Tutorial:One Way ANOVA

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Contents

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 Browser dialog 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 Browser dialog.

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.

Minimum Origin Version Required: Origin 8.0 SR6

What you will learn

This 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

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.

Image:Tutorial_ANOVA_008.png

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

Image:Tutorial_ANOVA_009.png

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 .txt from the drop-down menu Files of type. First, we should perform a normality 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 Worksheet from the Worksheet menu and choose Ascending.
  3. Highlight the second column from row 1 to row 20 - which belongs to "PLANT1" - and open the Normality Test dialog by choosing the menu item Statistics: Descriptive Statistics: Normality Test.
    Image:Tutorial_ANOVA_001.png
  4. Use the default setting of the dialog and click OK. From the p-value of result,p-value=0.58545, 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 ANOVA. Set the Input Data mode as Indexed, assign the "plant" and "nitrogen" column as Factor and Data respectively using the right-arrow buttons. Click the + to expand the Means Comparison node, set Significance Level as 0.05 and check the Tukey Means Comparison method. Check Levene | | from Tests for Equal Variance branch. Click the OK button to perform One-Way ANOVA.

    Image:Tutorial_ANOVA_002.png

Explaining the result:

  • From the "Homogeneity of Variance Test" table of one-way ANOVA result, we can see that the four groups have equal variance, since the p-value is bigger than 0.05.

    Image:Tutorial_ANOVA_003.png

  • From the result of Overall ANOVA we can conclude that at least two groups of the four have significant different means, since the p-value is smaller than 0.05.

    Image:Tutorial_ANOVA_004.png

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

    Image:Tutorial_ANOVA_005.png

    Here we see that PLANT4 has significantly different means when compared to each of the other three groups.

raw data mode

  1. Select File : Open and choose WorkBooks from Files of type drop-down list, and browse to \Samples\Statistics folder and open the file Body.ogw
  2. Select menu item Statistics : ANOVA : One-Way ANOVA to bring up the ANOVAOneWay dialog. Choose Raw as Input Data mode. Enter the Level1 Name and Level2 Name as "Male Weight" and "Female Weight" respectively.
  3. Now we will use the Data Browser to select data in the Data branch. Click the triangle icon beside Male Weight edit box, in the fly-out menu, select Select Columns... to open the Column Browser dialog.

    Image:Tutorial_ANOVA_006.png

    In the Column Browser dialog, you can select in Current Book from List Columns drop-down list to see all available worksheet columns in the current book. Select Weight in the sheet [Body]Male and click Add and OK to add it to Male Weight edit box. Similarly, assign Weight from [Body]Female to Female Weight edit box.

    Image:Tutorial_ANOVA_007.png

  4. 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.
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