NMath Stats User's Guide

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 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

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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