Statistics

Origin provides a number of options for performing general statistical analysis including: descriptive statistics, one-sample and two-sample hypothesis tests, and one-way and two-way analysis of variance (ANOVA). Also, several types of statistical charts are supported, including histograms and box charts.

Advanced statistical analysis tools, such as repeated measures ANOVA, multivariate analysis, receiver operating characteristic (ROC) curves, power and sample size calculations, and nonparametric tests are available in OriginPro.

• Descriptive Statistics
• Regression
• ANOVA
• Parametric and Nonparametric Testing
• Quality Control and Improvement PRO
• Time Series Exploration and Analysis PRO
• Survival and Reliability Analysis PRO
• Machine Learning PRO
• Multivariate Analysis PRO
• Apps

The Statistics on Columns/Rows operation performs column-wise/row-wise descriptive statistics on selected worksheet data.

Statistics on Columns

Performs column-wise descriptive statistics on grouped or raw data.

Statistics on Rows

Performs row-wise descriptive statistics to generate statistics for rows in worksheet.

Graphical Summary

The Graphical Summary provides a complete visual and statistical overview of your data. It's ideal for initial exploratory analysis and checking distributional assumptions.

Cross Tabulation PRO

Cross tabulation (also known as contingency table) is a table to reveal the frequency distribution of the variables. Analysis based on the table can determine whether there is a significant relationship, obtain the strength and direction of the relationship, and measure and test the agreement of matched-pairs data. It is widely used to analyze categorical data.

Discrete Frequency

Discrete frequency analysis is one common method to analyze discrete variables. It counts the frequency of discrete data, including percentage and cumulative percentage.

Frequency Counts

This function computes the frequency counts for 1D data and helps produce histogram in desired way.

2D Frequency Count/Binning

A useful tool to compute the frequency counts and plot a 2D histogram for 2D/bivariate data.

Distributions

Normality Test

A normality test is used to determine whether sample data has been drawn from a normally distributed population (within some tolerance).

Six different normality tests are available in Origin:

• Shapiro-Wilk
• Kolmogorov-Smirnov
• Lilliefors
• Anderson-Darling
• D'Agostino's K-Squared
• Chen-Shapiro

Distribution Fit PRO

Knowing the distribution model of the data helps you to continue with the right analysis, or make an estimation of your data. The Distribution Fit tool helps users examine the distribution of their data, and estimate parameters for the distribution

Correlation Coefficient PRO

The correlation coefficient, also called the cross-correlation coefficient, is a measure of the strength of the relationship between pairs of variables. Origin provides both parametric and non-parametric measures of correlation.

• Pearson's r Correlation
• Spearman's Rank Order Correlation
• Kendall's tau Correlation

Partial Correlation Coefficient PRO

Partial correlation measures the linear relationship between two random variables, after excluding the effects of one or more control variables.

The Partial Correlation tool measures the linear relationship between two random variables, after excluding the effects of one or more control variables.

An outlier is an observation that is dramatically distant from the rest of the data. Origin provides two tools to help detect the outliers.

The General Linear Regression app enables users to build models that include main effects, interactions, and higher order terms.

Key Features

• Flexible Model Specification
• Stepwise Regression
• Optimizer Tool
• Comprehensive Coefficient Estimates
• Robust Fit Statistics
• Extensive Model Diagnostics
• Graphical Analysis
• Prediction and Forecasting
• K-fold Cross-validation

Best Subset Selection

With Origin’s intuitive interface, easily tailor your model using the built-in options:

• Force the inclusion of key predictors
• Control model complexity by specifying the minimum and maximum number of predictors
• Filter results to show only the best models that meet model evaluation criteria such as:
  • adjusted R2
  • PRESS
  • Mallow’s CP
  • Root MSE
  • AICc
  • BIC and more
• Seamlessly run a Multiple Linear Regression once the best model is identified

Logistic Regression

Origin’s Logistic Regression tool supports classification analyses that include Binary, Multinomial, and Ordinal Response Variables.

Flexible modeling options with support for:

• Continuous and categorical predictor variables
• Interaction terms to capture complex relationships
• Choice of link functions under Ordinal logistic regression:
  • Logit
  • Probit
  • Negative log-log
  • Cauchit
• Prediction and forecasting

Easily toggle options to show:

• Odds ratios and their 95% Confidence Intervals
• Classification tables to evaluate prediction accuracy
• Correlation and covariance matrices of model predictors
• Influential data points displaying high-leverage cases
• Residual plots for model diagnostics

One-way, two-way, and three-way ANOVA consider a completely randomized design for an experiment.

One-Way ANOVA

One-way ANOVA compares three or more levels within one factor.

Two-Way ANOVA

Two-way ANOVA is useful to compare the effect of multiple levels of two factors. Two-way ANOVA is an appropriate method to analyze the main effects of and interactions between two factors.

Three-Way ANOVA PRO

Three-way ANOVA tests for interaction effects between three independent variables on a continuous dependent variable (i.e., if a three-way interaction exists).

Repeated measure ANOVA tools in Origin consider three possible designs:

• One-way Repeated Measures PRO

ANOVA with one repeated-measures factor.

• Two-way Repeated Measures PRO

ANOVA with two repeated-measures factors.

• Two-way Mixed-Design PRO

The two-way mixed-design is also known as two-way split-plot design (SPANOVA). It is ANOVA with one repeated-measures factor and one between-groups factor.

Multivariate Analysis of Variance (MANOVA) is a statistical technique used to analyze the differences between group means across multiple dependent variables simultaneously.

One-Way MANOVA PRO

Compare the means of multiple dependent variables across different levels of a single independent variable (factor).

• Multiple Dependent Variables
• Comprehensive Statistical Output
• Post-Hoc Comparisons

Two-Way MANOVA PRO

Extends the concept of One-Way MANOVA by allowing the analysis of the effects of two categorical independent variables (factors) on multiple continuous dependent variables.

• Dual-Factor Analysis
• Comprehensive Statistical Output
• Post-Hoc Comparisons

The mean comparison tests in ANOVA, also known as Post Hoc tests, are useful to perform additional comparisons of subsets of the means.

All four ANOVA tools in Origin, one and two-way ANOVA, one and two-way repeated measure ANOVA, provide seven means comparison tests:

• Tukey
• Bonferroni
• Dunn-Sidak
• Fisher LSD
• Scheffé
• Holm-Bonferroni
• Holm-Sidak

Linear Mixed Effects Models PRO

Linear Mixed Effects Models (LMMs) are powerful statistical tools used to analyze data with hierarchical or nested structures.

• Fixed and Random Effects
• Flexible in Model Specification
• Robust Model Diagnostics
• Support for Complex Data Structures

Parametric Tests

Power and Sample Size PRO

The following testings are available:

Nonparametric Tests PRO

Analyze data without making any assumptions about the underlying distribution of the data.

Statistical Process Control (SPC)

Measurement System Analysis (MSA)

Gage R&R Study

• Type 1 Gage Study
• Gage Linear Bias Analysis
• Crossed Gage R&R Study
• Nested Gage R&R Study
• Expanded Gage R&R Study
• Attribute Gage Study
• Create Gage Worksheet

Attribute Agreement Analysis

• Kappa Statistics
• Kendall's Coefficient of Concordance
• Within Appraisers Analysis
• All Appraisers vs. Standard Analysis
• Agreement Graphs
• Confidence Intervals
• Misclassification Rates

Tolerance Interval

• Normal and Non-normal distributions
• Parametric and non-parametric tolerance intervals
• Sample size & Maximum Population Percentage in Interval
• Graphical report including interval plot, histogram, and probability plots

Design of Experiments (DOE)

Power and sample size

• Decide the sample size or power for the experiment

Define Custom Design

Create a design from data in the worksheet

Design

• Definitive Screening Design

Analysis

• Linear+ Interaction+Square models
• Analyze design with stepwise
• Goodness-of-fit
• Fits and residual diagnostics
• Find Y from X
• Pseudo-components
• Coding schemes for categorical factors
• Report regression equation.

Graphics

Optimize

• Optimize the process conditions to achieve the desired result

Read More>>

Kaplan-Meier Estimator PRO

Kaplan-Meier Estimator, a non-parametric estimator, uses product-limit methods to estimate the survival function from lifetime data.

In addition to estimating the survival functions, Kaplan-Meier Estimator in Origin provides three other methods to compare the survival function between two samples:

• Log Rank
• Breslow
• Tarone-Ware

Cox Proportional Hazard Model PRO

The proportional hazards model, also called Cox model, is a classical semi-parameter method. It relates the time of an event, usually death or failure, to a number of explanatory variables known as covariates.

Weibull Fit PRO

Weibull fit is a parameter method to analyze the relationship between the survival function and the failure time. We suppose that the survival function follows a Weibull distribution and fit the model with a maximum likelihood estimation.

Probit Analysis PRO

The Probit Analysis tool can be used to examine the model of the relationship between a binary-response variable and a continuous-dose variable, to fit a probit sigmoid dose-response curve and calculate values (with 95% CI) of the dose variable that correspond to a series of probabilities. The tool in Origin provides the following features:

• Binary-Response Modeling
• Maximum Likelihood Estimation
• Graphical display of estimated probit regression equation

ROC Curve PRO

ROC (Receiver Operating Characteristic) curve analysis is mainly used for diagnostic studies in Clinical Chemistry, Pharmacology, and Physiology. It has been widely accepted as the standard tool for describing and comparing the accuracy of diagnostic tests.

For example, you can use ROC Curve analysis to test a diagnostic to determine if an incident had occurred, or compare the accuracy of two methods that are used to discriminate diseased cases versus healthy cases.

Reliability and Survival Analysis App

Origin also provides a Reliability and Survival Analysis app which supports the following additional features

• Parametric Distribution Analysis for Right Censoring
• Nonparametric Distribution Analysis for Arbitrary Censoring
• Warranty Analysis
• Accelerated Life Testing

The ROC Curve analysis can be used to test a diagnostic to determine if an incident had occurred, or compare the accuracy of two methods that are used to discriminate diseased cases versus healthy cases.

Classification

• Decision Tree Analysis
• Neural Networks
• SVM
• Logistic Regression
• Discriminant Analysis

Regression

• Neural Networks
• Linear Regression (Simple, Polynomial, Multiple)
• Nonlinear
• Partial Least Squares
• GLM, GAM, GLMM, LME
• Bayesian Ridge Regression
• Quantile Regression
• Poisson Regression

Clustering

• K-Means
• Hierarchical
• Gaussian Mixture
• Optimal Cluster Number

Data Reduction

• PCA
• RDA
• ICA
• CCA
• Sparse PCA
• Factor Analysis
• nMDS

Principal Component Analysis PRO

Principal Component Analysis (PCA) is used to explain the variance-covariance structure of a set of variables through linear combinations of those variables. PCA is thus often used as a technique for reducing dimensionality.

Cluster Analysis PRO

Cluster analysis is used to construct smaller groups with similar properties from a large set of heterogeneous data. This form of analysis is an effective way to discover relationships within a large number of variables or observations.

Hierarchical PRO

In this method, elements are grouped into successively larger clusters by some measures of similarity or distance.

K-means PRO

Use K-means clustering to classify observations through K number of clusters.

Faster than Hierarchical, but user needs to know the centroid of the observations, or at least the number of groups to be clustered.

Discriminant Analysis PRO

Discriminant analysis is used to distinguish distinct sets of observations, and to allocate new observations to previously defined groups.

Partial Least Squares Regression PRO

Partial Least Squares regression (PLS) is used for constructing predictive models when there are many highly collinear factors.

There are two primary reasons for using PLS:

• Prediction
  PLS is most commonly used for constructing predictive models when the information is contained in a large number of original variables that are highly collinear.




• Interpretation
  PLS can be used to discover important features of a large data set. It often reveals relationships that were previously unsuspected, thereby allowing interpretations of the data that may not ordinarily result from examination of the data.

Decision Tree Analysis PRO

Origin offers a tool for decision tree analysis that allows users to create a binary decision tree to solve classification problems or perform regression for a binomial or multinomial categorical response with multiple continuous and categorical predictors.

• Decision Tree Classification
• Decision Tree Regression

The Partial Least Squares in Origin is used for constructing predictive models when there are many highly collinear factors. The Variable Importance Plot can help to judge the importance of each variable.