# 16 Statistics

## Basic Statistics

Origin provides several tools and methods to compute basic statistics on data from either the worksheet or from a graph.

 Origin 2016 introduced add-on tools called Apps. Since being introduced, many new exploratory and analysis-related tools have been added to OriginLab's File Exchange and more tools are being released all the time. Please visit the File Exchange to review available tools.

### Basic Statistics on Worksheet

Descriptive Statistics Menu entry with worksheet active
• Statistics on Columns
• Statistics on Rows
Statistics:Descriptive Statistics
• Cross Tabulation (Pro Only)
Statistics:Descriptive Statistics
Frequencies/Counts
• Frequency Counts
• 2D Frequency Counts/Binning
• Discrete Frequency
Statistics:Descriptive Statistics
Distribution
• Normality Test
• Distribution Fit (Pro Only)
Statistics:Descriptive Statistics
Relationship
• Correlation Coefficient (Pro Only)
• Partial Correlation Coefficient (Pro Only)
Statistics:Descriptive Statistics
Detecting Outliers
• Grubbs Test
• Dixon's Q-test
Statistics:Descriptive Statistics

### Descriptive Statistics on Graph

Origin provides a couple of gadgets to explore and summarize data plotted in graphs.

Descriptive Statistics Menu entry with graph active

### Statistics on Selected Range

Origin provides some quick ways to obtain basic statistics on a selected range of worksheet cells, or data plot(s) in a graph.

#### Status Bar

Select a range of cells in a worksheet. Note that the selection can include cells from one or more columns, and you can use the CTRL key to select non-contiguous groups of cells.

Basic statistics (average, sum, count, min, max) for your selected data will be displayed in the status bar. Right click on the status bar to customize what quantities to display.

#### Command or Script Window

Statistics, Report to Script/Command Window

1. Select a range of cells in a worksheet, or click and select a group of data plots or an individual data plot in a graph.
2. Open the Command Window or the Script Window from the Windows menu, and type one of these commands, then press ENTER:
stats
moments
quantiles

With the Command Window, the results are typed out below the command line. With the Script Window, you will need to issue an additional command to return your results:

stats;
stats.=;

## Statistical Graphs

Origin provides numerous statistical graph types. All graphs can be easily customized and saved as a template for repeat use. View the Graphing and Customizing Graphs chapters of this guide for more information.

Box Charts: Box, Interval Plot, Marginal Box Charts, Bar Charts, Box Overlap, Box Normal, Bar Overlap, Bar Normal, Scatter Interval.

Plot > 2D: Box...

Box Charts, Grouped: Grouped Box Charts - Indexed Data, Grouped Box Charts - Raw Data.

Plot > 2D: Group Plot...

Histograms: Histogram, Histogram + Probabilities, Stacked Histograms, Marginal Histograms, Histogram + Distribution, Histogram + Label.

Plot > 2D: Histogram...

2D Kernel Density

Plot > 2D: 2D Kernel Density

Probability: Probability Plot, Q-Q Plot.

Plot > 2D: Probability...

Pareto: Pareto Chart - Binned Data, Pareto Chart - Raw Data.

Plot > 2D: Pareto...

Scatter Matrix

Plot > 2D: Scatter Matrix

QC (X-bar R) Chart

Plot > 2D: QC (X-bar R Chart)

 Trellis Plot

Plot > 2D: Trellis

Some statistical graphs are only available within the Plots branch of the statistical analysis dialogs.

• Means Plot
• Means Comparison Plot
Statistics: ANOVA: One-Way ANOVA, Two-Way ANOVA

Statistics: ANOVA: One-Way Repeated Measure ANOVA (Pro Only)
• Survival Curve
• One Minus Survival Curve
• Hazard Curve
• Log Survival Curve
Statistics: Survival Analysis: Kaplan-Meier Estimator (Pro Only)
• Scree Plot
• Component Plot
Statistics: Multivariate Analysis: Principal Component Analysis (Pro Only)
• Dendrogram
Statistics: Multivariate Analysis: Hierarchical Cluster Analysis (Pro Only)
• Classification Summary Plot
• Classification Fit Plot
• Canonical Score Plot
Statistics: Multivariate Analysis: Discriminant Analysis (Pro Only)
• ROC Curve
Statistics: ROC Curve (Pro Only)

## Comparing One, Two or More Groups

Origin provides parametric and non-parametric tests to compare one, two, three or more groups.

### Parametric Hypothesis Tests

• One-Sample t-Test
• Two-Sample t-Test
• Pair-Sample t-Test
• One-Sample Test for Variance (Pro Only)
• Two-Sample Test for Variance (Pro Only)
Statistics: Hypothesis Testing
• One-Sample Proportion Test (Pro Only)
• Two-Sample Proportion Test (Pro Only)
Statistics: Hypothesis Testing
• Two-Sample t-Test on Rows (Pro Only)
• Pair-Sample t-Test on Rows (Pro Only)
Statistics: Hypothesis Testing

### ANOVA

• One-Way ANOVA
• Two-Way ANOVA
• Three-Way ANOVA
• One-Way Repeated-Measures ANOVA (Pro Only)
• Two-Way Repeated-Measures ANOVA (Pro Only)
(Supports both Balanced and Unbalanced data)
Statistics: ANOVA

### Non-parametric Tests

These non-parametric tests are available only in OriginPro

• One-Sample Wilcoxon Signed Rank Test
• Paired-Sample Wilcoxon Signed Rank Test
• Paired-Sample Sign Test
• Mann-Whitney Test
• Two-Sample Kolmogorov-Smirnov Test
• Kruskal-Wallis ANOVA
• Moods Median Test
• Friedman ANOVA
Statistics:Nonparametric Tests
 Notes: Multiple nonparametric tests can be run simultaneously. (Accessible from the Statistics:Nonparametric Tests menu ) Available options are: (NPH) K Independent Samples: Kruskal-Wallis ANOVA and Mood's Median Test (NPH) Paired Samples: Paired-Sample Wilcoxon Signed Rank Test and Paired-Sample Sign Test (NPH) Two Independent Samples: Mann-Whitney Test and Two-Sample Kolmogorov-Smirnov Test

Several additional tools are available in OriginPro.

### Multivariate Analysis

Origin offers several multivariate analysis methods to help you simplify, classify, or make predictions from your data.

• Principal Component Analysis
• K-Means Cluster
• Hierarchical Cluster
• Discriminant Analysis
• Canonical Discriminant Analysis
• Partial Least Squares
Statistics:Multivariate Analysis
 Notes: Canonical Discriminant Analysis is integrated with Discriminant Analysis. It is accessible from the Statistics:Multivariate Analysis:Discriminant Analysis: Canonical Discriminant Analysis(System) menu.

### Survival Analysis

OriginPro includes widely used survival tests to quantify survivorship in a population.

• Kaplan-Meier Product-limit Estimator
• Comparing Survival Curves
• Cox Proportional Hazards Model
• Weibull Fit Model
Statistics:Survival Analysis
 Notes: Comparing Survival Curves is accessible in the Kaplan-Meier Product-limit Estimator feature.

### Power and Sample Size

Statistics, Power and Sample Size Origin provides eight types of power and sample size analysis, useful in designing experiments. Origin can compute the power of the experiment for a given sample size and can also compute the required sample size for given power values.

• One-Proportion Test
• Two-Proportion Test
• One-Sample t-Test
• Two-Sample t-Test
• Paired-Sample t-Test
• One-Variance Test
• Two-Variance Test
• One-Way ANOVA
Statistics: Power and Sample Size

### ROC Curve

ROC Curve analysis is useful in determining if an incident has occurred, or in comparing the accuracy of two methods that are used to discriminate between diseased and healthy cases.