Statistics
Origin provides a number of options for performing general statistical analysis including: descriptive statistics, onesample and twosample hypothesis tests, and oneway and twoway 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.
The graph shows a Custom Report of numerical and graphical results from multiple statistical tools, created from Origin's flexible worksheet. Once created, such reports can be automatically generated, greatly simplifying your statistical analysis tasks.
Descriptive Statistics
Origin provides the following tools to help you summarize your continuous and discrete data.
Descriptive
The Statistics on Columns/Rows operation performs columnwise/rowwise descriptive statistics on selected worksheet data.
Statistics on Columns
Performs columnwise descriptive statistics on grouped or raw data.
Statistics on Rows
Performs rowwise descriptive statistics to generate statistics for rows in worksheet.
Cross tabulation(also known as contingency table) is a table to reveal the frequency distribution of the variables. The mosaic graph can be plotted in the report.
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 matchedpairs data. It is widely used to analysis categorical data.
Frequencies
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
The function computes the frequency counts for 1D data and help to produce histogram in desired way.
2D Frequency Count/Binning
A useful tool to compute the frequency counts and plot 2D histogram for 2D/bivariate data.
The Frequency Counts
tool is to measure the number of times a value is encountered that falls within each bin for a range of data. Then the results can be used to generate a histogram which allow more customization such as label on top of bars or having uneven bin size ect.
The 2D Frequency Counts/Binning tool is similar to the Frequency Counts but for twodimension variables. With the tool, we can generate 2D histogram to visually detect the distribution for 2D data.
Use Normality Test to determine whether data has been drawn from a normally distributed population (within some tolerance). Origin supports six methods for the normality test, ShapiroWilk, KolmogorovSmirnov, Lilliefors, AndersonDarling, D'Agostino's KSquared and ChenShapiro
The Distribution Fit tool helps users to examine the distribution of their data, and estimate parameters for the distribution
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:
 ShapiroWilk
 KolmogorovSmirnov
 Lilliefors
 AndersonDarling
 D'Agostino's KSquared
 ChenShapiro
Distribution Fit PRO
Knowing the distribution model of the data helps you to continue with the right analysis. or make estimation of your data. The Distribution Fit tool helps users to examine the distribution of their data, and estimate parameters for the distribution
Correlation Coefficient PRO
Correlation Coefficient PRO
The correlation coefficient, also called the crosscorrelation coefficient, is a measure of the strength of the relationship between pairs of variables. Origin provides both parametric and nonparametric 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.
The image displays the Dialog of Correlation Coefficient tool in Origin. The tool supports three tests, Pearson's r Correlation, Spearman's Rank Order Correlation and Kendall's tau Correlation. And user can choose whether to flag the significant correlations in result
Detecting Outliers
An outlier is an observation that is dramatically distant from the rest of the data. Origin provides two tools to help detecting the outliers.
Two tools in Origin can be used to detect outliers in data, Grubb's Test and the Dixon's Qtest. The outliers plot in the tools can help user to visually judge how the outlier is distant from other observations.
ANOVA
Analysis of variance (ANOVA) is used to examine the differences between group means. In addition to determining that differences exist among the means, ANOVA tools in Origin provide multiple means comparisons in order to identify which particular means are different.
OneWay, TwoWay and ThreeWay ANOVA
Oneway, twoway and threeway ANOVA consider a completely randomized design for an experiment.
OneWay ANOVA
Oneway ANOVA compares three or more levels within one factor.
TwoWay ANOVA
Twoway 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.
ThreeWay ANOVA PRO
Threeway ANOVA ests for interaction effects between three independent variables on a continuous dependent variable (i.e., if a threeway interaction exists).
The graph displays the Mean+SE plot and Means comparison plot in oneway anova. They are help to visually compare multiple groups, determine whether their means are different.
The image displays results got in the oneway anova tool. The Overall ANOVA table reports a pvalue that is smaller than 0.05, hence at least two of the four groups have significantly different means. There are also expandable Homogeneity of Variance Test and Means Comparisons table in result which helps to judge whether the groups have equal variance and provides pairwise comparison.
Repeated Measure ANOVA PRO
The repeated measures design is also known as a withinsubject design. It has the same subjects performed under every condition.
The repeated measures ANOVA is used for comparing three or more means when all subjects are measured under a number of different conditions.
Repeated measure ANOVA tools in Origin consider three possible designs:
 Oneway Repeated Measures PRO
ANOVA with one repeatedmeasures factor.
 Twoway Repeated Measures PRO
ANOVA with two repeatedmeasures factors.
The twoway mixeddesign is also known as two way splitplot design (SPANOVA). It is ANOVA with one repeatedmeasures factor and one betweengroups factor.
Means Comparison / Posthoc Tests
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 twoway ANOVA, one and twoway repeated measure ANOVA, provide seven means comparison tests:
 Tukey
 Bonferroni
 DunnSidak
 Fisher LSD
 Sheff'
 HolmBonferroni
 HolmSidak
An Origin Analysis Report Sheet, this one created by the Oneway Repeated Measures ANOVA tool. The image shows two of the embedded graphs opened for further editing. Edit an embedded graph by doubleclicking on the thumbnail image in the report. Once customizations are made, put the graphs back into the report and see your modifications.
Parametric Hypothesis Tests
Parametric Hypothesis tests are frequently used to measure the quality of sample parameters or to test whether estimates on a given parameter are equal for two samples.
TTests for Means
TTests on Rows PRO
 PairSample TTest on Rows PRO




 TwoSample TTest on Rows PRO




Variance Tests PRO
 OneSample Test for Variance PRO




 TwoSample Test for Variance PRO




Proportion Tests PRO
 OneSample Proportion Test PRO




 TwoSample Proportion Test PRO




Origin supports different input mode for hypothesis testing. User don't need to transform their data before using the tools.
The example shows the results of twosample ttest, a footnote is provided in the table(s) to help draw conclusions. Origin also support Welch's test for the case that variance is not equal.
Nonparametric Tests PRO
Nonparametric tests are useful for testing whether group means or medians are distributed the same across groups. In these types of tests, we rank (or place in order) each observation from our data set. Nonparametric tests are widely used when you do not know whether your data follows normal distribution, or you have confirmed that your data do not follow normal distribution. Meanwhile, hypothesis tests are parametric tests based on the assumption that the population follows a normal distribution with a set of parameters.
OneSample
Wilcoxon Signed Rank Test PRO
The OneSample Wilcoxon Signed Rank Test is a nonparametric alternative to a onesample ttest. The test determines whether the median of the sample is equal to some specified value. Data should be distributed symmetrically about the median.
The One Sample Wilcoxon Signed Rank Test in Origin enable user to examine the population median relative to a specified value. In resuts, a footnote is provided in the table(s) to help to draw conclusions.
Paired Samples
 Wilcoxon Signed Rank Test PRO
Two Samples
 KolmogorovSmirnov Test PRO
Multiple Independent Samples
Multiple Related Samples
Friedman ANOVA PRO
Friedman ANOVA is a nonparametric alternative to the one way repeated measure ANOVA.
Friedman ANOVA can be used to compare dependent samples or observations that are repeated on the same subjects. Thus, the test is wellsuited to randomized block designs.
The graphs shows the data and results of Friedman ANOVA. The tool in Origin can be used to compare three or more related samples. It is a nonparametric alternative to the one way repeated measure ANOVA.
Multivariate Analysis PRO
Multivariate analysis is a set of techniques used to analyze data that corresponds to more than one variable. The main objective of this analysis is to study how the variables are related to one another, and how they work in combination to distinguish between multiple cases of observations.
Principal Component Analysis PRO
Principal Component Analysis (PCA) is used to explain the variancecovariance 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.
Kmeans PRO
Use Kmeans clustering to classify observations through K number of clusters.
It is faster than Hierarchical but need user 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 model when the information contained in a large number of original variables and they 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.
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.
The Principal Component Analysis (PCA) tool is used to explain the variancecovariance structure of a set of variables through linear combinations. The scree plot is a useful visual aid for determining an appropriate number of principal components. And the Loading and Score plot can be used for interpreting relations among observations and variables.
A Dendrogram plot created by the Hierarchical Cluster Analysis tool, which can be used to list all samples and indicates at what level of similarity any two clusters were joined
A Canonical Score Plot created by the Discriminant Analysis tool in OriginPro. This plot can be used to classify observations across groups.
Survival Analysis PRO
Survival Analysis is widely used in the biosciences to quantify survivorship in a population under study. OriginPro includes three widely used tests  the KaplanMeier (productlimit) Estimator, the Cox Proportional Hazards Model and the Weibull Fit.
The graph displays the survival function plot in KaplanMeier Estimator. A logrank test is perform to compare the two survival function.
The image displays a part of reports of the Cox Proportional Hazard Regression, which is a semiparameter method to forecast changes in the hazard rate along with a variety of fixed covariates.
The Weibull Fit is a parameter method to analyze the relationship between the survival function and the failure time. User can see the parameter estimation of the Weibull model from the result table and visually decide whether the data are drop from Weibull distribution from the Weibull Probability Plot
KaplanMeier Estimator PRO
KaplanMeier Estimator, a nonparametric estimator, uses productlimit methods to estimate the survival function from lifetime data.
In addition to estimating the survival functions, KaplanMeier Estimator in Origin provides three other methods to compare the survival function between two samples:
 Log Rank
 Breslow
 TaroneWare
Cox Proportional Hazard Model PRO
The proportional hazards model, also called Cox model, is a classical semiparameter 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.
Power and Sample Size PRO
Power and Sample Size analysis is useful for researchers to design their experiments. It can compute the power of the experiment for a given sample size, and can also compute the required sample size for given power values.
The following testings are available:






 (PSS)PairedSample tTest


















Power and Sample Size Analysis includes both sample size analysis and power analysis. The sample size analysis is used to determine whether an experiment is likely to yield useful information with a given sample size, Conversely, power analysis can be useful in determining the minimum sample size needed to produce a statistically significant experiment. The graph displays the the power curve for the two variances test.
ROC Curve PRO
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.
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.