An Overview of Aabel Statistics

The Stats Analyzer UI

The Aabel Stats Analyzer has a modern interface that is designed to provide flexibility and ease of use. It is an integral part of the graphic viewer that allows: Creating presentation and publication quality graphic outputs (tables and charts) Data exploration using data brushing, data filtering, and X-zooming into diagrams to walk through hierarchies of numeric or categorical data

A Glance at the Stats Analyzer 00.00.32

Inferential and Exploratory Statistical Methods

Analysis of Variance (ANOVA) One-way analysis of variance Repeated measures one-way ANOVA Two-way ANOVA (completely randomized factorial) For more information regarding the ANOVA methods in Aabel, click here.

Homogeneity of Variance and Sphericity Hartley's Fmax statistic (testing for homogeneity of variance) Bartlett's chi-square statistic (testing for homogeneity of variance) Sphericity tests and corrections (specific to repeated measures ANOVA)

Multiple Comparisons/Post-Hoc Tests Tukey's HSD test Tukey B test on ordered means Fisher's LSD test The Newman-Keuls (Neuman-Keuls) test on ordered means Tukey Kramer test Scheffe test Bonferroni test For more information, click here.

Analysis of Covariance (ANCOVA) The single-factor between subjects ANCOVA implementation in Aabel is an analysis of variance where an extra variable (the covariate), which has a linear correlation with the dependent variable, is used to remove the variability on the dependent variable that can be attributed to the covariate. The output results are presented in table format. View examples.

Contingency Analysis (Mosaic/Parquet) A graphical method for visualizing n x m contingency tables, with the areas of the diagram tiles being proportional to the observed (mosaic) or expected (parquet) frequency of groups in the contingency table. In Aabel, the diagram tiles can be color-coded based on several statistical models, observed frequencies, expected frequencies, rows or columns. For identifying categories with missing data, you can color rows or columns of tiles by category. For more information, click here.

Contingency Tables 2-D (n x m) contingency tables (an example of table format output for this method is shown below)

The data used to plot the matrix diagram below is from the report on the loss of the Titanic (S.S.), British Board of Trade Inquiry (1990).

Correlations

Correlations and covariance matrices (you can use a table or a heatmap diagram to display the output) Pearson product-moment correlation coefficient Spearman's Rank-Order Correlation Coefficient (Spearman's ρ) Kendall's Rank Correlation Coefficient (Kendall's τ) For more information regarding Pearson r, Spearman's ρ and (Kendall's τ, click here.

t-Tests Single sample t-test Paired (dependent) samples t-test Unpaired (independent) samples t-test For more information, click here.

Z-Tests Paired samples z-test Unpaired samples z-test For more information, click here.

Chi-Square Tests The χ2 goodness-of-fit test The single-sample χ2 test for a population variance The output results are presented in table format. View examples.

F-Test Unpaired samples F-test For more information, click here.

Non-Parametric Tests Wilcoxon signed-ranks test Wilcoxon matched pairs signed-ranks test Mann-Whitney U test (Wilcoxon rank-sum test) Kruskal-Wallis one-way analysis of variance by ranks Friedman two-way analysis of variance Spearman rank correlation Kendall's tau (Kendall's rank correlation coefficient) Kolmogorov-Smirnov goodness-of-fit test for a single sample For more information, click here.

Data Transformations Several of the statistical methods allow optional pre-processing of the data prior to the main analysis. The data transformations are also available as a separate method that can be used for transforming data outside the context of a given statistical analysis. This method lets you create a transformed version of data or subsets of data. It will transform all selected variables and place the results in a new, auto-generated worksheet. Examples are standardizing, normalizing, logarithmisizing, log centering, mean centering, ranking variables individually, ranking variables jointly, etc.

Kaplan-Meier Survival Analysis and Logrank Test

Performing Kaplan-Meier analysis of either raw or summarized survival data allows: Generating survival curves as well as life table and/or the log rank table computation results Comparing survival data using the built-in non-parametric logrank test Censored observations can optionally be displayed on the survival curves The logrank test results (the hazard ratio, the chi-square the chi-square p values) are presented in table format. The survival curves displayed on the right-hand side image were generated in Aabel using the published data of Bland, M. (2000): gallstone-free survival after the dissolution of single and multiple gallstones. For more information, click here.

Bland & Altman Plot for Comparing Two Methods of Measurement (Difference Plot)

Sensitivity and Specificity (Receiver Operating Characteristic Curves) - ROC

Aabel's implementation of ROC allows plotting: ROC for a single test ROC for two tests on paired samples ROC for two tests on unpaired samples To directly visualize the optimal test value(s) on an ROC curve, you can use the Aabel ROC, i.e., Aabel provides a specific implementation to allow projecting the values onto the diagonal line. The ROC curves shown here were generated in Aabel using the published data of Hanley and McNeil (1983).

Principal Component Analysis (PCA) PCA analysis allows optional pre-processing of the data prior to the main analysis. PCA results can be stored in the source worksheet or in a new worksheet. The scores and loadings can be graphically displayed using Aabel charts and tables. The example below shows a matrix plot of PC scores for the widely known Iris data of Fisher. The table shows the corresponding loadings. Source of data: Fisher (1936), reproduced by Andrews and Herzberg (1985). For more information, click here.

Factor Analysis Factor analysis allows optional pre-processing of the data prior to the main analysis. Aabel provides R-mode and Q-mode factor analyses and the option for Kaiser varimax rotation. The loadings, communality, and "unique" data will be placed in an auto-generated worksheet. You can use Aabel charts to represent the data graphically. For example, factor analysis loadings can be displayed using a binary scatter chart with the X- and Y-axes plotted through zero. Multiple-Y column graphs can be used to compare the fraction of variance of the variables explained by the model (i.e., communality) and the fraction that is not (i.e., "unique"). For more information, click here.

Hierarchical Cluster Analysis

Regression Analyses of Continuous Data Linear (X on Y and through zero) Major axis Reduced major axis Polynomial Exponential Logarithmic Power Cubic spline interpolation Multiple regression Partial least squares regression (PLS) For more information regarding regression methods in Aabel, click here.

User-defined, Non-Linear Regression User-defined regression is provided with a library of functions and an interactive interface. For more information, click here. Logistic Regression Logistic regression in Aabel includes probability and logit (probability) and allows flexible customizing of the generated charts. Probability charts with multiple dimension projections also generate a table of statistics. For more information and examples, click here.

Polynomial Trend Surface Analysis (Map Analysis) Polynomial trend surface analysis of XYZ data Polynomial trend surface analysis of matrix data Matrix cellwise operations The map analysis output includes new matrices and/or XYZ estimates of trend and residuals, as well as an ANOVA report for significance of regression of Kth order polynomial trend surface. For more information, click here.

Statistical Quality Control Using Shewhart and Other Control Charts

Quality control charts in Aabel including Shewhart control charts for variables, Shewhart control charts for attributes, and other related charts are: Xbar (R) chart Xbar (S) chart R chart S chart Levey-Jennings chart Individual measurements chart Moving range chart p chart np chart c chart u chart The Westgard multi-rules procedure and Western Electric Company (WECO) warning rules can be optionally applied to the appropriate quality control charts. For more information, click here.

Histogram of Categorical Data Each listed chart type can be plotted as a vertical or horiziontal chart. Histogram (absolute count) Relative histogram Pareto chart Ogive chart Spine chart For more information, click here. Probability Charts Probability charts display the cumulative distribution relative to a uniform (linear) or normal distribution function. For more information, click here.

Histogram of Continuous Data Each listed chart type can be plotted as a vertical or horizontal chart. Histogram (absolute count) Relative histogram Cumulative histogram Cumulative relative histogram Cumulative frequency Cumulative relative frequency For more information, click here.

Box & Whisker and Box-Percentile Charts Regular box & whisker Notched box & whisker The following options are available for plotting the whisker and outliers: Whiskers are extended to extreme data points Q1 - 1.5 * IQR, Q3 + 1.5 * IQR Q1 - 1.5 * IQR, Q3 + 1.5 * IQR (and outliers) 10th percentile, 90th percentile 10th percentile, 90th percentile (and outliers) 5th percentile, 95th percentile 5th percentile, 95th percentile (and outliers) Box-percentile is a box chart that uses width to encode information about the shape of the distributions. For more information, click here.

Clustered Box & Whisker and Box-Percentile These charts are designed for data layouts where responses from different groups are stored in the same data column, and a grouping variable is used to split the data.

Univariate Bar and Line Chart Mean bar (comparing mean values as a bar graph) Median bar (comparing median values as a bar graph) Max. bar (comparing maximum values as a bar graph) Min. bar (comparing minimum values as a bar graphs) Mean line (comparing mean values as a line graphs) Median line (comparing median values as a line graph) Max. line (comparing maximum values as a line graph) Min. line (comparing minimum values as a line graph) To view examples, click here.

Clustered Univariate Bar and Line Chart These bar/line charts are designed for data layouts where responses from different groups are stored in the same data column, and a grouping variable is used to split the data. Diamond Mean Comparison Plots The diamond plot options in Aabel are: Diamond mean comparison charts, where each diamond represents a variable Clustered diamond mean comparison charts, where each diamond represents a group within a variable and a grouping variable is used to split the data (see the left-hand side image) For more information and examples, click here.

Descriptive Statistics

Data Presentation