NMath Stats User's Guide

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Contents

Chapter 1. Introduction

1.1 Product Features
1.2 Software Requirements
1.3 Namespaces
1.4 Building and Deploying NMath Stats Applications
1.5 Documentation
This Manual
1.6 Visualization
1.7 Technical Support

Chapter 2. Data Frames

2.1 Column Types
Creating Columns
Adding and Removing Data
Accessing Column Data
Column Properties
Reordering Column Data
Missing Values
Transforming Column Data
Exporting Column Data
2.2 Creating DataFrames
Creating Empty DataFrames
Creating DataFrames from Arrays of Columns
Creating DataFrames from Matrices
Creating DataFrames from ADO.NET Objects
Creating DataFrames from Strings
2.3 Adding and Removing Columns
2.4 Adding and Removing Rows
Modifying Row Keys
2.5 Properties of DataFrames
2.6 Accessing DataFrames
Accessing Elements
Accessing Columns
Accessing Rows
2.7 Subsets
Creating Subsets
Properties of Subsets
Accessing Elements
Logical Operations on Subsets
Arithmetic Operations on Subsets
Manipulating Subsets
Groupings
Random Samples
2.8 Accessing Sub-Frames
2.9 Reordering DataFrames
Sorting Rows
Permuting Rows and Columns
2.10 Factors
Creating Factors
Properties of Factors
Accessing Factors
Creating Groupings with Factors
2.11 Cross-Tabulation
Column Delegates
Applying Column Delegates to Tabulated Data
2.12 Exporting Data from DataFrames
Exporting to a Matrix
Exporting to a String
Exporting to an ADO.NET DataTable
Binary and SOAP Serialization

Chapter 3. Descriptive Statistics

3.1 Column Types
3.2 Missing Values
3.3 Counts and Sums
3.4 Min/Max Functions
3.5 Ranks, Percentiles, Deciles, and Quartiles
3.6 Central Tendency
3.7 Spread
3.8 Shape
3.9 Covariance, Correlation, and Autocorrelation
3.10 Sorting
3.11 Logical Functions

Chapter 4. Special Functions

4.1 Combinatorial Functions
4.2 Gamma Function
4.3 Beta Function

Chapter 5. Probability Distributions

5.1 Distribution Classes
Beta Distribution
Binomial Distribution
Chi-Square Distribution
Exponential Distribution
F Distribution
Gamma Distribution
Geometric Distribution
Johnson Distribution
Logistic Distribution
Log-Normal Distribution
Negative Binomial Distribution
Normal Distribution
Poisson Distribution
Student's t Distribution
Triangular Distribution
Uniform Distribution
Weibull Distribution
5.2 Correlated Random Inputs
Constructing Correlator Instances
Correlating Random Inputs
Correlator Properties
Convenience Method

Chapter 6. Hypothesis Tests

6.1 Common Interface
Static Properties
Creating Hypothesis Test Objects
Properties of Hypothesis Test Objects
Modifying Hypothesis Test Objects
Printing Results
6.2 One Sample Z-Test
6.3 One Sample T-Test
6.4 Two Sample Paired T-Test
6.5 Two Sample Unpaired T-Test
6.6 Two Sample F-Test
6.7 Pearson's Chi-Square Test

Chapter 7. Linear Regression

7.1 Creating Linear Regressions
Parameter Calculation by Least Squares Minimization
Intercept Parameters
7.2 Regression Results
Variance Inflation Factor
7.3 Predictions
7.4 Accessing and Modifying the Model
Accessing and Modifying Predictors
Accessing and Modifying Observations
Accessing and Modifying the Intercept Option
Updating the Entire Model
7.5 Significance of Parameters
Creating Linear Regression Parameter Objects
Properties Linear Regression Parameters
Hypothesis Tests
Updating Linear Regression Parameters
7.6 Significance of the Overall Model

Chapter 8. Analysis of Variance

8.1 One-Way ANOVA
Creating One-Way ANOVA Objects
The One-Way ANOVA Table
Grand Mean, Group Means, and Group Sizes
Critical Value of the F Statistic
Updating One-Way ANOVA Objects
8.2 One-Way Repeated Measures ANOVA
Creating One-Way RANOVA Objects
The One-Way RANOVA Table
Grand Mean, Subject Means, and Treatment Means
Critical Value of the F Statistic
Updating One-Way RANOVA Objects
8.3 Two-Way ANOVA
Creating Two-Way ANOVA Objects
The Two-Way ANOVA Table
Cell Data
Grand Mean, Cell Means, and Group Means
ANOVA Regression Parameters
8.4 Two-Way Repeated Measures ANOVA
Creating Two-Way RANOVA Objects
Two-Way RANOVA Tables

Chapter 9. Non-Parametric Tests

9.1 One Sample Kolmogorov-Smirnov Test
9.2 Two Sample Kolmogorov-Smirnov Test
9.3 Kruskall-Wallis Test
Creating Kruskall-Wallis Objects
The Kruskall-Wallis Table
Ranks, Grand Mean Ranks, Group Means Ranks, and Group Sizes
Critical Value of the Test Statistic
Updating Kruskall-Wallis Test Objects

Chapter 10. Multivariate Techniques

10.1 Principal Component Analysis
Creating Principal Component Analyses
Principal Component Analysis Results
10.2 Hierarchical Cluster Analysis
Distance Functions
Linkage Functions
Creating Cluster Analyses
Cluster Analysis Results
Reusing Cluster Analysis Objects
10.3 K-Means Clustering
Creating KMeansClustering Objects
Stopping Criteria
Clustering
Cluster Analysis Results

Chapter 11. Nonnegative Matrix Factorization

11.1 Nonnegative Matrix Factorization
Update Algorithms
11.2 Data Clustering Using NMF
Creating NMFClustering Instances
Performing the Factorization
Cluster Results
Computing a Consensus Matrix

Chapter 12. Partial Least Squares

12.1 Computing a PLS Regression
12.2 Error Checking
12.3 Predicted Values
12.4 Analysis of Variance
12.5 PLS Algorithms
12.6 Cross Validation

Chapter 13. Goodness of Fit

13.1 Significance of the Overall Model
13.2 Significance of Parameters
Creating Goodness of Fit Parameter Objects
Properties of Goodness of Fit Parameters
Hypothesis Tests

Index


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