5.4.1 Nonparametric Statistics OverviewNonparametricStatisticsOverview
Summary
Nonparametric tests are used when you don't know whether your data are normally distributed, or when you have confirmed that your data are not normally distributed.
What you will learn
This tutorial will show you:
 An introduction on nonparametric tests in Origin
 How to run the nonparametric tests for different practical situations
 How to calculate correlation coefficient in nonparametric statistics
Introduction: Nonparametric Tests in Origin
Nonparametric tests do not require the assumption of normality. They are commonly used in the following situations:
 Small sample size.
 Categorical/Binary/Ordinal data.
 Normal distribution cannot be assumed.


Nonparametric

Parametric



Data from any distribution

Data from normal distribution

Small Samples

Large Samples

One Sample


Wilcoxon Signed Rank Test

One Sample TTest

Two Samples

Independent Samples

 MannWhitney test
 KolmogorovSmirnov test

Two Sample TTest

Paired Samples

 Wilcoxon signed rank Test
 Sign Test

Paired Sample TTest

Multiple Samples

Independent Samples

 KruskalWallis ANOVA
 Mood's Median Test

One Way ANOVA

Related Samples

Friedman ANOVA

One Way Repeated Measure ANOVA

Examples
One Sample Independent Tests
The OneSample Wilcoxon Signed Rank test is designed to examine the population median relative to a specified value. You may choose a one or twotailed test. The Wilcoxon signed rank test hypotheses are
H0: median = hypothesized median versus H1: median ≠ hypothesized median.
In this example, a quality engineer in a production shop is interested in whether median (or average) of the weight of product is equal to 166. So select 10 product at random and measured their weight . The data measured as following:
151.5 152.4 153.2 156.3 179.1 180.2 160.5 180.8 149.2 188.0
The engineer perform Normality Test to determine if the distribution of the data is normal distribution
 Open a new worksheet and input the above data in col(A). Select Statistics: Descriptive Statistics: Normality Test... to open the Normality Test dialog.
 Select A(X) as Data range.
 Click the OK button to generate results.
According to result,Pvalue=0.03814,the distribution of the data is not normal distribution at the 0.05 level. So, perform OneSample Wilcoxon Signed Rank test:
 Select Statistics: Nonparametric Tests: Onesample Wilcoxon Signed Rank Test... to open the dialog.
 Set column A as Data Range.
 Input 166 in Test Median text box.

 Click the OK button to generate results
According to the result, it fails to reject null hypothesis at the 0.05 level and concludes that the median is equal to 166.
Two Sample Independent Tests
Origin provides two tests for nonparametric statistics of two sample independent system: the MannWhitney Test and Two Sample KolmogorovSmirnov Test.
This following example shows the practical use of MannWhitney Test. The abrasions(in mg) are measured for two types of tires(A and B), 8 experiments were carried out for each tire type. The data is indexed and stored in abrasion_indexed.dat file.
 Import the abrasion_indexed.dat file from \Samples\Statistics\
 Select Statistics: Nonparametric Tests: MannWhitney Test to open the dialog.
 Keep Input Data Form as Index
 Set column A as Group Range, set column B as Data Range.
 Select the Exact P Value check box.

 Click the OK button to generate results, which should be in the MannWhitney1 sheet
 U: The U statistic can be simply calculated from the rank of two groups. It is the number of times a score in the 2nd group is larger than a score in the 1st group.
 Z: The approximate Normal test statistic. It provides an excellent approximation as the sample size grows.
 Exact Prob: The exact pvalue, only available when Exact P Value is selected in the dialog. However, it could be very CPUtime consuming for large sample size.
 Asymp.Prob: The asymptotic pvalue calculated from the approximate Normal test statistic, Z
Nonparametric Measures of Correlation
Correlation coefficient is used as a measure of relationship between two variables.It is possible to calculate the correlation coefficient for nonparametric statistics.
Origin provides two nonparametric methods to measure the correlations between variables:
 Spearman: common substitution of Pearson correlation coefficient,Spearman's coefficient can be used when both dependent ( variable and independent variable are ordinal numeric, or when one variable is a ordinal numeric and the other is a continuous variable. However, it can also be appropriate to use Spearman's correlation when both variables are continuous.
 Kendall: Used with ordinal variables for assessing agreement among raters
The following example shows how to calculate correlation coefficient for nonparametric situations.
 Import the abrasion_raw.dat file from Samples\Statistics;
 Highlight Column A and column B. Select Statistics:Descriptive Statistics:Correlation Coefficient to open the corrcoef dialog;
 Check Spearman and uncheck Pearson;
 Click the OK button to generate the results, in the CorrCoef1 sheet.
From the value of Spearman Corr., it can be concluded that the abrasion between tire A and tire B are strongly related.
Paired Sample wilcoxon Signed Rank Tests
We will compare the two medians of tire A and tire B in above example.
 Continue with the abrasion_raw.dat file from Samples\Statistics;
 Select Statistics: Nonparametric Tests: Paired Sample wilcoxon Signed Rank Tests to open the dialog;
 Selcet Column A as 1st Range Data and column B as 2nd range Data;
 Click the OK button to generate the results.
We can conclude that two medians are significantly different. Obviously, median of group A is larger than that of group B.
Multiple Independent Samples Test
In this example, the gas mileage of four car makers are measured. Several experiments are carried out for each car makers. The results are listed in the sample data table.
GMC/mpg

Infinity/mpg

Saab/mpg

Kia/mpg

26.1

32.2

24.5

28.4

28.4

34.3

23.5

34.2

24.3

29.5

26.4

29.5

26.2

35.6

27.1

32.2

27.8

32.5

29.9


30.6

30.2



28.1




To evaluate whether the gas mileage of the four car makers are equal, and which one is the most efficient, KruskalWallis ANOVA is chosen as the nonparametric test method.
 Create a new workbook in Origin, copy the sample data and paste into it;
 Select Statistics:Nonparametric Tests:KruskalWallis ANOVA to open the kwanova dialog;
 Specify Raw as Input Data Form;
 Click the triangle button next to Input, and select All Columns in the context menu;
 Click the OK button to generate results, the results are stored in a new worksheet KWANOVA1.
From the pvalue we can conclude that gas mileage of the four car makers are significant different.
Multiple Related Samples Test
Ophthalmologists are investigating whether laser HeNe therapy works for children. They have data from 2 groups, 610 Years Old and 1116 Years Old. Each data set contains study of 5 persons' nakedeye eyesight difference after 3 period of therapy. The results are stored in the eyesight.dat.
Due to the small sample size, nonparametric statistics would be needed in analysis, following the steps below:
 Import the eyesight.dat file from \Samples\Statistics\;
 Select Statistics:Nonparametric Tests:Friedman ANOVA to open the friedman dialog;
 Select Column A as Data Range, Column C as Factor Range, and Column D as Subject Range;
 Click the OK button to generate results.
The pvalue of is 0.0067379, which is less than 0.05. The populations are significantly different, indicating that the therapy are effective for the age group 610.
In a similar way, choose column B as Data Range and the rest setting of Input are the same with Step 3 previously.
Check the result, we can see that pvalue of is 0.02599, less than 0.05 or 0.10. So we can also conclude that eyesight of 1116 years old kids is better after 3 period of therapy.
And we can see that >,that means, laser HeNe therapy works better on 610 years old kids. The earlier children are to be involved in therapy, the more their eyesight can be improved.
