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running, the dialog will open with your theme selected. You can now

view the settings of the theme, make any changes, and resave the theme.

2.6 ANOVA

2.6.1 Summary

There are two main modes of datasets in Statistics - indexed and raw.

When you perform an analysis, you do not need to use the whole dataset,

so Origin provides several ways to select data. For example, you can use

the interactive Regional Data Selector button to graphically select the

data or you can use the Column Browserdialog to make your selection.

In this tutorial, you'll use the Analysis of Variance (ANOVA) statistical

test, to learn how to use these two different modes of data to perform

analysis and how to select data by using the Column Browserdialog.

ANOVA is a kind of parametric method for means comparison and is an

extension of t-test. When there are more than two groups to be compared,

pairwise t-test is not appropriate and ANOVA should be used. ANOVA

requires normality and equal variance. Otherwise, non-parametric

analysis should be used.

2.6.2 What you will LearnThis tutorial will show you how to:

Use different input data mode on statistical analysis dialog Test normality for special part of dataset Perform one-way ANOVA Select data by Column Browser

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2.6.3 Steps

Origin can calculate ANOVA in indexed as well as raw data mode. For

One-Way ANOVA, when using indexed mode, data should be organized

in two columns: one for Factor and the other for data.

When using Raw data mode, the different levels are in different columns.

Indexed Data Mode

Nitrogen content has been recorded in milligrams for 4 kinds of plant,and we are interested in whether different plants have different nitrogen

content. We will perform One-Way ANOVA using index data mode for

this example.

1. Start with a new workbook and import the file

\Samples\Statistics\nitrogen.txt. Make sure you select .txtfrom the

drop-down menufiles of type. First, we should perform a normality

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test on each group of data to determine if they are from a normal

distribution.

2. Highlight the first column, right-click and select Sort Worksheetfrom

the Worksheet menu nnd selectAscending.

3. Highlight the second column from row 1 to row 20 - which belongs to

"Plant1" - and open the Normality Testdialog by choosing the menuitem Statistics: Descriptive Statistics: Normality Test.

4. Use the default setting of the dialog and click OK. From the p-value

of result, we can see "Plant1" follows a normal distribution.

5. In a similar way, you can highlight the range of data "Plant2",

"Plant3" and "Plant4" and test for Normality. Our sample data has

normal distribution for all plants.

6. With our nitrogen data worksheet active, open the ANOVAOneWay

dialog by using the menu item Statistics: ANOVA: One-Way

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ANOVA. Set the Input Datamode asIndexed, assign theplantandnitrogencolumn as FactorandDatarespectively using the right-arrow buttons. Click the + to expand the Means Comparisonnode,

set Significance Levelas 0.05 and check the TukeyMeans Comparisonmethod. CheckLevene | |from Tests for Equal Variancebranch.Click the OKbutton to perform One-Way ANOVA.

Explaining the result:

From the "Homogeneity of Variance Test" table of one-way ANOVAresult, we can see that the four groups have equal variance, since the

p-value is bigger than 0.05.

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From the result of Overall ANOVA we can conclude that at least twogroups of the four have significant different means, since the p-value

is smaller than 0.05.

To research further, we expand the results of "Means Comparisons".

Here we see that PLANT4 has significantly different means when

compared to each of the other three groups.

Raw Data Mode

1. Select File : Openand choose WorkBooksfrom Files of typedrop-

down list, and browse to \Samples\Statisticsfolder and open the fileBody.ogw

2. Select menu item Statistics : ANOVA : One-Way ANOVAto bring

up theANOVAOneWaydialog. ChooseRawas Input Datamode.

Enter theLevel1 NameandLevel2 NameasMale Weightand Female

Weightrespectively.

3. Now we will use the Data Browserto select data in the Databranch.

Click the triangle icon besideMale Weightedit box, in the fly-out

menu, select Select Columns...to open the Column Browserdialog.

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4. In the Column Browser dialog, you can select in Current Bookfrom

List Datasetsdrop-down list to see all available worksheet columns inthe current book. Select Weightin the sheet [Body]Maleand click

Addand OKto add it toMale Weightedit box. Similarly, assign

Weightfrom [Body]Femaleto Female Weightedit box.

5. Accept other default settings in the ANOVAOneWay dialog and click

OK. From the output report footnote, we can conclude that at the 0.05

level, the population weight means between male and female are not

significantly different.