box
• Individual legend items property settings – select individual legend items and use the mini tool bar to change the properties
• Legend box blank region control through cursor
• Cursor over corner handle
• allows proportional resizing
• Add simple direct labeling
• Support “Direct Labeling” in properties dialog using the checkbox control “Direct Labeling”
• Ungroup legend items – the individual legend items can be moved to preferred locations and move in conjunction with the graph
• Legend Title support has been added (no title by default). The user can add a title to the legend box using the legend properties panel
• Reverse the legend items using the right click context menu
• Open Legend Properties by double clicking either Legend Solid or Legend Text
• Reset has been added to legends to reset legend options to default
New Analysis Features Include:
• Principal Component Analysis (PCA)
• Analysis of Covariance (ANCOVA)
• Added P values to multiple comparisons for nonparametric ANOVAs
• Removed the combo box choices for multiple comparison significant levels and tied the significance level of multiple comparisons to the main (omnibus) test
• Added the Akaike Information Criterion to Regression Wizard and Dynamic Fit Wizard reports and the Report Options dialog
• Added back the Rerun button in the SigmaStat group
• Updated the fit library standard.jfl
o Added probability functions, to now include 24, for curve fitting or function visualization
o The tolerance value for all equations has been modified to use “enotation” instead of fixed decimal. This allows the user to read the value without scrolling.
o Add seven weighting functions to all curve fit equations in standard.jfl. There is a slight variant added for 3D equations.
New User Interface Features
• Rearrange Notebook items in a section by dragging
• New SigmaPlot tutorial PDF file
• Line widths from a worksheet column
New Import/Export Features
• Added the SVG and SWF file formats for scalable vector graphics export
• Added Vector PDF export to improve on the existing raster PDF
• File import and export support is added for Versions 13 and 14 of Minitab, Version 9 of SAS, Version 19 of SPSS and Version 13 of Symphony
SigmaPlot Product Features
Forest Plot
A forest plot is one form of “metaanalysis” which is used to combine multiple analyses addressing the same question. Metaanalysis statistically combines the samples of each contributing study to create an overall summary statistic that is more precise than the effect size in the individual studies. Individual study values and their 95% confidence intervals are shown as square symbols with horizontal error bars and the overall summary statistic as a diamond with width equal to its 95% confidence interval.
Kernel Density
The kernel density feature will generate an estimate of the underlying data distribution. This should be compared to the steplike histogram. It has advantages (no bars) and disadvantages (loss of count information) over a histogram and should be used in conjunction with the histogram. They can be created simultaneously.
Dot Density with Mean & Standard Error Bars
The mean plus standard error bar computation, symbol plus error bars, has been added to the Dot Density graph. This enhances the other possible dot density display statistics – mean, median, percentiles and boxplot.
New Color Schemes
Ten new color schemes have been implemented. Three examples are shown below:
Legend Improvements – Shapes
Vertical, horizontal and rectangular legend shapes are now available.
Reverse Legend Order
You can now select to reverse the legend item order. This provides a more logical order for some graph types.
Reorder Legend Items
There are three ways to reorder the legend items. As shown here, you canmove one or multiple legend items up or down using the up/down arrow controls in the Legends panel of Graph Properties. Even easier, just select the item in the legend and use the keyboard up and down arrow keys. Or select the legend item and drag it to the new position with the mouse cursor.
MiniToolbar Editing of Legend Items
Legend items may now be edited by clicking on the item and using the minitoolbar.
Direct Labeling
The legend can now be ungrouped and individual legend items placed adjacent to the appropriate plots. The labels will move with the graph to maintain position with respect to the graph. Since the label is adjacent to the plot, visual identification of each plot is now much easier.
Principal Component Analysis (PCA)
Principal component analysis (PCA) is a technique for reducing the complexity of highdimensional data by approximating the data with fewer dimensions. Each new dimension is called a principal component and represents a linear combination of the original variables. The first principal component accounts for as much variation in the data as possible. Each subsequent principal component accounts for as much of the remaining variation as possible and is orthogonal to all of the previous principal components.
You can examine principal components to understand the sources of variation in your data. You can also use them in forming predictive models. If most of the variation in your data exists in a lowdimensional subset, you might be able to model your response variable in terms of the principal components. You can use principal components to reduce the number of variables in regression, clustering, and other statistical techniques.
The primary goal of Principal Components Analysis is to explain the sources of variability in the data and to represent the data with fewer variables while preserving most of the total variance.
Graphical output consists of Scree, Component Loadings and Component Scores plots.
Analysis of Covariance (ANCOVA)
A singlefactor ANOVA model is based on a completely randomized design in which the subjects of a study are randomly sampled from a population and then each subject is randomly assigned to one of several factor levels or treatments so that each subject has an equal probability of receiving a treatment. A common assumption of this design is that the subjects are homogeneous. This means that any other variable, where differences between the subjects exist,does not significantly alter the treatment effect and need not be included in the model. However, there are often variables, outside the investigator’s control, that affect the observations within one or more factor groups, leading to necessary adjustments in the group means, their errors, the sources of variability,and the Pvalues of the group effect, including multiple comparisons.
These variables are called covariates. They are typically continuous variables, but can also be categorical. Since they are usually of secondary importance to the study and, as mentioned above, not controllable by the investigator, they do not represent additional maineffects factors, but can still be included into the model to improve the precision of the results. Covariates are also known as nuisancevariables or concomitant variables.
ANCOVA (Analysis of Covariance) is an extension of ANOVA obtained by specifying one or more covariates as additional variables in the model. If you arrange ANCOVA data in a SigmaPlot worksheet using the indexed data format, one column will represent the factor and one column will represent the dependent variable (the observations) as in an ANOVA design. In addition, you will have one column for each covariate. When using a model that includes the effects of covariates, there is more explained variability in the value of the dependent variable.
This generally reduces the unexplained variance that is attributed to random sampling variability, which increases the sensitivity of the ANCOVA as compared to the same model without covariates (the ANOVA model). Higher test sensitivity means that smaller mean differences between treatments will become significant as compared to a standard ANOVA model, thereby increasing statistical power.
As a simple example of using ANCOVA, consider an experiment where students are randomly assigned to one of three types of teaching methods and their achievement scores are measured. The goal is to measure the effect of the different methods and determine if one method achieves a significantly higher average score than the others. The methods are Lecture, Selfpaced, and Cooperative Learning.
Performing a One Way ANOVA on this hypothetical data gives the results in the table below, under the ANOVA column heading. We conclude there is no significant difference among the teaching methods. Also note that the variance unexplained by the ANOVA model which is due to the random sampling variability in the observations is estimated as 35.17.
It is possible that students in our study may benefit more from one method than the others, based on their previous academic performance. Suppose we refine the study to include a covariate that measures some prior ability, such as a statesanctioned Standards Based Assessment (SBA). Performing a One Way ANCOVA on this data gives the results in the table below, under the ANCOVA column heading.
ANOVA  ANCOVA  
Method  Mean  Std. Error  Adjusted Mean  Std. Error 
Coop  79.33  2.421  82.09  0.782 
Self  83.33  2.421  82.44  0.751 
Lecture  86.83  2.421  84.97  0.764 
P = 0.124  P = 0.039  
MSres = 35.17  MSres = 3.355 
The adjusted mean that is given in the table for each method is a correction to the group mean to control for the effects of the covariate. The results show the adjusted means are significantly different with the Lecture method as the more successful. Notice how the standard errors of the means have decreased by almost a factor of three while the variance due to random sample variability has decreased by a factor of ten. A reduction in error is the usual consequence of introducing covariates and performing an ANCOVA analysis.
There are four ANCOVA result graphs – Regression Lines in Groups, Scatter Plot of Residuals, Adjusted Means with Confidence Intervals, and Normality Probability Plot:
P Values for Nonparametric ANOVAs
The nonparametric ANOVA tests in SigmaPlot are the KruskalWallis test (OneWay ANOVA on Ranks) and the Friedman test (OneWay Repeated Measures ANOVA on Ranks). Both of these provide four posthoc testing procedures to determine the source of significant effects in the treatment factor. The four procedures are Tukey, SNK, Dunn’s, and Dunnett’s.
The first three procedures can be used to test the significance of each pairwise comparison of the treatment groups, while the last two can be used to test the significance of comparisons against a control group. Dunn’s method is the only procedure available if the treatment groups have unequal sample sizes.
When a posthoc testing procedure is used, a table is given in the report listing the results for the pairwise comparisons of the treatment levels. The last column of the table shows whether the difference in ranks is significant or not. In previous versions of SigmaPlot there is no adjusted pvalue given that can be compared to the significance level of the ANOVA (usually .05) to determine significance.
This is because SigmaPlot had been determining significance by comparing the observed test statistic, computed for each comparison, to a critical value of the distribution of the statistic that is obtained from a lookup table. SigmaPlot had two sets of lookup tables for the probability distributions corresponding to the four posthoc methods, where one set was for a significance level of .05 and another set was for a significance level of .01.
This was recently changed to use analytical procedures to compute the pvalues of these distributions, making the lookup tables obsolete. Because of this change, we are now able to report the adjusted pvalues for each pairwise comparison. This change also makes it possible to remove the restriction of using .05 and .01 as the only significance levels for multiple comparisons. Thus the user can enter any valid P value significance level from 0 to 1.
[/toggle] [toggle border=’2′ title=’Akaike Information Criterion (AICc)’]
Akaike Information Criterion (AICc)
The Akaike Information Criterion (AIC) provides a method for measuring the relative performance in fitting a regression model to a given set of data. Founded on the concept of information entropy, the criterion offers a relative measure of the information lost in using a model to describe the data. More specifically, it gives a tradeoff between maximizing the likelihood for the estimated model (the same as minimizing the residual sum of squares if the data is normally distributed) and keeping the number of free parameters in the model to a minimum, reducing its complexity. Although goodnessoffit is almost always improved by adding more parameters, overfitting will increase the sensitivity of the model to changes in the input data and can ruin its predictive capability.
The basic reason for using AIC is as a guide to model selection. In practice, it is computed for a set of candidate models and a given data set. The model with the smallest AIC value is selected as the model in the set which best represents the “true” model, or the model that minimizes the information loss, which is what AIC is designed to estimate. After the model with the minimum AIC has been determined, a relative likelihood can also be computed for each of the other candidate models to measure the probability of reducing the information loss relative to the model with the minimum AIC. The relative likelihood can assist the investigator in deciding whether more than one model in the set should be kept for further consideration.
The computation of AIC is based on the following general formula obtained by Akaike
Nonlinear Regression Probability Functions
24 new probability fit functions have been added to the fit library standard.jfl. These functions and some equations and graph shapes are shown below.
Nonlinear Regression Weighting Functions
There are now seven different weighting functions built into each nonlinear regression equation (3D are slightly different). These functions are reciprocal y, reciprocal y squared, reciprocal x, reciprocal x squared, reciprocal predicteds, reciprocal predicteds squared and Cauchy. The iteratively reweighted least squares algorithm is used to allow the weights to change during each nonlinear regression iteration.In this way “weighting by predicteds”, a commonly used method, can be obtained by selecting the reciprocal_pred weighting option.
Also, Cauchy weighting (select weight_Cauchy) can be used to fit an equation to data that contains outliers and the effect of the outliers will be minimized. Users can create their own weighting methods in terms of residuals and/or parameters to implement other robust fitting methods. The equation section of a fit file is shown with the seven builtin weighting functions.
User Interface Features – Rearrange items in your notebook by dragging
Objects in a notebook section are not necessarily created in a logical order. You can now drag items within a section to new positions to place them more logically.
An Updated SigmaPlot Tutorial
The new tutorial makes creating graphs for the first time easy. It starts with simple examples and gradually becomes more complex.
Specify Plot Line Widths from a Worksheet Column
Line width values can now be entered in a worksheet column. These values may be used within a graph or across multiple graphs on the page.
New Vector Export File Formats
SVG (Scalable Vector Graphics), SWF (Adobe Flash Player) and Vector PDF file formats have been added. These are scalable formats where no resolution is lost when zooming to different levels. SVG is the standard graphics format for the web and SWF can be used with Adobe Flash Player. Because pdf is used so frequently, the vector PDF format is now attached to the Create PDF button on the Home ribbon.
Updated Application File Formats
File import and export support has been updated to Versions 13 and 14 of Minitab, Version 9 of SAS and Version 19 of SPSS.
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