# 15 Statistics

### Apps for Statistics

Origin 2016 introduced add-on tools called Apps. Since being introduced, a number of statistics-related graphing and analysis Apps have been added to OriginLab's File Exchange and more tools are being released all the time.

A few Apps are installed with your Origin software. Note that as of the fall of 2019, all Apps are available at no extra cost and they are easily added to Origin. Click Statistics: Find Apps. This opens the App Center to show only statistics-related Apps. Browse available Apps and click the Download and Install button to install an App.

Origin includes a pre-installed App called Stats Advisor. This App uses an interactive "wizard" interface to help you choose appropriate statistical tests and to tell you where to find them in your Origin software, or -- if the test is available from another add-on App -- where to find it on the OriginLab File Exchange.

## Basic Statistics

 Many of Origin's advanced statistical tests are available only in OriginPro. Users of standard Origin will see these Pro-only tests marked as (Pro) in the main menu. If you own the standard version of Origin but find that you need features of OriginPro, you can upgrade by contacting your Origin representative. If you wish to continue using standard Origin without seeing (Pro) menu commands, click Preferences: System Variables and enter the following in the Set System Variables dialog box and click OK (Comment is optional):

### Basic Statistics on Worksheet

Descriptive Statistics Menu entry with worksheet active
• Statistics on Columns
• Statistics on Rows
Statistics:Descriptive Statistics
• Statistics on Y by X Bin
No menu access. To open the dialog box:
1. Click Window: Script Window.
2. At the cursor, type statsxy -d and press Enter.
• Cross Tabulation and Chi-Square
Statistics:Descriptive Statistics
Frequencies/Counts
• Discrete Frequency
• Frequency Counts
• 2D Frequency Counts/Binning
Statistics:Descriptive Statistics
Distribution
• Distribution Fit
• Normality Test
Statistics:Descriptive Statistics
Relationship
• Correlation Coefficient
• Partial Correlation Coefficient
Statistics:Descriptive Statistics
Detecting Outliers
• Grubbs Test
• Dixon's Q-test
Statistics:Descriptive Statistics

 You can apply Conditional Formatting to a worksheet by applying mathematical expressions or statistics to cell values. For more information, see Conditional Formatting.

### 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

### Descriptive Statistics on Matrix

Descriptive Statistics Menu entry with matrix active
• Output descriptive statistics (mean, sd, min, max, etc.) on the matrix stack (series of matrix objects), for each pair of XY coordinates.
Analysis: Descriptive Statistics

### 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, Bar Charts, Box Overlap, Box Normal, Half Box, Bar Overlap, Bar Normal, Scatter Interval, Double-Y Box, Marginal Box Charts.

 Box Scale is available for box charts, diagramming key user-selected box statistics.

Statistical

Box Charts, Violin Plots, etc., Grouped: Grouped Scatter - Indexed Data, Grouped Box Charts - Indexed Data, Grouped Box Charts - Raw Data, Grouped Column Scatter - Indexed Data, Grouped Interval Plot - Indexed Data, Grouped Mean Bar - Indexed Data, Grouped Violin - Indexed Data, Grouped Half Violin - Indexed Data, Grouped Half Box - Indexed Data.

Categorical

Violin Plots: Violin Plot, Violin with Box, Violin with Point, Violin with Quartile, Violin with Stick, Split Violin, Half Violin.

Statistical

Histograms: Histogram, Histogram + Rug, Histogram + Probabilities, Multi-Panel Histogram, Distribution, Distribution + Rug, Histogram with Labels, Stacked Histograms, Marginal Histograms.

Statistical

Population Pyramid

Statistical

2D Kernel Density

Contour

Heatmap: Heatmap, Heatmap with Labels, Split Heatmap

Contour

Contour - Categorical Z

Contour

Cluster Plots

Categorical

Probability: Probability Plot, Q-Q Plot.

Statistical

Pareto and QC Chart: Pareto Chart - Binned Data, Pareto Chart - Raw Data, QC (X-bar R) Chart.

Statistical

Bland-Altman Plot (Tukey mean-difference)

Statistical

Scatter Matrix

Statistical

Trellis Plot: Trellis Plot, Double-Y Trellis Plot, Double-Y Trellis Plot

Categorical

Parallel Plot: Parallel Plot, Parallel Sets, Parallel Index.

Categorical

The following 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
• Survival Curve
• One Minus Survival Curve
• Hazard Curve
• Log Survival Curve
Statistics: Survival Analysis: Kaplan-Meier Estimator
• Scree Plot
• Component Plot
Statistics: Multivariate Analysis: Principal Component Analysis
• Dendrogram
Statistics: Multivariate Analysis: Hierarchical Cluster Analysis
• Classification Summary Plot
• Classification Fit Plot
• Canonical Score Plot
Statistics: Multivariate Analysis: Discriminant Analysis
• ROC Curve
Statistics: ROC Curve

## 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
• Two-Sample Test for Variance
Statistics: Hypothesis Testing
• One-Sample Proportion Test
• Two-Sample Proportion Test
Statistics: Hypothesis Testing
• Two-Sample t-Test on Rows
• Pair-Sample t-Test on Rows
Statistics: Hypothesis Testing

### ANOVA

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

### Non-parametric Tests

• 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.